SilverScreener:A ModelingApproach to Movie ScreensManagement · 2019-12-12 · SILVERSCREENER: A...

Marketing Science � 1999 INFORMSVol. 18, No. 3, 1999, pp. 352–372

0732-2399/99/1803/0352/$05.001526-548X electronic ISSN

SilverScreener: A Modeling Approach toMovie Screens Management

Sanjeev Swami • Jehoshua Eliashberg • Charles B. WeinbergDepartment of Industrial and Management Engineering, Indian Institute of Technology, Kanpur, India,

[email protected] Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104,

[email protected] of Commerce and Business Administration, University of British Columbia, 2053 Main Mall,

Vancouver, British Columbia V6T 1Z2, Canada, [email protected]

AbstractManaging the allocation of shelf space for new products is aproblem of significant importance for retailers. The problemis particularly complex for exhibitors—the retailers in themotion picture supply chain—because they face dynamicchallenges, given the short life cycles of movies, the changinglevel of demand over time, the scarcity of shelf space, andthe complex revenue sharing contract between the exhibitorand the distributor. In the face of this complexity, the aim ofcurrent research is to provide a structure for analyzing man-agement problems of exhibitors in the movie industry. Usinga mathematical programming approach and a fast, but read-ily accessible algorithm, we propose a decision supportmodel, SilverScreener, whose aim is to help exhibitors makeeffective and timely decisions regarding theater screensman-agement. The major objective is to help select and schedulemovies for a multiple-screens theater over a fixed planninghorizon in such a way that the exhibitor’s cumulative profitis maximized.

By treating the multiple screens as parallel machines andthe movies as jobs, we provide an analogy of the currentproblem to the parallel machine scheduling problem.We for-mulate the resulting problem as an integer program. We de-part from the typical parallel machine scheduling problemsby introducing the time-indexed formulation that is particularlyuseful for solving the current problem. An important dis-tinction between the current problem and typical machinescheduling problems is that the present approach allows forthe choice of which movies to play; typically, in machinescheduling, all jobs have to be scheduled.

We provide various analyses of normative versus actualdecision making, based on publicly available data. The de-veloped model is readily implementable and appears to leadto improved profitability in different comparative cases.Through sensitivity analysis, we demonstrate that the aboveresults are robust to variations in various parameters of theproblem. The main findings and insights from the normativepolicy suggest the following:

• Based on SilverScreener’s recommendations, the exhib-itor can achieve substantially higher cumulative profit.

• The improvement over actual decisions in terms of prof-itability appears to result from a combination of better selec-tion and scheduling of the movies.

• The general structure of the exhibitor’s normative deci-sion is: choose fewer “right” movies and run them longer.

We propose a two-tier integrated application of the modelto show how the model can be applied to realistic decisionmaking. The first tier involves development of a movie selec-tion plan to help the manager plan an entire season and bidfor movies before the start of that season. An ex ante revenueprediction scheme is developed, based intuitively on amatch-ing of the forthcoming movies with similar movies played inthis theater previously. If the forthcoming season’s schedul-ing plan can be visualized as a two-dimensional (week-by-screen) matrix, then that matrix contains only “empty cells”before the first tier. After a bid plan is developed, the exhib-itor can “fill” some of those empty cells. The remainingempty cells represent slots, which can be decided during theseason by either extending movies the exhibitor booked be-fore the season or by scheduling other movies which maybecome available later in the season. This motivates the sec-ond tier—adaptive scheduling approach—of the integrated ap-proach. The second tier helps the exhibitor in weekly deci-sion making during the season. This application involves“rolling,” and updating data, from one time window to an-other. The approaches followed in the two tiers of the inte-grated application are quite general in that they can incor-porate a sophisticated demand predictionmodel,managerialjudgments, or a combination of both. We also propose analternative behavioral decision rule (heuristic), which ex-emplifies relationship dilemmas in the movie industry. Thisheuristic shows that the exhibitors need to be selective intheir choice of movies and may suffer a substantial loss inprofitability if they place too much emphasis on accommo-dating distributors.(Movies; Decision Support Systems; Retailing; Scheduling; Inte-ger Programming)

SILVERSCREENER: A MODELING APPROACHTO MOVIE SCREENS MANAGEMENT

Marketing Science/Vol. 18, No. 3, 1999 353

1. IntroductionRetailing is becoming an increasingly important areaof management attention and academic research.Much of the research has focused on the strategic as-pects of retail management—both within the distri-bution channel and between retailers (or retailer-manufacturer systems)—but another important areahas been the development of decision support modelsto help retailers improve their decision making. Forexample, Bultez and Naert’s (1988) SHARP modelhelps retailers decide on shelf space allocations andAbraham and Lodish’s (1993) PROMOTIONSCANsystem helps managers in developing and evaluatingshort-term retail promotions. Our work is in a similarspirit to these models; its aim is to help retailers im-prove their decision making.

Most published research in this area focuses on con-sumer packaged goods sold through supermarkets.However, other retail formats and industry settingspose different challenges and intriguing problems. Wefocus on products, which have relatively short life cy-cles, so that effective retail management requires reg-ular attention to the issue of which products should bestocked. In particular, we concentrate on the motionpicture industry, though other entertainment (e.g.,books, video games) and fashion goods industrieshave similar characteristics.

The motion picture industry is emerging as an areaof increased interest to marketing scholars and re-searchers. A stream of research, addressing various as-pects related to the marketing of movies, has begun toemerge in the marketing literature. At the consumerbehavior level, some of the research has questioned therelevance of the traditional information-seeking frame-work for studying the consumption of movies (e.g.,Hirschman and Holbrook 1982, Holbrook andHirschman 1982). Another stream of research has fo-cused on forecasting the enjoyment of movies at theindividual level (Eliashberg and Sawhney 1994) aswellas forecasting the commercial success of movies at theaggregate level (Smith and Smith 1986, Austin andGordon 1987, Dodds and Holbrook 1988, Sawhney and

Eliashberg 1996, Eliashberg and Shugan 1997). Addi-tionally, some research has begun to emerge address-ing diffusion (Mahajan et al. 1984, Jones and Ritz 1991),seasonality (Radas and Shugan 1998), release timing(Krider and Weinberg 1998), clustering (Jedidi et al.1998), sequential products (Lehmann and Weinberg1998, Prasad et al. 1998), contract design (Swami et al.1998), and the impact of advertising (Zufryden 1996),all in the context of motion pictures.

There are more than 300 exhibitors in the U.S. andCanada. Though the total number of theater screensowned by these exhibitors has remained relatively con-stant in the last five years, the total number of massmarket movies released by the major studios, espe-cially during the summer peak season, seems to be ris-ing steadily. This trend suggests that movies’ distrib-utors (i.e., studios) will face limited screen availabilityfor their films, while exhibitors will have to managetheir bookings and screens very effectively to maintainand improve profitability. In reviewing the situationfor the summer of 1997, a Wall Street Journal articlecomments:

After an epic binge on production of big-budget movies, thefilm industry now faces a glut of expensive “event” picturesand too few summer weekend slots to release them all. . .[There] aren’t enough movie screens to keep big films runningfor the months they need to recoup their costs. By July 4th,1997, many are predicting gridlock. Films that are performingonly moderately well will likely be scaled back in favor of thenew releases. (Bannon 1997, p. B1)

A theater owner with an objective of effectivescreens management thus faces a complex scenario.The complexity comes from various sources. First, theincreased supply of movies by various studios in-creases the difficulty of deciding which movie to play.This decision is further complicated because it is madefor a number of screens in a multiple screens theater(i.e., a multiplex). Second, an additional supply ofmovies brings more pressure from the studios to guar-antee sufficient playtime for their movies. Relationshipmanagement in the motion picture industry is consid-ered by many as very crucial. On the other hand, thescarcity of “shelf space” requires special attention inmanaging the screens effectively and profitably. Third,

SWAMI, ELIASHBERG, AND WEINBERGModeling Approach to Movie Screens Management

354 Marketing Science/Vol. 18, No. 3, 1999

the nature of the distributor-exhibitor contract in themotion picture industry is unique. In signing a contractto play a film in its theaters, the exhibitor becomes ob-ligated to play the film for a certain period of time,even when consumer demand is weak. This minimumobligation period (playtime), which is negotiated be-tween the two parties, may vary by movie as well asby studio. The financial arrangements between studiosand exhibitors are also apparently unique to the mo-tion picture industry. Unlike wholesale/retail pricingpractices commonly employed in the consumer goodsindustry, box-office grosses are split between the ex-hibitors and distributors of motion pictures. The man-ner in which the box-office grosses are split favors thestudio (distributors) in the first few weeks of themovieplaying, but shifts to the exhibitor’s favor later on. Dis-tributors thus have a strong incentive to promote themovies intensively in their initial play period. On theother hand, the longer the exhibitor plays the movie,the larger becomes his/her share of the box-office re-ceipts. At the same time, theater attendance for amovietypically declines the longer it plays.

In the face of this complexity, the aim of current re-search is to provide a structure for analyzing manage-ment problems of exhibitors, the retailers of the movieindustry. Using a mathematical programming ap-proach and a fast, but readily accessible algorithm, wepropose a decision support model to help the exhibitormake effective and timely decisions regarding theaterscreens management. The major objective is to help theexhibitor both select and schedule movies at his/hertheater. The developed model is readily implementa-ble, as we demonstrate in an illustrative example, andappears to lead to improved profitability. An inte-grated two-tier application of the model is presentedto show how the model can be used as an effectivemanagerial aid. Through sensitivity analysis, the re-sults are shown to be robust to various parameters ofthe problem. The rest of this paper is organized as fol-lows. The screens management model, SilverScreener,its properties, and solution procedures are presentedin the next section. An illustrative application of themodel and implications for screens management pol-icy are given in §3. We provide concluding remarksand suggest directions for further research in §4.

2. Problem Formulation andModeling Approach

2.1. The Exhibitor ProblemEvery week, motion picture exhibitors must make animportant decision regarding the replacement of themovies playing at the screens in their theaters. Moviesare a seasonal product, both demand and supply in-crease in the two key seasons, Summer and Christmas.The dynamic environment thus induced gives rise tothe notions of decay and aging of movies. Decay is theintrinsic weekly decline in the box-office attraction andgross revenues (grosses in industry jargon) of a movieplaying at a theater (Krider and Weinberg 1998). Agingis the decline in the value, that is, gross generatingpower, of a movie from an exhibitor’s perspective ifthere is a delay (by week) in exhibiting the movie atthe theater. Aging, therefore, results in an opportunitycost of not being able to play a particular movie.

The above scenario is further complicated by the na-ture of the contract between the distributor and theexhibitor. The basic structure of the contract is fairlystandard between different distributor-exhibitor pairsalthough the individual terms may vary depending onthe relationship between the two parties. A typical ex-hibition contract states a fixed obligation period and adifferential revenue sharing scheme in different weeksbetween the distributor and the exhibitor. The obliga-tion period limits the ability of an exhibitor to replacea movie with less than satisfactory box-office perfor-mance in the initial weeks after its release.1

In a given week, the revenue sharing scheme splitsthe gross of a movie between a distributor and exhib-itor by one of two rules: (a) 90%/10% over house nut,2

or (b) minimum gross percentage. If the 90%/10% overhouse nut rule operates, then the distributor receives90% of the gross after the exhibitor has deducted andretained the house nut amount. Accordingly, underthis rule, the exhibitor keeps 10% of the gross over

1The obligation period may range from two to ten weeks dependingon the respective bargaining power of the distributor and exhibitorand the marketability of a particular movie.2House nut is a small negotiated amount, which the exhibitor re-ceives from the distributor. It does not necessarily bear any relation-ship to the theater’s actual expenses, and is only meant to allow forsome cushion in the exhibitor’s profit margins.



house nut plus the house nut amount. The exhibitioncontract also contains minimum percentage figures asspecified by the distributor for every week of the ex-pected play length of a movie. These figures will beused if the minimum gross percentage rule is invoked forrevenue sharing. Under this rule, the whole grossamount (without house nut deduction) is split accord-ing to the specifiedminimumpercentage for thatweek.The splitting terms (in favor of distributor and exhib-itor, respectively) specified by the distributor under atypical contract may appear as follows (see, for ex-ample, Squire (1992, p. 315) for the movie Batman):3

90%/10% Over Approved House Allowancewith Minimum of

First week at 70%/30%Next two weeks at 60%/40%Next week at 50%/50%Next week at 40%/60%Balance at 35%/65%

In addition to the revenue earned from the box-officegross, the exhibitor also earns some income from con-cession sales such as popcorn, candies, and soft drinks.The concession sales, however, depend on individualdemands generated by the movies playing at the the-ater. The exhibitor does not share the concession in-come with the distributor. Most theaters have multiplemovies playing at multiple screens. Given the com-plexity of the revenue sharing scheme and the dynam-ics of movie availability and decisionmaking, theman-agers of such multiplexes are faced with nontrivialdecisions of selecting and scheduling movies on dif-ferent screens in a fixed planning horizon. In the nextsubsection, we present a mathematical model whichaims at helping managers address the above problem.

2.2. SilverScreener: The Screens ManagementModel

2.2.1. Assumptions. We formulate the exhibitorproblem of the previous section as an integer program.To simplify the exposition, we assume the following:

3If a movie grossed $10,000 in the second week of its run and thehouse nut was $5,000, the distributor would receive $6,000 (60% of$10,000), which is greater than $4,500 (90% of ($10,000–$5,000)).

Assumption 1. The availability of the movies to be re-leased during the planning horizon is known in advance.

Assumption 2. The weekly revenues to be generated bythe movies considered during the planning horizon can beestimated in advance.

Assumption 3. The replacement decisions are made ona weekly basis.

Assumption 4. All the screens in the multiplex are ofequal capacity.

Assumption 5. There is no time lag between placing anorder for a new movie and its arrival.

Assumptions 1, 3, and 5 are not limiting and, in fact,reflect current industry practice. Assumption 2 is astrong assumption about a priori knowledge of movierevenues. However, we relax this assumption partiallyin the empirical analysis section. Moreover, data col-lected from Variety suggest that managers have a rea-sonable estimate of box-office gross revenue of amovie. In the empirical analysis section, we show howthe forecast data can be incorporated in our optimi-zation model using an adaptive approach. We also dis-cuss an ex ante revenue prediction scheme that can beused in conjunction with our optimization model. Weassume equal capacity screens for the current analysis(Assumption 4), which addresses the questions regard-ing which movies to pick and how long to show them.This is done for the simplicity of the current analysis.In the last section, we discuss how this assumption canbe relaxed in future work.

2.2.2. Definition of Variables.W length of planning horizon,H number of screens in the multiplex,N total number of movies considered

during the planning horizon,rj release date of movie j,dj due date (if applicable) of movie j,



xjiw binary (decision) 0–1 variable whichtakes value 1 if movie j is scheduledfor i weeks beyond its obligation pe-riod starting in week w,

Pjiw profit received by the exhibitor if xjiwis equal to 1,

GROSSjw box-office gross revenue generated bymovie j in week w,

POPjw concession profit generated by moviej in week w,

VCjw variable cost due to movie j in weekw,

FCw fixed cost of multiplex in week w,EXSHAREjw exhibitor’s share of box-office revenue

for movie j in week w,OPDj obligation period of movie j,C house nut.

2.2.3. Problem Formulation. Motivation. The for-mulation of the exhibitor problem is similar to the par-allel machine scheduling problems (Baker 1993, Pinedo1995). The usual setting of these problems is as follows.A set of N jobs has to be scheduled on H parallel ma-chines. Each job j, (j � 1, . . . ,N), must be processedwithout interruption during a period of length OPDj.A machine can handle no more than one job at a time,and is continuously available from time zero onwards.Each job j has a release date rj and a due date dj, the timeby which it should ideally be completed. The goal isto find an optimal feasible schedule, that is, a set ofstart times such that the capacities, availability andtime limit constraints are met, and a given objectivefunction is optimized.

A special case of these problems is when all of theparallel machines are identical in terms of their capac-ities, and the processing period is restricted to be atleast OPDj. When applied to the exhibitor problem, theanalogy is obvious: the screens are machines and mov-ies are jobs. Each job (i.e., movie) has its own releasedate rj. Except for a few special cases, we assume thatall the movies have a common due date, end-of-the-horizon, W. However, the framework is flexible to in-corporate movie specific due dates. This flexibility al-lows the exhibitor to book certain slots forprecommitments and still arrive at an optimal feasibleschedule for the rest of the planning horizon. We use

this property of the modeling framework in our em-pirical analysis section to specify a movie bidding planfor the exhibitor.Time-Indexed Formulation.We depart from the typical

parallel machine scheduling problems by introducingthe time-indexed formulation (Sousa and Wolsey 1992,Williams 1997) that is particularly useful for solvingthe exhibitor problem. This formulation is based on theidea of dividing the planning horizon [0, . . . ,W] intoW discrete intervals of unit length. To model the screenmanagement problem, we define a binary variable,xjiw, which equals 1 if movie j is shown for i weeksbeyond its obligation period starting in week w of theplanning horizon, and 0 otherwise. Notice that the ob-ligation period constraint is included in the definitionof xjiw itself. For example, if the obligation period ofMovie Number 3 is two weeks, then x301 � 1 impliesthat it is shown for two weeks starting in week 1. Thisformulation can also be generalized to encompass suchextensions as screen capacities, precedence constraintsbetween movies, and movies’ specific due dates.

The time-indexed formulation highlights some keydifferences between the exhibitor problem and typicalmachine scheduling problems. First, all movies do nothave to be played in the exhibitor problem, while alljobs have to be scheduled in the machine schedulingproblems. Accordingly, the proposed formulation isaimed at helping the exhibitor decide about two criticaldecision variables: choice of movies to play and decid-ing play lengths of the chosen movies. Second, the fol-lowing types of decision-making goals are found to beprevalent in machine scheduling problems: turn-around, timeliness, and throughput. In contrast, theexhibitor problem offers a situation inwhich the sched-uling decisions directly affect profitability, a more rele-vant decision-making goal, both by affecting gross rev-enue and concession profits. Finally, the mainparameters of interest in machine scheduling are thelengths of the jobs, and their release and due dates. Theexhibitor problem, on the other hand, deals with ad-ditional variables such as complicated contract termsand an exponentially decaying demand function.Profit Function.We define Pjiw, the total profit the ex-

hibitor receives corresponding to each xjiw, as:



w�SCR �1ji

P � (�FC � POP � VC )jiw � u ju juu�w

� I * {0.1 * (GROSS � C) � C}h juju

� (1 � I ) * EXSHARE * GROSS ,h ju juju

j � 1, •••, N, i � 0, •••, k , w � r ,j j

•••, d � SCR � 1, (1)j ji

where hjw is a logical condition given by

h � (0.9 * (GROSS � C)jw jw

� (1 � EXSHARE ) * (GROSS ),jw jw

and

1, if X � TRUE,I �X �0, otherwise.

kj � dj � rj � OPDj � 1 � maximum possible numberof weeks movie j can be shown beyond its obligationperiod starting in rj or any feasible week thereafter, andSCRji � OPDj � i � total screening period for moviej if it is shown for i weeks beyond its obligation period,where i � 0, . . . ,kj.

The expression for the profit to the exhibitor consistsof two portions corresponding to the two different con-ditions of the contract terms. The two conditions, op-erationalized by the logical variable I, follow directlyfrom the revenue sharing terms described earlier. Inaddition, there are variables for fixed and variablecosts. Fixed costs (e.g., rent, lights, and weekly main-tenance) are the costs that the exhibitor has to incurirrespective of the traffic generated by themovies play-ing in a particular week. Variable costs, such as salariesof the temporary staff hired for a particular movie,vary by movies as well as weeks.

The above operationalization of Pjiw simplifies thesolution procedure considerably since they can now becomputed independently of the optimization routine.Furthermore, the variables kj and SCRji help us “cover”all feasible (P, x) pairs for a movie. For example, sup-pose movie j has parameters: OPDj � 2, rj � 1, and dj� 4. If the movie is scheduled in Week 1 (i.e., w � 1),then it can be shown for 2, 3 or 4 weeks, that is, for 0,1 or 2 weeks beyond the obligation period. We now

show how variables kj and SCRji parsimoniously cap-ture these possibilities. Since kj � 2, i varies from 0 to2. The corresponding values of SCRji (� 2 � i) are 2,3, and 4, respectively. Therefore, the corresponding (P,x) pairs are (Pj01, xj01), (Pj11, xj11), and (Pj21, xj21),respectively.Demand Function. We use the following two-

parameter exponentially declining function to estimatebox-office gross revenue. Consistent with the empiricalresults in Krider and Weinberg (1998), Lehmann andWeinberg (1998), and Sawhney and Eliashberg (1996),as well as our own empirical analysis presented in thenext section, the exponential function appears to be areasonable model of the revenue patterns of most ma-jor movies:4

b w��jGROSS � � e (2)jw j

where �j � 0 and bj � 0 are opening and decay factorsrespectively of movie j and � � normal (0, r2). Specificapproaches to estimating GROSSjw are discussed in theempirical analysis section.

The reader may note that the revenue generatingfunction employed does not explicitly incorporatecompetitive effects among movie theaters. This as-sumption, made to aid model development, is consis-tent with some empirical evidence (Davis 1998) thatsuggests that there exists geographic market power inthe film-exhibition industry and that consumers arewilling to spend a limited amount of effort to travel towatch a movie (even a blockbuster). Moreover, the es-timated cross price elasticities of demand between the-aters are low and decline as the distance between the-aters increases (Davis 1998), suggesting that fortheaters which charge the same price, the competitionis even less intensive. In fact, the Justice Departmenthas recently launched an investigation into monopolyissues in the theater business (Orwall and Lipman1999, p. B9). Such an environment makes any incor-poration of competitive behavior into a forecast to beof limited value from an accuracy standpoint. At the

4The exponential demand function used in the current research is aspecial case of the three-parameter generalized gamma demandfunction introduced by Sawhney and Eliashberg (1996). In mostcases, their model reduces to a demand function similar to the oneused in this research.



general level of specification of the model in the cur-rent study, therefore, we implicitly assume that to theextent competitive effects exist, either from other the-aters or alternative forms of entertainment, they aresummarized in the demand parameters or randomlyaffect the error term in the demand function. However,the sources of such effects may be so varied that itwould be difficult to estimate with any accuracy andinclude them in the current framework. The consid-eration of such effects raises interesting theoretical is-sues for future research, which are discussed in theconcluding section.Problem Statement. Based on the above discussion,

the time-indexed formulation of the exhibitor problemis presented as follows:

N k d�SCR �1j j ji

max P x (3)� � � jiw jiwj�1 i�0 w�rj

subject to

k d�SCR �1j j ji

x � 1, j � 1, . . . , N, (4)� � jiwi�0 w�rj

N k wj

x � H, w � 1, . . . , W, (5)� � � jiqjj�1 i�0 q�w�SCR �1j ji

r � q � d � SCR � 1, j � 1, . . . , N;j j j ji

i � 0, . . . , k , (6)j

x � {0,1}. (7)jiw

In the above model, (3) denotes the objective func-tion, which is to maximize cumulative profit over theseason. Constraint (4) ensures that a movie is playedin only consecutive weeks. It also allows a movie notto be scheduled at all. The next constraint restricts thetotal number of movies scheduled in any week of theplanning horizon to the total number of screens in themultiplex. In doing so, it sums up all themovies, whichare released earlier than or in the week under consid-eration. The set of inequalities denoted by Constraint(6) is an indexing constraint, which restricts the vari-able qj in Constraint (5) to feasible values. Constraint(7) defines xjiw to be a binary variable. We coded the

above model in AMPL (Fourer et al. 1993), a modelinglanguage for mathematical programming.5

Our model can be applied to realistic decision mak-ing in two different ways. The first is for developing amaster plan by a one-shot application of the model. Theresulting schedule can help the exhibition managersplan and bid for selected movies before the start of aseason. The second instance of the model’s applicationcan be for weekly decisions, possibly after the devel-opment of the bidding plan. This adaptive applicationinvolves “rolling” from one time window (i.e., a week)to another and focuses on decisions about whether ornot a movie should continue to be shown. These ap-plications of the model can be compared to other plau-sible decision making rules (heuristics) that the exhib-itors may use. The next section presents an empiricalanalysis of exhibitor decision making and is organizedas follows. We first choose a representative theater andderive normative policy implications using the datacollected for that theater. We then present an inte-grated application of the model, combining the masterplan and rolling horizon approaches. Finally, we com-pare the model’s performance with a behavioralheuristic.

3. A Case Study of the 84th St.Sixplex in New York

The 84th St. Sixplex is a six-screen theater, located at84th Street and Broadway in New York City’s UpperWest Side. We collected the empirical data for this the-ater from Variety (1989). We chose this theater for thefollowing reasons. It is a reasonable size theater, andusually plays first-run movies. It faced a minimal levelof competition from the theaters in its vicinity.6 More-over, it is one of the few theaters in New York whosedata for the year 1989 are publicly available in Variety.The year 1989 was chosen because the contract termsof a major movie in 1989, Batman, are available from

5The analysis can be conducted on an Intel Pentium class computer.Thus, the model formulation allows for user-friendly implementa-tion. The time taken to solve such problems was of the order of afew seconds.6Except for a small theater with two screens and less than 20% of theSixplex’s capacity, there were no other first-run theaters north of70th St. on Manhattan’s West Side.



Table 1 Movies Consideration Set

Movie Number Title Movie Number Title

1 New York Stories (NYS) 2 Chances Are (CA)3 Dangerous Liaisons (DL) 4 Lean on Me (LOM)5 Police Academy VI (PA6) 6 Leviathan (LTHN)7 Dead Bang (DB) 8 Heathers (H)9 Sing (SING) 10 Major League (ML)

11 Dead Calm (DC) 12 The Accused (TA)13 Disorganized Crime (DOC) 14 See You in the Morning (SYM)15 Lover Boy (LB) 16 Pet Semetary (PS)17 Speed Zone (SZ) 18 Scandal (SDL)19 Miss Firecracker (MF) 20 See No Evil, Hear No Evil (SNEHNE)21 Earth Girls Are Easy (EGE) 22 For Queen and Country (FQC)23 Pink Cadillac (PC) 24 Indiana Jones and the Last Crusade (IJ)25 Dead Poets Society (DPS) 26 No Holds Barred (NHB)27 Star Trek V (ST5) 28 Batman (B)29 Honey I Shrunk the Kids (HISK) 30 Lethal Weapon II (LW2)31 The Package (TP) 32 Peter Pan (PP)33 Night Game (NG) 34 License to Kill (LTK)35 Look Up (LU) 36 Turner and Hooch (TH)37 Friday the 13th VIII (FT8) 38 A Nightmare on Elm Street V (NES5)39 UHF (UHF) 40 Rude Awakening (RA)41 Cookie (C) 42 Let It Ride (LIR)43 Relentless (RL)

Squire (1992). Since Batmanwas played by this theater,we use its contract terms as representative of those ofthe other movies.

Specifically, the data items used in the followinganalyses and their respective sources are as follows:

1. Schedule of the movies actually played (see Table1) by the theater (Source: “Domestic Box-Office” datafrom Variety).

2. Gross revenues generated by the movies actuallyplayed at the theater (Source: “Domestic Box-Office”data from Variety).

3. One-week ahead gross revenue forecasts for themovies actually played at the theater (Source: “Do-mestic Box-Office” data from Variety).

4. House nut amounts (Source: “Domestic Box-Office” data from Variety).

5. Costs (variable and fixed) and concession profits(Source: “Financial Statements” of major theater chainsfrom Security and Exchange Commission (SEC) filings onthe Internet).

The actual schedule followed by the exhibitor for the

27 weeks of the planning horizon is given in Table 2A.As shown in the table, the theater showed a total of 43different movies. There are a number of movies withplay length of one or two weeks. In addition, threemovies, Indiana Jones and the Last Crusade (IJ), Star TrekV (ST5), and Batman (B), were double-booked, that is,played simultaneously on two screens for someperiod.We treat such cases as two different movies.

In the analysis that follows, we compare the actualschedule to the schedules based on our model. Begin-ning with ex post information, we derive normativepolicy implications for the scheduling decisions. Weassume the obligation period to be two weeks for allthe movies considered. This is the minimum of theplay lengths of most movies in the actual schedule.7

The revenue sharing terms for the movie Batman in

7Although the actual case schedules a number of movies for onlyone week, we proceed with a two-week obligation period for thesake of consistency. It is clear that this extra restriction works againstour comparison approaches, and our profit results will be conser-vative to this extent.



Table 2 Comparative Schedules

A. Actual ScheduleScreen

B. Optimal Schedule Using Ex Post DataScreen

Week 1 2 3 4 5 6 1 2 3 4 5 6

1 NYS CA DL LOM PA6 LTHN NYS CA DL LOM LTHN PA62 NYS CA DL LOM DB LTHN NYS CA DL LOM LTHN PA63 DL NYS CA H DB SING NYS CA DL LOM LTHN H4 DL NYS ML H DC TA NYS DC DL TA ML H5 DOC ML NYS H DC TA NYS DC DL TA ML H6 SYM ML DOC PS SZ H NYS DC PS TA ML H7 SYM LB ML SDL PS H NYS DC PS TA ML H8 SYM LB ML SDL PS MF SDL DC PS TA ML H9 SNEHNE EGE ML SDL PS MF SDL DC MF TA EGE H

10 SNEHNE EGE FQC SDL PS MF SDL DC MF TA EGE H11 EGE PC IJ IJ SDL SNEHNE SDL DC MF IJ EGE IJ12 DPS NHB IJ IJ SNEHNE PC SDL DPS MF IJ EGE IJ13 DPS ST5 ST5 IJ IJ SNEHNE SDL DPS ST5 IJ ST5 IJ14 DPS ST5 ST5 IJ IJ SNEHNE SDL DPS ST5 IJ ST5 IJ15 IJ ST5 DPS B B HISK B DPS B IJ HISK IJ16 IJ ST5 DPS B B HISK B DPS B IJ HISK IJ17 IJ LW2 DPS B B HISK B DPS B LW2 HISK IJ18 LTK LW2 B IJ PP HISK B DPS B LW2 HISK LTK19 LTK LW2 B IJ UHF HISK B DPS B LW2 HISK LTK20 LTK LW2 B TH FT8 HISK B DPS B LW2 TH LTK21 LTK LW2 B TH FT8 LU B DPS B LW2 TH LU22 LTK LU B TH LW2 NES5 B DPS B LW2 NES5 LU23 RA LIR B LU LW2 NES5 B DPS B LW2 NES5 LU24 LIR TP B LU LW2 C TP DPS B LW2 C LU25 DPS TP B RL LW2 C TP DPS B LW2 C RL26 DPS TP B RL LW2 C TP DPS B LW2 C RL27 RL TP B C LW2 NG TP DPS B LW2 C RL

1989 were as specified in the previous section. Thehouse nut amount for all the screens of 84th St. Sixplexwas $14,500 in 1989 (see Variety 1989).

We have no public information available on the vari-able and fixed costs, and concession profits for the 84thSt. Sixplex. Therefore, we used the financial statementsof four major theatrical chains, AMC, Cineplex Odeon,United Artists, and Carmike, to examine how their costdata vary with box-office revenue. Quarterly and an-nual financial statements from these companies, ob-tained from the Internet and based on Security andExchange Commission (SEC) filings, indicate that theoperating costs typically vary from 56% to 66% of box-office revenue. The concession profits vary from 30%

to 40% of box-office revenue. These ranges conformwith the industry standards available from othersources such as Squire (1992). To present results for arepresentative case in the comparative analyses thatfollow, we assume operating costs of 66% and conces-sion profits of 40%.8 We generate cumulative net rev-enues for various comparison cases, which include

8The break-up of operating costs into fixed and variable costs is notavailable from the financial statements. We make an assumption thatone half of the operating costs is fixed cost and the other half isvariable cost. Thus, for the representative case, fixed and variablecosts are each 33% of the box-office revenue. In the sensitivity anal-ysis section, we examine the robustness of our results to these as-sumptions, as well as our other assumptions about contract terms.



variables that vary with weekly revenues and movies,that is, concession profit, variable cost, and share of thebox-office revenue. To obtain cumulative profit, wethen subtract from the cumulative net revenue the cu-mulative fixed cost over the season which is commonacross all the comparison cases. To calculate the cu-mulative fixed cost, we use the cumulative box-officerevenue for the actual case of all the movies that playedat the theater during the season.

3.1. Normative Policy Versus Actual DecisionMaking

3.1.1. Comparison Approach: Ex Post Data, Re-stricted Set of Movies. In this approach, we consideronly those movies that were actually played at the the-ater. To compare the schedule produced by our modelwith the actual decisions of the exhibitor, we use expost information concerning the revenues. We alsoneed to predict, however, box-office gross revenues forthe weeks beyond the actual play length of a movie.We fit the linear regression version of the demandmodel introduced in Equation (2) of the previous sec-tion after log-transforming their gross revenues. Afterdeleting two “outlier” movies, an average adjusted R2

was found to be 0.92 for the movies tested.9 To gen-erate revenue estimates for the later weeks of the mov-ies that actually played only for one week at the the-ater, we use a median decay rate across all the moviesshown at the theater. From here onward, we use theterm “optimal restricted set schedule (approach)” todenote the schedule produced by the algorithm usingthe revenue data generated in the above fashion.

3.1.2. SilverScreener’s Normative Results. Theresults presented in this section were obtained by theimplementation of the SilverScreenermodel on the em-pirical data collected. The optimal schedule generatedby the model is given in Table 2B. A summary char-acterization of the results is provided in Table 3.

Tables 2B and 3 (first two columns) suggest thefollowing:

9The average adjusted R2 does not include the two outlier movies orthe movies that played only for one week. The revenue of the twooutlier movies first increases for a brief period and then exponen-tially decreases. We also do not include the movies that played forexactly two weeks, since their R2 value is equal to one and wouldinflate the average R2.

• The use of the optimization approach estimates themultiplex exhibitor to be capable of earning a highercumulative profit than for the actual schedule (37.7%).The substantial profitability improvement is achieveddespite the fact that it is a stringent test, given the dataavailable, of our optimization approach. Recall that weuse a limited consideration set, which includes sub-optimal choices of movies made by the exhibitor. Weonly allow double-booking for the three movies thatthe theater double-booked. An estimated improve-ment of 37.7%, therefore, attests to the potential effec-tiveness of our approach in rather unconstrainedcases.10

• The improvement over actual decisions is achievedfrom two sources. One is better selection, that is, choos-ing the “right” movie to show, and the other is betterscheduling, that is, deciding the “right” run-length ofthe movie chosen. As shown in Table 3, the nature ofthe normative optimal policy is to choose fewer “right”movies and run them longer. (This result also held for theexpanded data set described in Footnote 10.)

• The optimal schedule retains 27 movies of the 43movies actually scheduled by the exhibitor. Thus, ourmodel significantly improves upon actual decisions,while retaining approximately 63% of managerialchoices. Managerial decisions may gradually convergewith the model’s recommendation as themodel is usedover an extended period of time. Thus, our approachseems ideally suited to situations in which the model“evolves” with usage (Weinberg 1986).

• The distributors’ net revenue for the optimal re-stricted set schedule remains about the same (�0.27%)as compared to the actual returns. While some distrib-utors gain and others lose from this one theater’s im-proved scheduling, this implies that a possibility of a

10To provide a further test of our approach, we also ran the modelon an expanded set of movies, namely all 87 movies that were re-leased during the 1989 summer season and were listed at least oncein Variety’s “Top 50 List of Movies.” Using an audience forecastingsystem based on the relationship between national (per theater)movie attendance and the Sixplex’s attendance (described fully inSwami (1998)) that had an adjusted R2 of 0.80, an optimal schedulewas generated. A summary of the results obtained is shown in thefourth column of Table 3. As shown in the table, the results aresimilar in direction to that reported in the text, namely a limitednumber of movies (25) was chosen for showing, and these wereshown for an average of 6.5 weeks. The cumulative profit improve-ment was estimated at 121%.



Table 3 Characterization of Solutions

Actual ScheduleOptimal Restricted

Set ScheduleOptimal Expanded

Set ScheduleDistributors’

Pressure Heuristic

Cumulative profit ($’s) 585,175 805,988 1,294,408 571,990Percentage improvement over actual — 37.7 121.2 �2.2Number of different movies scheduled 43 27 25 43Average run length (screening slots) 3.8* 6 6.5 3.8

Percentage of Movies Scheduled for1 week 18.6 0 0 48.82 weeks 27.9 11.1 20 20.93 weeks 14 22.2 16 30.3�4 weeks 39.5 66.7 64 11

Double Booking for (Weeks)Batman 3 9 3 11Indiana Jones 4 6 4 6Star Trek V 2 2 0 2

Screening Slots forBatman 16 21 9 22Indiana Jones 13 13 11 13Lethal Weapon II 11 11 11 11Dead Poets Society 8 16 16 7New York Stories 5 6 5 3Scandal 5 8 6 5

*(27 weeks * 6 screens)/43 movies � 3.8 slots.

“win-win” situation exists from an overall systemstandpoint.

To summarize, the use of optimization approacheslike SilverScreener holds promise to improve mana-gerial decisions in the movie exhibition business. Theprescriptive advice to the manager, as compared tocurrent practice, is to concentrate on a smaller numberof movies, which are selected to maximize profits, andconsequently to play these movies for a longer periodof time.

3.1.3. Sensitivity Analyses. Gross Revenue. Oneof the key assumptions underlying the evaluation ofthe exhibitor’s decision making quality presented in §2is the deterministic knowledge of movie revenues.However, in practice, the manager would not have theex post data available when making his/her schedul-ing decisions. Section 3.2 presents a two-tier approach

that includes the use of ex ante predictions to capturemore directly the exhibitor’s decision environment andinformation set. However, at this stage, it is useful toexamine the sensitivity of the results in the previoussection to the changes in revenues from their deter-ministic levels. For a limited number of years, includ-ing those covered in our study, Variety published theexhibitor’s forecast for box-office gross revenue for thefollowing week for each screen in the theater of inter-est. Using these data, we can examine the impact ofapparently judgmental forecasting errors on the opti-mal policy and improvement over actual decisions. Acorrelation analysis of the Variety forecasts with the expost data suggests that these forecasts tend to be quiteaccurate, achieving an R2 of 0.96. We used these one-week ahead forecast data in a similar fashion to thatof the restricted set approach of the previous section.Thus, for the weeks a movie played at the theater, we



used the forecast data from Variety; for the weeks be-yond, we used the two-parameter exponential modelfor prediction.11

SilverScreener was run to generate an optimalschedule, but after the optimal schedule was gener-ated, its profitability was recalculated using the actual(ex post) revenue data. Although we observe some de-crease in the percentage improvement in profit termsas compared to the optimal restricted set approach(31.4% vs. 37.7% improvement as compared to actual),the policy results are similar to those reported earlier.In particular, only 31 of the original 43 movies wereretained in the optimal schedule. As compared to theoptimal ex post restricted set schedule, the most sig-nificant change was the reduction of screening slots ofBatman to 16 and the scheduling of 8 as compared to3 movies for 2-week runs. However, both schedulessuggested that 18 movies run for 4 or more weeks andthat, as compared to the actual schedule, fewer moviesshould be shown and for longer run lengths. In sum-mary, the nature and character of the schedule usingthe ex ante data from Varietywere quite similar to thatfor the ex post data, suggesting that the improved re-sults are robust with respect to revenue streams input.Other Parameters. The analysis on fixed and variable

costs, and concession profits considers two values of op-erating costs, 56% and 66% (of box-office gross reve-nue), and concession profits, 30% and 40%, respec-tively. Three different cases for the split of operatingcosts into fixed and variable costs are considered: fullyvariable; 50% fixed, 50% variable; and fully fixed.Across the 12 cases of assumptions about operatingcosts and concession profits, the model shows a widerange of improvement over actual profits (from 18.2%to 483.9%). However, these differences are mainly dueto changes in the relative levels of fixed and variable

11There is always the possibility that an exhibitor has dropped amovie from the schedule just before it is about to undergo a suddenand idiosyncratic drop in box office revenue. However, this is un-likely to be a general result given the considerable success of theexponential decay model to capture a movie’s revenue a few weeksafter its opening (Sawhney and Eliashberg 1996, Jedidi et al. 1998;Krider and Weinberg 1998). Looked at on a national basis, the boxoffice revenues for the movies in our sample did not show any sys-tematic, unusual sales declines at the time they were dropped by thistheater.

costs rather than to substantial differences in sched-uling. To conduct analysis on obligation period,we treatthe cumulative revenue of the play length of a movieas an indicator of its strength. We sort these data anddivide them into two halves with a median split. Weassume the obligation period of those movies that havecumulative revenue below themedian to be lower (twoweeks), and those above the median to be higher (fourweeks). The results show that the added obligation pe-riod restriction causes a slight decrease in profitabilityas compared to the optimal restricted set approach(30.2% vs. 37.7%), but the policy results are quite com-parable to earlier results. Finally, the analysis on reve-nue sharing terms is conducted by using a sample ofrevenue sharing terms used by a major theater chainin 1996. The model improves in profitability (from 15%to 38%) over actual decisions across different contractterms.

To summarize, our model leads to a robust improve-ment in profitability for the exhibitor under a broadrange of parameter estimates, cost assumptions, con-tract terms, and decision-making structures. We nextdiscuss the integrated two-tier application of ourmodel.

3.2. SilverScreener’s Two-Tier Application: AnIntegrated Approach

The major objective of this section is to show that ourmodel would be an effective managerial decision aid.Toward this end, we propose an integrated applicationof our model, which consists of two phases: 1) MovieSelection, and 2) Adaptive Scheduling.

3.2.1. Tier 1: Movie Selection—Which Movies toPlay? Motivation. Before a season begins, exhibitorsselect a set of movies to book and develop a tentativeschedule (or “master plan”). Our personal interviewswith several exhibitors showed them to have keen in-terest in a mathematical model-based master plan be-cause it would help them in their bidding and seasonplanning decisions.12 Approximately three to fourmonths before the summer season, distributors screen

12In fact, most exhibitors revealed that they develop a “sort-of-master-plan” before the start of a season. However, the plan opti-mization task may be too complicated to be done on a pencil-and-paper level.



their movies for exhibitors at a major trade show usu-ally held in Las Vegas. After the screening, distributorssend out bid solicitations to most exhibitors. A typicalbid invitation (see Squire 1992, p. 315 and pp. 344–345)contains the release date of the movie, the contractterms (i.e., obligation period and sharing terms) thatvary by both movies and distributors, bid return dead-line, and so on. The cover letter, which accompaniesthe bid invitation letter, might feature a brief synopsisof the movie, along with the name of the stars, director,producer, and writer.

Using the information about the contract terms forvarious movies from the distributors’ bid invitationletters, and a suitable ex ante revenue predictionscheme (which could either be historical-data based, ormanagerial-judgment based), the exhibitor can thencome up with a tentative preseason schedule for amul-tiplex using the model. Such a schedule can help theexhibitor decide whether or not to bid for a particularmovie. The preseason schedule would reject somemovies outright, either because their contract terms aretoo unattractive, or their estimated profit potential isnot attractive enough as compared to other movies.However, in a spirit similar to CALLPLAN (Lodish1971) and ARTS PLAN (Weinberg and Shachmut 1978)models, the exhibitor would have flexibility to over-ride some of the model’s recommendations and re-schedule the season.13

Estimating Ex Ante Movie Revenues. To demonstratehow the exhibitor of 84th St. Sixplex could have de-veloped a bidding plan for the summer of 1989, weneed to show how the revenue estimates of the moviescould have been derived before the summer season.To put ourselves in the exhibitor’s shoes, we employ

13Another benefit that the master plan offers comes simply from itsability to recommend the play length for a movie. This may be ben-eficial in the cases when the distributor’s bid invitation letter con-tains more complicated contract terms. For example, the contractterms for a movie may contain different sets of obligation period andrevenue sharing terms. The lowest value of the obligation periodmay have the least attractive of the three sharing terms for the ex-hibitor. The next higher value of the obligation period may havebetter sharing terms, and so on. Based on the model’s recommen-dations, the exhibitor can examine the impact of different sets ofobligation periods and the associated sharing terms on his/her prof-itability, and can then decide whether or not to bid, and if chosen tobid, the set of contract terms for bidding.

an ex ante revenue prediction scheme toward this end,which is based rather intuitively upon a matching ofthe forthcoming movies with similar movies played inthis theater previously. This analogical reasoning isdone using five attributes of a movie: Genre, MPAA(Motion Pictures Association of America) Rating, Se-quel, Stars, and Distributor. While the exhibitor maynot be aware of it, these attributes are based on pre-vious studies such as Wallace et al. (1993), Sawhneyand Eliashberg (1996), and Jedidi et al. (1998), whichhave reported some success in forecasting revenuesbased on such attributes.14

The ex ante revenue prediction scheme is explainedin greater detail in Appendix 1. The scheme yields anoverall R2 � 0.28 in terms of correlation between ac-tual and predicted Summer 1989 revenues. The rela-tively low R2 value reflects the difficulty associatedwith an a priori attribute-based revenue prediction ofnew movies. Previous researchers have also met withonly partial success in relying on such analogical rea-soning efforts (Sawhney and Eliashberg 1996).Bidding Plan Results. The critical output at this stage

is the determination of a subset (from the considerationset) of movies on which to bid. The bidding plan isbased on the above discussed ex ante revenue predic-tions and the SilverScreener optimization algorithm.The consideration set consists of the 43 different mov-ies that actually played in the theater. In this case, thealgorithm suggests that only 31 movies should be bidon (see Table 4A). We include all the movies in thesubset for bidding whose play length recommendedby the algorithm exceeds a cut-off period. The schedulepresented in Table 4A corresponds to a cut-off valueof two weeks.15 The 31 movies thus chosen by the bid-ding plan algorithm consist of 23 movies from the expost analysis in §3.1.2 as well as 8 other movies. Hence,4 movies from the ex post analysis were not chosen forbidding.

14We do not suggest that the overall appeal of a movie can be re-duced to some function of its attributes. Instead, the objective of theproposed revenue prediction scheme is to present a sample appli-cation of our model. Therefore, we do not rule out the possibility ofbetter prediction schemes to be used in conjunction with our modelin the future.15A similar output was generated for a cut-off value of six weeks,but with fewer movies selected.



Table 4 Integrated Schedules

A. Integrated Schedule (Recommendations BasedOnly on Bidding Plan)

Screen

B. Integrated Actual Implied Schedule (Using Both Bidding Plan andAdaptive Scheduling Approaches)

Screen

Week 1 2 3 4 5 6 1 2 3 4 5 6

1 NYS CA DL LOM PA6 LTHN NYS CA DL LOM PA6 LTHN2 NYS CA DL LOM PA6 LTHN NYS CA DL LOM PA6 LTHN3 SING H NYS CA DL LOM SING H4 DC TA ML SING H NYS DC TA ML SING H5 DC TA ML DOC NYS DC TA ML DOC H6 SYM DOC PS SYM TA ML DOC H7 SYM PS SYM TA ML SDL H8 MF PS MF TA ML SDL H9 EGE MF SNEHNE EGE MF SNEHNE ML SDL PS

10 EGE SNEHNE EGE FQC SNEHNE ML SDL PS11 PC IJ IJ PC IJ SNEHNE IJ SDL PS12 PC IJ DPS IJ NHB PC IJ DPS IJ SDL NHB13 ST5 DPS NHB ST5 IJ DPS IJ SDL NHB14 ST5 ST5 IJ DPS IJ SDL ST515 B B HISK B IJ DPS IJ B HISK16 B B HISK B IJ DPS IJ B HISK17 LW2 B IJ DPS LW2 B HISK18 LTK LW2 B LTK DPS LW2 B HISK19 LTK B LTK DPS LW2 B HISK20 B LTK DPS LW2 B FT821 LU22 LU NES523 RA NES524 RA TP C25 RL TP C26 RL27

If the forthcoming season’s scheduling plan could bevisualized as a two-dimensional (week-by-screen)ma-trix, then that matrix contains only “empty cells” be-fore the bid planning process begins. After the bid planis developed and finalized with the distributors, theexhibitor can “fill” some of those empty cells. Assum-ing an obligation period of two weeks, the two-dimensional week-by-screen matrix for this case isshown in Table 4A. The occupied cells in the table rep-resent the slots, which the exhibitor fills by biddingbefore the season. The empty cells represent slots,which can be decided during the season by either ex-tending movies the exhibitor booked before the seasonor by scheduling other movies which may become

available later in the season. This leads us into the sec-ond tier—adaptive scheduling—of the integratedapproach.

3.2.2. Tier 2: Adaptive Scheduling—How LongShould Movies Play? Motivation. In practice, exhib-itors decide once a week (normally on Monday), onwhich movies to play starting later in the week (usu-ally Friday). This is an adaptive decision-makingmodeof behavior. Our model is capable of incorporatingsuch weekly decisions for the rest of the schedule (i.e.,filling the empty cells). In such situations, the exhibitoris likely to choose a shorter planning horizon (a timewindow) than the one chosen for preseason bidding



because he/she will be relatively more certain of theavailability and revenue potentials of the various mov-ies. The exhibitor in fact makes weekly decisions “roll-ing” from one time window to another. To simulatethis managerial behavior, we use the minimal infor-mation that an exhibitor has about each movie’s rev-enue potential. After a movie plays at the theater (if itis chosen to play), and the corresponding actual reve-nue data becomes available, the exhibitor can updatethe revenue prediction model on the basis of the newdata. For example, the manager may begin usingSilverScreener with an eight-week time window in thefirst week of the season using his/her judgment of rev-enue stream estimates. Depending on the model’s rec-ommendation, he/she arrives at the first eight weekcomplete scheduling decision. In the second week,however, he/she may update the revenue estimatesfor the next eight weeks on the basis of the actual rev-enue received in the first week. Based on the model’srecommendation for the second to ninth week, he/shemakes the second week scheduling decision. From thethird week onwards, the manager could use a combi-nation of the two-parameter estimated exponentialmodel (for the movies that have played for two weeks)as well as managerial estimates for the prediction ofrevenues for the third to tenth week, and so on.Methodology. To analyze the adaptive scheduling de-

cisions more in line with the actual decision making,we assume that the only information available to theexhibitor about the revenue of a movie before its re-lease is its first-week forecast. This weekly forecast isin fact published in Variety (1989); see §3.1.3. To gen-erate predictions for the later weeks, we use amedian16

exponential decay rate (calculated across all the mov-ies played in the 84th St. Sixplex). The idea is that withno a priori information, the executive is likely to relyon an average across all movies or a similar historicalsummary measure. This is in the same spirit as usinga prior distribution over the decay rate. After a moviehas played for one week, we fit the two-parameter ex-ponential model using the actual data from the firstweek and the second week’s forecast from Variety togenerate predictions for the later weeks. In a similar

16The distribution of decay rates is skewed to the right, therefore weused median instead of mean.

fashion, after a movie has played for two weeks, we fitthe two-parameter exponential model to the actualdataof such movies.Results.We follow the adaptive decision-making ap-

proach for the first 20 time windows (each with aneight-week time horizon), covering the entire 1989summer season. In each of the eight-week windows,the adaptive approach, relying on forecasts, schedulesconsistently fewer movies than it “considers,” consis-tent with the normative optimal policy in §3.1.2, whichrelies on ex post information. Although a schedule isgenerated for all eight weeks within a time window, itis really the first-week recommendation that is usedfor weekly decision making. We term the schedule ob-tained by stacking the first-week recommendation ofall time windows as the actual implied schedule.17 Theactual implied schedule compiled from the first 20 timewindows of the adaptive scheduling approach consid-ering the cut-off value of two weeks for bidding isgiven in Table 4B.

The actual implied schedule results derived in anintegrated manner are quite similar to the optimalschedule results derived in a one-shot manner for the20 weeks planning horizon.18 We find that when thecut-off criterion for bidding is two weeks (i.e., a highdegree of precommitment by bidding), 43% of the es-timated optimal (ex post data-based) profit improve-ment is retained; when the cut-off criterion is sixweeks(i.e., a low degree of precommitment), 90% of the op-timal profit improvement is retained. Thus, the valueof using our modeling approach in an adaptive frame-work depends upon the quality of revenue estimatesavailable to the management and the degree of adapt-ability retained in the system.

To summarize, in this section we presented an in-tegrated two-tier application of our model. The firsttier generates choices of the movies for bidding, whichare then used in the second tier, an adaptive approachfor the in-season weekly scheduling. In both cases, we

17We must emphasize here that this schedule is arrived at using nohindsight revenue data.18A difference is that there are a few movies that are scheduled forone week because we do not impose obligation period restrictionfrom one week to another in constructing the actual implied sched-ule.



use minimal information that is available to the exhib-itor at a decision point. Our results show that the min-imal information based integrated schedulesmimic thepolicy recommendations and can achieve a level of im-provement of the same order from a hindsight basedoptimization. The approaches are quite general in thatthey can incorporate a sophisticated demand predic-tion model, managerial judgments, or a combinationof both. In the next section, we examine another intu-itive decision rule (heuristic) that is consistent with thereality of the film business environment.

3.3. Relationship Dilemmas

3.3.1. Motivation. The decision rule considered inthis section is called distributors’ pressure heuristic torepresent the channel relationship dilemmas that someexhibitors face in the real world. This heuristic consid-ers the case of an exhibitor who acts under a lot ofpressure from the distributors to schedule their mov-ies, perhaps to maintain good relations with them.Such a manager may use the decision rule: Each week,if a new movie becomes available, to maintain a good rela-tionship with the distributor, I will replace my weakest ofthe existing movies that are not in their obligation periodswith the new movie. If more than one new movie becomeavailable in a week, then I will consider the next to the weak-est existing movie applying the same criterion as before, andso on. Notice that the manager following this heuristictries to accommodate the new movies released by all19

the distributors as long as he/she has “space” to showthem. However, with some element of smartness in thedecisions, the exhibitor replaces only his/her worstperforming movies (in terms of expected revenue) atany decision point.

3.3.2. Analysis and Results. To abstract from is-sues relating to forecasting, under this scenario wenow return to the assumptions of §3.1.2. That is, weuse the ex post (hindsight) data used in the optimalrestricted set approach. This level is representative ofthe cases in which the manager has access to a sophis-ticated system that produces “perfect” informationabout the revenue of a movie.20

19“All” could be replaced by “the most favored” distributors.20Though we generate the revenue data set being used before arriv-

The results obtained from the application of thisheuristic are presented in the last column of Table 3.The exhibitor following the distributors’ pressure heu-ristic performs much worse on the profitability crite-rion (relative to the optimal case).21 The decrease inprofit results generally from a huge proportion of themovies that are scheduled for shorter play lengths, thatis, in the opposite direction to that suggested by theoptimal policy. On the other hand, the manager comesclose to the actual case in profit terms. Given that thetotal number of movies scheduled under the maintain-ing good relationship heuristic are equal to those inthe actual case, these results are interesting becausethey provide a possible explanation to the short aver-age play lengths by the manager in the actual case. Inother words, perhaps the 84th St. Sixplex manager waspredisposed to show the 43 movies of all the distrib-utors he/she had good relations with, and, therefore,quickly replaced the already playing movies in manyinstances.

In summary, our results show that the level of prof-itability that a manager might achieve in an applicationsetting depends importantly on the quality of infor-mation and a good scheduling algorithm that takes along-term view into account. We find that if the re-placement rule is ad hoc, then even good informationcannot bring extra value to the manager, as exempli-fied by the distributor pressure heuristic with ex postinformation.

4. Conclusion: Discussion,Limitations, and Future Research

Like other retail space allocation decisions, the choiceof which movies to schedule in a theater is a complexone, involving trade-offs among numerous alterna-tives and with implications for both current and future

ing at the schedules, the heuristic is applied as if the manager knowsthe data corresponding to a decision point only at that decisionpoint. Thus, this is a myopic heuristic, which does not take into ac-count the future realizations of revenues.21Though the scheduling decisions are arrived at following the dis-tributors’ pressure heuristic, the profit calculations are based on thecombination of ex post actual revenue data and the two-parameterexponential prediction model of optimal restricted set approach.



profits. The movie industry poses some particularlychallenging opportunities for managers (and for mod-elers) as new products are introduced every week, andthe attractiveness of existing products decays system-atically and usually rapidly over time. Moreover, con-tract terms are complex and designed in ways to favorthe distributors, making the choice of the most profit-able set of movies to schedule difficult for the exhibi-tors. Using an integer programming model, the specialstructure of the underlying problem, an analogousproduction scheduling problem, and a powerful, butreadily available, mathematical programming lan-guage, we are able to structure the exhibitor’s problemand investigate different types of managerial behaviorwith various kinds of available information.

4.1. Managerial ImpactUsing the most representative data, SilverScreener ap-pears to lead to a 37.7% improvement in profit whenthe exhibitor is restricted to the movies actually sched-uled. We further presented an integrated two-tier ap-plication of our model to show how a manager mightuse our model. Using no hindsight data, the applica-tion shows that the implementation of our model hasthe potential to significantly improve managerial de-cision making. In a real world application, the systemcould benefit even more from additional inputs froman experienced manager. Finally, we studied a behav-ioral heuristic, which shows that no matter how goodthe information is, the exhibitor could lose money if he/she tries to please all the distributors in the market. Thislends further support to our normative policy that theexhibitors need to be more selective about their sched-uling decisions and should run their movies longer in-stead of replacing them quickly.

Besides the benefits of the model discussed in its ap-plications, the model also offers other potential man-agerial gains. For example, the model can be used as ascenario analysis tool. Using themodel, themanager canexamine the impact of different contract terms for thesame movie. A related managerial benefit from themodel is its availability as a marketing information sys-tem. The model can easily be adapted to provide a sum-mary of potential profits to be obtained from differentdistributors/movies. When compared with similar

data over previous seasons, these summaries can pro-vide a more concrete way of estimating the cost of hon-oring relationships with the distributors. Overall, themodel provides a more profitable way of schedulingmovies.

An important area of future research deals with theissues involved with the manager-model interface.How will the manager use the schedules suggested bythe model and how will this change over time? In thecase of ARTS PLAN, the manager extensively used theARTS PLAN model as it reduced uncertainty andsaved time, but the manager also made personalchoices in scheduling and revised model forecasts. Inthe movie industry, the theater owner has ongoing re-lationships with the distributors, and likely will notmake decisions on a single transaction basis. The avail-ability of the model both provides an optimal sched-ule, and an estimate of the value of honoring a rela-tionship as compared to making a more profitable, butperhaps short-term decision. Will such informationchange the nature of the relationship over time, andthe way decisions are made? It would also be intrigu-ing to examine the impact of contract terms on exhib-itor’s profitability and scheduling. Present contractingpractices were designed in an environment quite dif-ferent from the one existing now. Early results fromSwami et al. (1998) suggest that a win-win (distributor-exhibitor) situation could result under someconditions.

4.2. Model ExtensionsA limitation of the current research regards the issueof screen capacity,which is assumed equal in the currentformulation. The screen capacity is, of course, a criticalvariable to the problem formulation only if the de-mand of a movie exceeds screen capacity. Indeed, theprimary reason for the exhibitor to have differentscreen sizes is that the attendance varies for differentmovies and having different screen sizes increasesscheduling flexibility (while saving capital costs in theoriginal construction of the theater). The first major de-cision variable to be affected by different screen sizesis the multiple screenings (e.g., double booking) of amovie. This is usually done for blockbuster movieswhose demand is expected to exceed the capacity ofthe highest capacity screen. However, such movies are



rare in a season. The second variable is the allocationof movies on screens in the beginning and switchingmovies between screens later. A movie may beswitched from a higher to a lower capacity screen be-cause of its depleting demand and the availability of amore attractive movie for the higher capacity screen.The opposite case may also occur sometimes (althoughinfrequently) when a movie’s demand builds by word-of-mouth in the later weeks.

The nonequal screen capacity issues could be ad-dressed by modifying the original formulation of theproblem as follows.22 First, a new binary variable, xjisw,which equals 1 if movie j is shown for iweeks on screens starting in week w, and 0 otherwise, needs to be de-fined. The corresponding profit, Pjisw, depends on thevariable GROSSju (see Equation (1)), that is, the rele-vant box-office gross revenue, which would have to bemodeled differently for the different capacity case. Inthis case, it would have to be recast as min (MAXs,GROSSju), where MAXs is the maximum weekly reve-nue any movie can earn on screen s if that screeningroom is filled to its capacity.23 Different sets of con-straints would be needed to ensure the following con-ditions: (1) obligation periods of all the scheduledmovies are met; (2) a movie, if scheduled, is shownonly in consecutive weeks (i.e., no job splitting); (3) thetotal number of movies scheduled in any week is lessthan, or equal to, the total number of screens in themultiplex; (4) only one movie is scheduled on a givenscreen in a given week; and (5) a movie, if scheduled,is not shown on more than one screen in a given week.Finally, the release and due date constraints could alsobe added for the generality of the model. It is evidentthat the above formulation would be quite complex.24

22Algorithms to solve parallel machines with unequal capacityscheduling problems depend upon the characteristics of the partic-ular problem and usually involve heuristic or near optimal ap-proaches (Sawik 1982, Pinedo 1984, Pinedo and Shaw 1992).23In our empirical application, we do not have information availableon the MAXS variable.24Since capacity in the movie exhibition context can be operational-ized as number of seats available per week or maximum number oftickets that can be sold per week, a heuristic approach to addressthe nonequal seats available in various screening rooms is to equal-ize them implicitly by assuming that the number of shows per weekin the rooms with lower capacity can be increased proportionally.

In practice, however, it appears that switching betweenscreens is mainly decided on the basis of the rank-ordering of the movies. Thus, the different screen ca-pacity related decisions seem to follow the decisionabout “which-movies-to-show.” Moreover, in the ab-sence of the right kind of data for empirical applica-tion, we find that the equal capacity screens assump-tion, which provides “which-movies-to-show” and“how-long-to-play-them” solutions, gives us a reason-able starting point for the current problem.

The current research can be extended to address thecompetitive issues from a strategic viewpoint. For ex-ample, a theater’s bidding strategy for a film might beaffected by the anticipated competitive behavior of theother theaters.25 At a consumer level, to examine thepossibility, if any, of the effect of the competitive be-havior on demand, let us consider a two-theater (A andB) situation. The demand of a movie at theater A maybe different for the cases when both A and B are play-ing the movie than when only A is playing it, if A andB are sufficiently close in distance. At a national level,Krider and Weinberg (1998) have developed game the-oretic equilibrium strategies for motion picture releasetiming. Incorporating such an approach into a multi-plex owner’s weekly decision making would be a chal-lenging task. If the exhibitor has an estimate of sucheffects on demand, either subjectively or based onsome historical database, then availability of theSilverScreener model as a scenario analysis tool mayhelp the exhibitor examine the effect of competition onprofitability. While the above strategic competitive is-sues pose some interesting future research questions,they do not fit in the decision support objectives of the

For example, if two screens are available, one with 200 seats and theother with 400 seats, the problem can be “equalized” by increasingthe number of play times in the first screen by a factor of two. Oncethe problem is solved as originally formulated, in a second step, theexhibitor can solve in a relatively straightforward manner, usingcost/benefit analysis, the problem of assigning movies to screensand determining the number of times movies should be shown perweek.25To some extent, ownership of exhibitors by motion picture studios(e.g., Sony Pictures now owns Cineplex-Odeon and Loews theaters)limits the extent of competition.



current study. Moreover, from an empirical stand-point, it appears difficult to predict the impact of com-petition on demand parameters. In sum, therefore, weimplicitly assume that the competitive effects, if theyexist, are summarized in demand parameters or affectrandomly the error term in the demand function, andleave to future research the incorporation of competi-tive effects on demand.

In conclusion, in this paper we present a mathemat-ical model, SilverScreener, which is aimed at helpingexhibition managers make better decisions in a com-plex environment. An integrated 2-tier application ofthe model, involving movie selection plans and adap-tive scheduling approaches, shows how the modelcould assist the multiplex exhibitors in making prof-itable scheduling decisions. At a broad level, ourmodel would benefit managers in two different ways.One is by helping the managers improve their biddingand scheduling techniques. That is, the model couldhelp the manager adopt a new decision-making stylewhich is based on an analytical approach. The secondis by helping the manager perform the same schedul-ing task in a more efficient way. The availability of acomputer-based algorithm may automate part of thescheduling process and help save management’s time.This benefit would be especially valuable for the man-agers of theater chains who have to make such sched-uling decisions for a number of theaters on a regularbasis.26

Appendix 1: Revenue Prediction Scheme forMaster Plan Development

Description of Estimation DataAssuming that a typical manager has access to at least as much his-torical data as those that appear in Variety, we propose an ex anterevenue prediction scheme, which uses the previous year’s data togenerate revenue estimates of forthcoming movies. It is clear thatthis scheme does not suffer from any hindsight effects. In the biddingplan stage, we use the same movie consideration set as that for theoptimal restricted set. In generating revenue estimates for 1989 in

26This work was supported in part by grants from the Social Sciencesand Humanities Research Council of Canada and was begun whileJehoshua Eliashberg was a Visiting Scholar at the University of Brit-ish Columbia. The authors thank the three anonymous reviewers,the area editor and editor ofMarketing Science, David Williams, andEunkyu Lee for their helpful comments.

our bidding plan example, we use the data from 84th St. Sixplex forthe year 1988 for the corresponding season of 27 weeks.27

Demand ModelWe use the two-parameter exponential model for revenue predic-tion, which is the same as the demand equation presented in §2 andis restated here for convenience:

bw��jGROSS � � e , (2)jw j

where GROSSjw denotes box-office gross revenue of Movie j in Weekw of the movie’s run (w � 0, 1, 2, . . .), �j � 0 and bj � 0 are openingand decay factors respectively of movie j and � � normal (0, r2). Ouruse of the term revenue prediction implies estimation of � and b fordifferent movies. Alternatively, a manager can use some other rev-enue prediction model depending on the level of sophistication re-quired for the manager’s situation. A simple model could be in termsof percentage declines. For example, a manager might say, “I expectMovie X to open at a and decline at b% every week.” It is clear thatwe capture open and decline by � and b, respectively, in our estima-tion scheme. The revenue data of 1988 movies were collected to es-timate � and b’s (using Equation (2) for the corresponding moviesof the Summer season of 1989).28

Movies Classification ProcedureWe collect data on some key attributes (to be described later) of both1988 and 1989 movies. The objective of this data collection procedureis to classify the movies according to these variables. We use a genre-based approach for classification purposes. Once such a classificationis done, we can predict the revenue for a 1989 movie with certainattributes by “matching” the movie with similar movies from 1988.By collecting the relevant data and matching it with the previousyear’s movies, we attempt to mimic the managerial behavior of thefollowing type: When faced with a new movie, the manager says, “Lastyear, the movies of this type generated X dollars on average in their firstweek, and dropped by Y percent every week on average. Therefore, I expectthis movie to open at X and drop at the rate of Y every week.”29

AttributesThe first attribute is the genre of the movie. We include the followinggenres in our analysis: Action, Comedy, Drama, Horror, Crime, andScience Fiction. The second attribute, MPAA Rating, captured theMotion Picture of America Association’s (MPAA) classification ofthe movie as R, PG, or PG-13. The Sequel attribute (Yes/No variable)indicates whether the movie was a sequel or not. We used the Block-buster Entertainment Guide (Castell 1996) to gather data on the abovevariables. The fourth attribute, Stars (Yes/No variable), indicates

27Though a few data used for estimation are from the years preced-ing 1988 (e.g., in case of sequels), most of the prediction data areused from the year 1988.28We collected data on 44 movies of the 1988 season, similar to 43from the 1989 season. We also collected data for a few movies from1987.29Notice that since the year-to-year variations would be fixed acrossall movies, they would not affect the schedule generation process.



whether the movie included major stars (as classified by Quigley’sMotion Picture Almanac; see Klain 1990) or not. Finally, theDistributorattribute (Yes/No variable) indicates whether the movie was beingdistributed by a major distributor or not. The following distributorsare recognized as major distributors: Warner Brothers, TriStar,Touchstone, Buena Vista, Walt Disney, Paramount, and United Art-ists. Notice that the above five attributes of a movie can be collectedex ante and are assumed to be known to the exhibitor at the time ofreceiving the bid invitation letter.

Estimation of Demand ParametersWe estimate the two parameters of the demand model for the vari-ous movies of 1989 using the corresponding 1988 movie estimates.The following scheme applies to all the movies that are neither block-busters (e.g., Indiana Jones) nor sequels (e.g., Lethal Weapon II):

1) If, for any 1989 movie, there is a unique corresponding 1988movie (i.e., matches on all five attributes and is the only suchmovie),then we use the � and b of that movie as estimates of the 1989 movie.

2) If there are multiple movies from 1988 that match on all fiveattributes, then we use the average of � and b’s of all such moviesas estimates of the 1989 movie.

3) If there is no movie from 1988 that matches the 1989 movie onall five attributes, then we examine whether there are movies in 1988data that match on the next four attributes (including Genre andMPAA) and use the relevant averages of their estimates. If not, thenwe match on the next three variables, and proceed similarly as be-fore. We therefore adopt a stepped approach and match the moviesnext on Genre and MPAA, then on Genre alone, and use the relevantaverages.

4) Finally, if there is no movie in 1988 data set that matches the1989 movie even on genre, then we use averages of all the moviesin 1988 data set.30 In this case, we envision the manager as saying,“Faced with a completely different movie about which I have nospecific classifying information, I’ll use the estimates that are basedon all the movies in my last year’s information set.”

The following scheme is used for blockbuster movies, that is, thosemovies that involve huge production budgets, and are supported byheavy upfront advertising (e.g., Jurassic Park, Independence Day, orTitanic in recent years). It is therefore easy to see that in the 1989data set for the 84th St. Sixplex, only Batman and Indiana Jones canbe treated as blockbusters. This is also reflected in their longer playlengths and double booking status in the actual schedule. For theblockbuster movies of 1989, we choose as their estimates the maxi-mum � and minimum b (assuming a negative value of b) of all themovies from 1988. In this case, therefore, the manager uses the fol-lowing rule, “Since these are blockbuster movies, I expect them toopen like the movie with the best opening last year, and sustain likethe movie with the strongest legs (i.e., minimum decay rate) from lastyear.”

30This occurs for the movie SING that has Music as its Genre ac-cording to the Blockbuster Entertainment Guide (Castell 1996).

For a sequel movie, we use as its estimates the � and b of its im-mediate predecessor from the most recent previous year. The pre-decessors of Friday the 13th Part VIII and A Nightmare on Elm St. 5are available from 1988 data. We use 1987 data for the estimates ofLicense to Kill and Lethal Weapon II. The estimates of some movies arenot available under this scheme because either the movie was notplayed by the theater, or the predecessor was released more thantwo years ago. In such cases, their estimates are based on their Genretype attributes.

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