The Pennsylvania State University

The Graduate School

Department of Industrial and Manufacturing Engineering

DEVELOPMENT OF OPERATIONAL STRATEGIES FOR AN ON-DEMAND FOOD

DELIVERY SYSTEM IN HEALTH CARE

A Thesis in

Industrial Engineering and Operations Research

by

Caitlin Cronk

2012 Caitlin Cronk

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2012

The thesis of Caitlin Cronk was reviewed and approved* by the following:

Deborah J. Medeiros

Associate Professor of Industrial Engineering

Thesis Advisor

Jack C. Hayya

Professor Emeritus of Supply Chain and Information Systems

Paul Griffin

Professor of Industrial Engineering

Head of the Harold and Inge Marcus Department of Industrial and Manufacturing

Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

As hospitals strive to improve measures of service for patients under their care, every

element of the patient care process is examined for opportunities to improve the quality of care

and the presence of a patient-centered approach. Some hospitals have implemented an “on-

demand” style food service system in an effort to be more patient-centric. This system allows

patients to order from a menu and have it delivered to their room, much like a hotel room service

system. Geisinger Medical Center, in Danville PA, is among the hospitals looking to improve

their inpatient food service to better meet the needs of patients by implementing such an on-

demand delivery style system.

This research develops operational recommendations for an on-demand food delivery

system for the inpatients at Geisinger Medical Center. The recommendations made will allow the

system to achieve service level standards set by Geisinger’s Guest Service management team.

Specifically, several combinations of meal delivery cart capacities and dispatching strategies were

analyzed for effectiveness with the use of a discrete event simulation model. The model captures

all material handling and routing throughout the Geisinger Medical Center facility and was used

to understand how different delivery strategies affect operational performance and service levels.

To reduce the percent of meals delivered late, more resources will be required, however,

they will not necessarily be utilized efficiently. The operational strategy that allowed for the best

balance between resource utilization and patient service levels used twelve-tray delivery carts,

and a dispatch timer setting of ten minutes, provided the meal preparation required less than

fifteen minutes. This policy suggests that approximately 94.3% of patients will receive their

meals within 45 minutes of placing an order. The results also provide an expectation for the

number of carts needed, as well as information to assist planning for host staffing levels

depending on the operational policy chosen.

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TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................................. vi

LIST OF TABLES ................................................................................................................... vii

ACKNOWLEDGEMENTS ..................................................................................................... viii

Chapter 1 Introduction ............................................................................................................. 1

1.1 Motivation .................................................................................................................. 1 1.2 Scope .......................................................................................................................... 1 1.3 Objectives................................................................................................................... 2 1.4 Organization ............................................................................................................... 2

Chapter 2 Literature Review .................................................................................................... 4

2.1 Current Hospital Food Service Practices ................................................................... 4 2.1.1 Quality considerations in food service ............................................................ 4 2.1.2 The restaurant style system ............................................................................. 5

2.2 The Vehicle Routing Problem .................................................................................... 7 2.2.1 Capacitated vehicle routing problem ............................................................... 7 2.2.3 Vehicle routing problem with time windows .................................................. 8 2.2.4 Vehicle routing problem with time windows and multiple trips ..................... 9 2.2.5 Stochastic vehicle routing problem ................................................................. 10

2.3 The Pickup and Delivery Problem ............................................................................. 13 2.3.1 1-M-1 pickup and delivery problem ................................................................ 13 2.3.2 A tabu search algorithm for VRP with backhauls ........................................... 15

2.4 Order Batching ........................................................................................................... 17 2.4.1 A GA-based order batching method ................................................................ 18

Chapter 3 Model Development ................................................................................................ 21

3.1 Introduction ................................................................................................................ 21 3.2 System Description .................................................................................................... 21

3.2.1 Meal order arrival process ............................................................................... 22 3.2.2 Meal delivery process ...................................................................................... 23

3.3 Modeling Approach ................................................................................................... 26 3.3.1 Modeling assumptions ..................................................................................... 28

Chapter 4 Analysis of Results .................................................................................................. 30

4.1 Introduction ................................................................................................................ 30 4.2 Experimental Plan ...................................................................................................... 30

4.2.1 Performance Measures .................................................................................... 30 4.2.2 Experimental design ........................................................................................ 33

4.3 Results ........................................................................................................................ 34 4.4 System Limitations .................................................................................................... 39 4.5 Recommendations ...................................................................................................... 40

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Chapter 5 Conclusions and Future Research ........................................................................... 42

References ................................................................................................................................ 44

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LIST OF FIGURES

Figure 1. Illustration of Double Path Solution to VRPB, (Berbeglia et al. 2007).................... 14

Figure 2. Food Order Arrival Logic ......................................................................................... 23

Figure 3. Food Cart Routing Logic .......................................................................................... 25

Figure 4. Simul8 Modeling Environment ................................................................................ 27

Figure 5. Food Service Logic Modules .................................................................................... 27

Figure 6. Resource Performance Measures Plot for Twelve Tray Cart Scenarios ................... 36

Figure 7. Service Performance Measures Plot for Twelve Tray Cart Scenarios...................... 37

Figure 8. Cart Usage Profile Plot for each Twelve Tray Cart Scenario ................................... 38

Figure 9. Average Number of Carts in Use throughout a Day for all Twelve Tray Cart

Options ............................................................................................................................. 39

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LIST OF TABLES

Table 4-1. List of System Performance Measures (bold measures represent key

performance measures) .................................................................................................... 32

Table 4-2. Experimental Scenarios .......................................................................................... 33

Table 4-3. Experimental Results .............................................................................................. 34

Table 4-4. Average Number of Carts Filled to Capacity for Each Scenario ............................ 36

viii

ACKNOWLEDGEMENTS

I would like to thank, Dr. Deborah Medeiros for her support and guidance. She has been

not only a good thesis advisor, but also a great teacher and mentor to me throughout my time in

graduate school. In addition, I would like to thank Dr. Jack Hayya for the input he provided to

improve this document, as well as Seth Hostetler for his time and patience in helping me to learn

Simul8, and for acting as a great resource and sounding board throughout the duration of my

research work.

I would also like to thank the Supply Chain and Guest Services groups at Geisinger

Medical Center for providing me the opportunity to work with them on my thesis research. The

practical experience I gained by working with a top performing innovative hospital has proven to

be invaluable.

Finally I would like to thank my friends and family for their never-ending support in my

academic ventures. My family for continually encouraging me through the years, and my friends

for making sure I had fun along the way.

Chapter 1

Introduction

1.1 Motivation

This research is motivated by the growing interest in improving patient services within a

hospital environment. Food services are one additional element of caregiving which can be

examined for ways to improve a patient-centered experience. In an effort to enhance its food

service to inpatients, Geisinger Medical Center (GMC) is working to develop an on-demand food

delivery system that will allow for more flexibility in meal choices and delivery times.

The implementation of such an on-demand style food delivery system will require an

understanding of the strategic operational changes required to transition from their currently

utilized traditional food service system. Resource usage may require shifts in size and schedule,

and strategies for routing the food deliveries will likely change. Specifically, it is important to

consider questions, such as how to group orders together, how many delivery carts should be

used, or how long a partially filled cart should wait for additional meals before commencing

delivery.

1.2 Scope

Geisinger Medical Center is currently in the process of developing a discrete event

simulation model to capture all material handling throughout the facility. This research

capitalizes on the opportunity to include food delivery operations in the overall model and

analyze how to best structure operational policies while considering the facility layout as well as

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traffic and routing challenges. Using the simulation model, several food delivery cart capacities

and order batching strategies will be tested and analyzed for their effect on customer service

levels. The results of the analysis will yield recommendations for management regarding the best

strategies to achieve high patient service levels.

Whereas the modeling and analysis pertaining to this research is specific to GMC’s

inpatient system characteristics, the approach is one that can be applied to any hospital looking to

implement an on-demand food delivery system within their inpatient units. Therefore, this

research provides the opportunity for the generalization of modeling and quantitative analytical

techniques used to evaluate such operational strategies.

1.3 Objectives

The goal of this research is to develop and analyze operational policies of on-demand

distribution of food to inpatients at Geisinger Medical Center in Danville, PA. Specifically, it

will aim to provide recommended resource requirements and routing strategies to allow for the

achievement of high patient service levels. The objectives will be approached by simulating and

analyzing the various operational strategies in a discrete event simulation model representing the

food delivery process at GMC.

1.4 Organization

Chapter 2 provides a literature review of relevant research topics in the areas of hospital

food delivery, vehicle routing algorithms, pickup and delivery algorithms, and batching

strategies. Chapter 3 includes a description of the system parameters and constraints, as well as

data used for modeling and evaluation. This chapter also discusses the modeling approach used

3

to represent the food delivery system in a discrete event simulation. Chapter 4 contains the

experimentation methodology used to evaluate the scenarios. Results of the evaluation will also

be provided in this chapter, followed by recommendations for successful implementation of an

efficient on-demand food delivery model. Finally, Chapter 5 will provide a summary of

conclusions and will outline opportunities for future work.

Chapter 2

Literature Review

2.1 Current Hospital Food Service Practices

There are two predominant methods used by hospital food service providers to distribute

food to inpatients, the conventional method (often referred to as “plated”) and the cook-chill

method. In the conventional system, food is prepared hot and immediately served to patients [1].

In the cook-chill system, food can be prepared in advance, chilled, and then reheated just before it

is served to the patients. A third method, referred to as “hotel-style room service,” has been

introduced into hospital systems and studied for its effect on patient satisfaction [2] [3]. In 2000,

a survey conducted on current and future hospital food service trends found the conventional

method to be used in 81% of the 200 US hospitals surveyed. Reheating methods, such as the

cook-chill system, were found to be used in 6% of hospitals where the food is heated in the

kitchen, and 8% where the food is heated in the galleys [4]. The survey does not mention the use

of a hotel style delivery system, suggesting that it is either relatively new or uncommonly used in

US hospital systems.

2.1.1 Quality considerations in food service

There have been various studies examining the impact of food service delivery methods

on quality indicators of inpatient food. The common quality indicators studied in the surveys

include: cost, temperature, texture, menu style, and flavor. One study found that a “bulk trolley”

system, where food was served from a portable heated system, resulted in improved texture of all

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foods, more acceptable temperatures for some and better flavor for other foods, when compared

with the conventional “plated” system [5]. In contrast however, Mibey and Williams (2002) state

that research has shown that a central plating system, found in the conventional meal delivery

method, allows for better portion control, food quality, and diet monitoring.

Cook-chill systems, which can either be used to serve food in a bulk or plated method,

have been evaluated on common quality indicators as well. This system has been found to have

conflicting ratings. While managers have been found to be more satisfied with the conventional

system because of the perceived improvement in texture, food quality, and a reduction of

leftovers, they noted an improvement with the cook-chill system on measures of cost, waste,

labor utilization, and space [6] [7].

The effect of cook-chill versus conventional systems on labor utilization has been

disputed by several researchers in the field. In a study conducted on the food service trends in

New South Wales hospitals, researchers found that a cook-chill system allowed for a higher beds-

to-fulltime employee ratio. This, however, was noted by Mibey and Willams (2002) to be a

considerably “crude” indicator of resource utilization, which is further supported by their claim

that other researchers have found contradicting results. Additionally, Assaf et al. noted a similar

controversy of the notion of reduced skill requirements necessary in the cook-chill method [6].

Therefore, the measure of productivity in terms of employee utilization and skill requirements

cannot be considered a high priority quality indicator.

2.1.2 The restaurant style system

The restaurant style system (also referred to as hotel-style room service) has been found

to provide significant benefits to the patient. In this system, the patients are presented with more

options at meal time, have the ability to receive food at their personally preferred time, and can

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order their meal much closer to the time of consumption when compared with more traditional

systems [1]. A study focused on the pediatric oncology patients found that providing a restaurant

style food delivery system to the patients resulted in an improvement of dietary and caloric

intake, along with an increase in patient satisfaction. The study also found that the restaurant

style service increased the efficiency of the meal delivery system because patients were ordering

fewer times per day, but consuming more of the food at each meal [2]. These results suggest that

not only can this new approach to hospital food delivery support faster patient recovery, but can

also potentially allow for reduced food waste in the system and increase patient satisfaction.

Whereas the restaurant style delivery method presents many appealing attributes with

respect to improvement opportunities, the system also presents a few challenges. Of primary

concern is the time constraint placed on the delivery method. In the restaurant style delivery,

food leaves the kitchen hot and fresh and must be delivered to the patient within a tight time

constraint. Thirty to forty-five minutes was considered in one study to be the acceptable amount

of time between preparation and patient delivery [3]. This time limit presents a demanding

constraint on the system, as the size of the hospital layout and the number of inpatients to be

served grows. Along with time constraints, cost was presented as an additional issue with the

implementation of the restaurant style method. In a study surrounding best practices in hotel-

style inpatient meal service, one researcher found that an increased number of personnel were

required to effectively carry out the hotel-style system, adding to the cost of the food services

operation [3]. The study however does not mention any efforts taken to optimize the delivery

system, which could potentially reduce the cost of required resources.

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2.2 The Vehicle Routing Problem

The vehicle routing problem (VRP) can generally be represented in the form of a graph,

where vertices act as customer locations, and the arcs between them represent travel routes. One

vertex serves as a “depot”, where vehicles will originate from and return to after their route. The

goal is for each customer to be visited by one vehicle, one time, in such a way that associated

travel times, cost, and distance can be minimized. The problem is classified as NP-hard, and

therefore, heuristics are used to search for optimal solution strategies [8]. Furthermore, additional

constraints are commonly introduced into the general VRP, such as vehicle capacity constraints,

route duration constraints, or time window constraints [9]. Each of these additional constraints

has led to the creation of several classifications of the original VRP. Those related to the on-

demand food delivery problem are discussed in this section.

2.2.1 Capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP) extends the basic VRP by placing a

maximum allowable load on each vehicle [10]. The CVRP has been characterized by the

combination of two classic problems: the traveling salesman problem (TSP) and the Bin Packing

Problem [11] [12]. In the TSP, the objective is to find a route which can be executed in one tour

and reaches all customers in the shortest distance possible [13]. When applied to the CVRP, each

vehicle will use the TSP to find a route optimal to its assigned customers [14]. The Bin Packing

Problem seeks to find the minimum number of bins or carts required to handle a given capacity

[12]. Like the VRP, the Bin Packing Problem and TSP are considered NP-hard. By combining

techniques used to solve these two sub-problems, strategies have been developed to address the

challenges associated with the CVRP.

8

Among the heuristics used to address the CVRP, global search heuristics have been

applied frequently. Specifically, evolutionary computation methods, such as particle swarm

optimization, genetic algorithms, and ant colony optimization, have been found to provide near

optimal solutions to the CVRP [15]. One challenge to consider when using such methods is

developing an effective framework to represent the solution space in the algorithm. One must

consider how to represent a route plan as a solution, how to handle infeasible solutions, as well as

how to represent the objective function to be solved by the algorithm [14].

2.2.3 Vehicle routing problem with time windows

A second well known version of the vehicle routing problem is the vehicle routing

problem with time windows (VRPTW). The problem constrains the time period during which a

delivery to a customer can be made. The earliest and latest times considered acceptable for

delivery to a customer make up the delivery time window [8]. In practice, this is an important

aspect to consider because not only do late deliveries cause problems, but deliveries made too

early can pose challenges as well. For example, a delivery may arrive to a store before the store

is open. This will then force the resources to wait until the store is open and able to accept the

goods. Therefore, an important aspect of this problem is the inclusion of the cost of waiting time

in an early delivery, along with the cost of service time for unloading the goods. In the problem

space, this temporal cost is included with the travel distance cost found in the traditional VRP

[16] [8].

There have been several algorithms proposed for addressing the VRPTW. Due to the

NP-hard nature of the problem, many of the proposed solutions are approximation heuristics. In

his paper, Solomon reflects on many of the well-known heuristics developed to solve the VRP.

Among these heuristics are “tour-building” algorithms, “insertion” algorithms, and also a

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“savings” heuristic. Solomon also describes a significant characteristic which distinguishes the

mechanism of these algorithms: whether they develop solutions sequentially or in parallel. A

sequential algorithm will build one route at a time, iteratively adding additional customers onto a

route, provided the addition results in a feasible routing. The feasibility is determined based on

constraints such as the capacity of the vehicle, the distance from the previous customer, and of

course, the time window requirement of the customers. A parallel algorithm will construct

multiple routes simultaneously and then adjust the structure to improve the overall performance

[8].

2.2.4 Vehicle routing problem with time windows and multiple trips

A further variation of VRPTW discussed in the literature is the incorporation of the

ability for a vehicle to perform multiple tours in one solution. This VRP extension is known as

the “minimum multiple trip VRP” or MMTVRP. The objective of the MMTVRP is to minimize

the number of multiple routes required by a fleet of vehicles. Solving this problem will also

result in minimizing the size of the fleet [17]. This is a very practical problem as delivery

vehicles will often make a delivery and return to the depot for a second round of deliveries in a

given planning period [16]. The problem is also useful in practical applications because of its

ability to address the need for a limited number of vehicles to deliver a large demand, or when

tight time window restrictions are placed on the demand. This is especially relevant in problems

involving the delivery of prepared food, where time restrictions will be of high concern, and

multiple short trips are taken in a given delivery period. The use of a vehicle for multiple routes

may reduce the investment for delivery resources, however, it may also further constrain the

solution space [17].

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The MMTVRP can be solved by decomposition. Battarra et al. (2009) describe the efforts

of multiple researchers who have decomposed the problem into two parts. The first part solves a

general VRP using techniques such as a savings-based algorithm or a global search heuristic. The

second part then assigns multiple routes to a vehicle by modeling the problem after a bin packing

problem. This approach is similar to the approach discussed above with regard to the capacitated

VRP.

When combined with the VRPTW, the problem becomes known as the “vehicle routing

problem with time windows and multiple routes” or MVRPTW [16]. Battarra et al. (2009)

applied this problem in the context of delivering goods from a central depot to several

supermarkets and hypermarkets within specified time window constraints. As with the general

VRPTW, they approached the problem through decomposition; first they used an insertion

heuristic to devise feasible routes for the vehicles and then they used a bin packing problem to

aggregate the routes among a limited number of vehicles. To further enhance the effectiveness of

this approach, they utilized a “guidance mechanism” aimed at improving the creation of the initial

set of routes to allow for more effective aggregation in terms of minimizing the number of trips

necessary and reducing the time required by a vehicle. Although other studies have developed

exact algorithms for the solution of a such a problem, the intractable nature of many realistically-

sized problems will likely favor the relatively efficient near-optimal approaches which use

heuristics [18] [16].

2.2.5 Stochastic vehicle routing problem

The traditional VRP considers the fulfillment of deterministic customer demands. An

extension of this problem, which is perhaps more realistic, incorporates stochasticity into the

demands of customers. This VRP is referred to as the Stochastic VRP (SVRP), or the

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Probabilistic VRP (PVRP). The extension is often incorporated with others, such as the

capacitated VRP or VRP with time constraints. The prominent challenge of handling stochastic

demands involves effective decision making surrounding the scheduling and adjustment of routes

to accommodate changes in demand on a periodic basis.

There are three factors that can be influenced by stochasticity in the SVRP. The first is

stochastic customers, the second is stochastic demands, and the third involves stochastic timing.

In the first, the presence or absence of a customer is a random variable, while the demand, in

terms of quantity is considered deterministic. In the second, the quantity of demand for each

customer is the random variable [9]. These two random variables can also occur together in a

SVRP. Both types of problems must consider the capacity of the vehicle used and often require

return trips to the depot to accommodate the demand uncertainty. The third factor influenced by

stochasticity reflects the variable nature of service and travel times throughout the route [19].

These times may have a significant effect on the service level and time constraints of a VRP.

There are three prominent strategies to address the presence of stochastic demands in this

VRP as described by Benton and Rossetti (1992). The first strategy uses a set of fixed routes

determined in an a priori fashion to minimize the total travel cost. These fixed routes may either

be designed using the maximum expected demand in a given period or the expected non-zero

demand in a period. The cost of this strategy is determined using the a priori routing cost, along

with the cost associated with the probability of exceeding capacity on the fixed route. The

objective when solving this problem is to minimize the cost of exceeding vehicle capacity. The

second strategy creates a fixed a priori route as in the first strategy, and then modifies the route by

removing any stops in which the customer demand is zero. The authors refer to this method as

the “modified-fixed routes alternative.” The third strategy is different from the first two in that it

creates no fixed routes prior to the realization of customer demand. Rather, this method requires

the development of an efficient route for each period of demand. The authors refer to this method

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as the “variable routes alternative.” Although the routing of this method will be capable of

accommodating large variances in demand and may address issues related to capacity constraints,

the technological requirements and advanced management oversight needed may outweigh the

benefits of such a system. The three strategies discussed above are suggested as useful in

different scenarios of stochastic vehicle routing. When there is low likelihood that customer

demand will be zero, an a priori method may be more efficient. On the contrary, when there is a

high probability of zero demand by customers, it may be more appropriate to employ the variable

routes alternative [20]. In addition, the best choice of method may depend on when in the process

the demand information becomes available for use [9].

Laporte, Louveaux, and Van Hamme (2002) developed a methodology to address the

capacitated SVRP using recourse, referred to as the “L-shaped method.” The recourse policy

implemented in this strategy allows the vehicle to return to the depot at the point when capacity is

exceeded. The vehicle then returns to the point of failure and continues on its original path. One

important constraint introduced in their model requires that the expected total demand allocated

to a vehicle does not exceed the vehicle’s capacity. The objective of the algorithm is to minimize

the cost of the original planned route along with the cost associated with recourse. The original

route can be developed similar to that of the development of a deterministic VRP. The challenge

is presented in determining the cost of recourse [21].

Gendreau et al. (1996) introduce the use of “preventative breaks” strategically placed

along an a priori route. This strategy was suggested to allow the vehicle to return to the depot at a

point where it is likely to run out of capacity. At the point when the vehicle returns to the depot,

a re-optimization process may take place to improve the solution of the remaining stops on the

route. A challenge often noted with this type of strategy is the time required to re-optimize in the

midst of the service process. Some researchers suggest that it may be less costly to use a type of

a priori modified-fixed route schedule, as discussed above, to limit the complexity of the

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problem. These heuristic strategies have been found to be competitive with those of the

stochastic programming strategies that are capable of finding an exact solution (for a reasonable

problem size), but require a more significant computing cost [22].

2.3 The Pickup and Delivery Problem

The pickup and delivery problem (PDP) is a special version of the vehicle routing

problem. The problem can be characterized by a set of items that require pickup from a certain

location, followed by delivery at another specific location, [23]. The problem can be further

classified based on the number of distinct pickup locations as well as unique customer locations.

For example, the many-to-many problem (M-M) describes situations in which items may be

picked up from multiple locations and then delivered to multiple locations. By contrast, the one-

to-many-to-one problem (1-M-1) requires delivery items to originate from one central depot. The

items may then be delivered to customers at various locations. Items may also be picked up from

the customers at various locations and then returned to a central depot [24]. Reverse logistics is

often incorporated into the return of items from customers to the central depot. Due to the nature

of this research, the following section on pickup and delivery problems will be focused to the

subset of 1-M-1 problems.

2.3.1 1-M-1 pickup and delivery problem

In the food delivery application, 1-M-1 PDP could apply to the delivery of food from the

central kitchen to each patient unit, combined with the reverse logistics problem of picking up

empty patient trays and returning them to the central kitchen. There are two types of 1-M-1

problems: combined and single demand problems. In combined demands, customers may request

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both delivery and pickup of items, much like in a food distribution model. In single demand

problems, customers may only request either pickup or delivery of items [24]. These two types of

PDPs are each addressed by different types of routing strategies.

The 1-M-1 problems with combined demands have been addressed with various solution

models. Of particular interest is one developed by Berbeglia et al. (2007) referred to as the

“double-path solution.” In this solution, the vehicle visits each customer location for pickup

(delivery) of items. Once all customers have been visited, the vehicle will visit each customer a

second time for delivery (pickup) of the items. The last customer to be visited for the initial

pickup (delivery) will experience simultaneous pick-up and delivery and therefore will only be

visited one time in the solution route. All other customers will be visited twice in the solution

route. This problem is also referred to as the “1-M-1 PDP with Single Demands and Backhauls,”

or the “Vehicle routing problem with Backhauls” (VRPB). The solution can be visualized as a

cluster of nodes with a path spanning from the central depot through the different customer

locations, and ending at the farthest location. A second path then exists traveling in the opposite

direction as the first path. An illustration of the solution is shown in Figure 1.

Figure 1. Illustration of Double Path Solution to VRPB, (Berbeglia et al. 2007)

A significant challenge to solving the VRPB exists in the development of efficient

clusters of customers for service by one vehicle. Berbeglia et al. (2007) describe a number of

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heuristics used to solve the VRPB, including “cluster-first-route-second” and tabu search. The

authors also describe exact algorithms capable of handling a maximum of 100 customers and 12

vehicles.

2.3.2 A tabu search algorithm for VRP with backhauls

In an effort to create an efficient algorithm to address the VRPB, Brandão (2006)

developed and tested three variations of a tabu search algorithm aimed at solving and optimizing

routes containing both linehaul and backhaul customers. These algorithms focused on a specific

category of VRPB problems that require that linehaul customers are always served before any

backhaul customers in a given vehicle route. Additionally, there can be no routes with only

backhaul customers. The algorithms differed in one of two ways: either they differed in the

development of initial solutions used in creating a population for the tabu search algorithm, or

they differed in parameter settings of the tabu search algorithm.

The first variation is referred to as the TSA-Open because the initial solution is created

using a so-called “open initial solution” approach. In this approach, the linehaul and backhaul

customers are separated and addressed independently. The solutions are then joined together

using an approach dictated by what is called the Open VRP (OVRP). In the OVRP, it can be

assumed that at the end of a route, the vehicle does not need to return to the depot. Using this

assumption, it is possible to allow the last customer of a linehaul path to be connected to the first

customer of a backhaul path. Additionally, the paths can be routed from first to last customer or

last to first customer depending on the best way to connect the linehaul and backhaul routes. This

provides four possible ways to complete the route. The routing for each set of customers is

determined using a “nearest neighbor heuristic,” and then each solution is improved upon using a

tabu search algorithm. Once the algorithm has been run for each set of customers, the linehaul

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and backhaul paths are linked together in each of the four possible ways to determine which

alternative results in the least cost solution. These solutions are then ready to be optimized using

the tabu search algorithm.

The second and third initial solutions are created using what is referred to as the “K-tree

initial solution.” The initial solutions are first defined using a minimum cost K-tree approach to

solving a VRP. First, the linehaul and backhaul customers must be addressed independently as

VRP problems. Next, a minimum cost K-tree is used to formulate the solution to the VRP.

Finally, the capacity and precedence constraints are relaxed to create the initial solutions.

The three initial solution sets can then be optimized using a tabu search algorithm with

three phases: an initial phase to create feasible solutions, and two subsequent phases, which

improve upon the solutions. The two K-tree solutions are differentiated by one of the tabu

parameters. Specifically, one of the solutions uses a modification to the tabu search algorithm.

In this case the tenure parameter of the tabu search algorithm is allowed to be random, and

therefore it is referred to as the TSA-K-tree_r.

The performance of the three algorithms was tested against a series of previously

published VRPB algorithms using a suite of 95 test problems. The experimental results

demonstrated that the TSA-K-tree_r algorithm performed the same or better and took less

computing time when compared to previously published approaches. The TSA-K-tree algorithm

performed slightly worse than the TSA-K-tree_r, but required less computation time. The open

initial solution method produced fewer optimal solutions than the K-tree methods, although it

took less time to run. The results, therefore, illustrate that the K-tree initial solution method

combined with the tabu search algorithm utilizing a random tabu tenure is the best known

approach to addressing the VRPB [25].

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2.4 Order Batching

When developing a delivery system, the incorporation of strategic product batching to

allow for efficient routing can significantly impact the system performance. Order batching, also

known as “lot-sizing,” involves efforts to strategically group items that can be transported or

processed together [26]. The most notable benefits of incorporating batching into processes are

the realized reduction in resource requirements and the reduction in mean travel time to retrieve

and order. These benefits can lead to increased throughput and efficiency. Furthermore, batching

can lead to a reduction in “order holding time,” which affects how long customers wait to receive

their orders [27] [26].

Although batching is recognized to increase efficiency in order processing scenarios,

there are several system parameters which must be properly set to achieve the benefits.

Specifically, the size of the batch will affect the efficiency of operations. According to Won and

Olafsson (1994), a trade-off exists between the use of large and small batch sizes. Large batch

sizes will result in longer processing time, which will increase the time to customer delivery. In

contrast, small batches are less efficient, mainly because they require the use of more resources

and additional trips or travel distance. The trade-off space must be explored through

experimentation or multi-criteria optimization to understand the proper batch size for the system

under consideration. In addition, the process of creating the batches requires time and effort [28].

Therefore, analysis must be performed to understand the trade-off between taking time to create

batches and the resulting time saved in transporting or processing the batched orders. Logically,

only when the time required to batch is less than the realized time savings in the delivery process

should batching be incorporated into operations.

There are several heuristics that can be used to create batches from a given set of orders.

The first, and arguably simplest approach is described by Gibson and Sharp (1992) as the “first-

18

come, first-served heuristic,” also known as “naïve batching.” In this heuristic, orders are

batched together based on the sequence in which they arrive. Given a batch capacity, c, orders

will be batched together upon arrival until the batch capacity is met, at which point another batch

of size c will be initiated. While this batching strategy does not consider delivery location, it can

be used as a baseline to compare other more advanced batching techniques [28].

A second strategy described by Gibson and Sharp (1992) is referred to as the “sequential

minimum distance batching heuristic,” or SMD. This heuristic is considered a “greedy” heuristic,

because it batches orders based on their proximity to one another. To create the batches, a seed

order is chosen from the group of available orders. The next order to be added to the batch will

be the one with the closest delivery location to that of the seed order. The third order will be the

one that has the closest delivery location to that of the second order. This will continue until the

capacity of the batch is met, at which point, a new seed order will be chosen from the remaining

orders, and the process will be repeated.

2.4.1 A GA-based order batching method

One strategy, which was extensively tested against the first-come first-served and SMD

heuristic, is referred to as the “GA-based order batching method,” or GABM. This heuristic

claims to create efficient batches for both 2-D and 3-D facility systems. Given a set of orders to

be picked, the GABM utilizes a genetic algorithm (GA) to determine the best combination of

batches that minimizes total travel distance. Furthermore, the authors claim that their approach

can successfully accommodate any batch structure or facility layout [29].

The GA in this heuristic is encoded as follows. Each chromosome contains a gene for

every order required to be picked. In the place holder of a given order in the chromosome is a

number corresponding to the batch where the order will be placed. For example, the chromosome

19

(1, 3, 2, 1, 2) prescribes the first and fourth order to be in batch one, the third and fifth order to be

in batch two, and the second order to be in batch three. The GA tests many different

combinations of batches and evaluates each using a fitness measure. In GABM, the fitness is

calculated by taking the difference between the travel distance in the worst performing feasible

solution in the current population of solutions and the travel distance of the solution under

evaluation. The goal is to maximize this fitness value. To ensure that the tested solutions satisfy

capacity constraints, thus remaining feasible, a correction mechanism was devised to transfer

orders from over-capacitated batches to those which have available capacity.

The GA utilizes two techniques to promote diversity in the set of solutions: crossover and

mutation. The crossover mechanism allows for two chromosomes to swap parts of their encoded

solution, whereas the mutation mechanism allows for each gene in a solution to be swapped with

another gene with some low probability. Feasible solutions are chosen to join the mating pool

using a roulette wheel selection technique that provides a probability of being selected based on

their fitness value. A solution is able to survive into the next generation based on a second

probability-based approach that relies on the rank of the solution as compared to others in the

pool.

Hsu et al. (2005) conduct a study to compare the effectiveness of their GABM against

Gibson and Sharp’s SMD (1992) and the baseline first-come, first-served heuristic, using test

order sets and a rectangular facility layout with parallel aisles. The results of the experimentation

on the 2-D problems show that GABM performs in a superior manner to the SMD in terms of

number of batches, as well as total travel distance. Specifically, in seven experiments, the

GABM traveled between 0.85 to 0.91 times the distance traveled by the SMD, and between 0.69

and 0.81 times the distance of the first-come, first-served heuristic.

There are several factors that must be noted when considering the result of the

experiments by Hsu et al. As mentioned by the authors, the CPU time of the GABM to solve the

20

2-D problem was 0.7 hours, and 5.5 hours to solve the 3-D problem. These times were taken on

an IBM PC with a Pentium IV processor [29]. One important note to make regarding the

experiments is that they are tested only on scenarios in which all order data are known in advance

and batches can be planned hours before picking begins. Such a situation may allow for hours of

computation time; however, in a real-time, on-demand scenario, this may not be possible.

Additionally, on-demand scenarios may realize different test results because the heuristics may

handle the random arrival of batches in a different manner. It would likely be necessary to test

these three heuristics on real-time on-demand order batching problems to critically evaluate

which would perform best. Such an experiment, however, was not found in the literature search.

21

Chapter 3

Model Development

3.1 Introduction

This work undertakes the development of a model to allow for the analysis of a food

delivery system to be implemented within Geisinger Medical Center’s inpatient units. A discrete

event simulation model will be used to examine the impact of different batching and routing

strategies to deliver food to inpatients throughout the hospital. From the analysis, a

recommendation will be made to allow for routing of food in an on-demand fashion, that achieves

a sufficient level of service to the patient. Specifically, the model analysis will provide for insight

into the following operational strategies:

1. Food delivery cart size

2. Delivery resource requirements

3. Food cart dispatching rules

4. Routing strategies in the form of physical zoning of the facilities

The model will be developed to allow evaluation of different strategies on the basis of their effect

on patient service levels and the utilization of delivery resources.

3.2 System Description

The inpatient food delivery system to be modeled encompasses 345 licensed patient beds.

The beds are located across 19 units throughout the GMC hospital facility and will be occupied

22

by patients who require up to three meals per day. In the on-demand system, patients will be able

to order their meals between the hours of 6:30 am and 9:30 pm. Meals are ordered via telephone,

which allows the order to be sent to the kitchen staff. Each meal is prepared on an individual

basis (i.e., meals are prepared as the order arrives).

The facility layout of GMC lends itself to three natural spatial zones. Referenced by the

names of the elevators in the zones, the zones will be referred to as Zone A, Zone B, and Zone

JK. The zones contain six, seven, and five units, respectively. Meal orders will be segregated

into three batches, one for each zone. The batches of meals will be handled independently of

each other. This will allow for carts to be specifically allocated to one of the three zones.

3.2.1 Meal order arrival process

As food orders arrive to the kitchen, they will be identified by the zone and unit from

which the orders originated. A member of the food services team will then prepare the meal for

the patient. Once prepared, the meal will be placed on a cart designated for delivery to the zone.

If there is currently a cart designated for the zone with meals already on it, the meal will be added

to that cart. Otherwise, a new cart will be designated to that zone. The meals will continue to

accumulate on the cart until a time limit has been reached, or the capacity has been met,

whichever occurs first. Figure 2 demonstrates the logic of this portion of the food delivery

process.

23

Figure 2. Food Order Arrival Logic

To accurately model the order arrival process as it pertains to GMC, an estimate of

ordered meals in half hour increments is provided by Geisinger Health System. This estimate,

accompanied by data outlining how many beds are in each inpatient unit are used to develop

arrival distributions of meals in a given unit for every half hour between the operating times of

6:30 AM and 9:30 PM.

3.2.2 Meal delivery process

Once the food cart is ready for delivery, a member of the food services team will

transport the cart throughout the designated zone to deliver meals to the patients. For each zone,

24

there is a recommended routing to be used by the delivery host. Essentially, the routing follows a

nearest neighbor heuristic throughout the zone, starting at the units on the lowest floor served and

moving to the units on the highest floor served. In a zone, there may be more than one unit on a

given floor. These units are scheduled next to each other so that only one stop is made at a given

floor during the delivery route.

When on the delivery route, the delivery host will consider the next unit on the zone route

and determine whether there is a meal to be delivered in that unit. If so, the delivery host will

travel to that unit; otherwise, the host will consider the next unit on the zone route. Once the last

meal has been delivered, the delivery host will return the cart back to the food service kitchen to

allow the cart to be refilled. The logic for this delivery process is shown in Figure 3.

25

Figure 3. Food Cart Routing Logic

Once the delivery cart has arrived at a unit, all meals destined for patients in that unit will

be delivered. To enhance the quality of service, the delivery host will bring the meal to the

patient and take the necessary time to ensure that the patient has what they need to eat their meal.

If the patient has special dietary needs, the delivery host will also be required to inform the nurse

that the meal has been delivered so that the patient may be monitored. Additionally, if the patient

is an isolation patient, the delivery host will be required to put on a gown while they serve the

patient. This process will add to the service time spent with each isolation patient.

26

3.3 Modeling Approach

The discrete event simulation model representing the proposed food delivery system will

be built as an extension to an already existing simulation model representing all material routing

within Geisinger Medical Center. The model, which captures all units within the Danville

facility, was created in the simulation modeling program, Simul8.

By including all aspects of material handling flow within the hospital, the model captures

the essence of traffic throughout the GMC facility. This traffic is likely to have a significant

effect on service times of the food delivery system. In particular, system travelers often

experience a longer wait time for elevators during periods of increased traffic. The food delivery

carts rely on the elevators as well as on many of the heavily traveled hallways of the facility.

Therefore, including the general traffic as well as other material handling routing will better

reflect the performance of the system.

Figure 4 provides a partial snapshot of the Simul8 modeling environment. The GMC

model is unique in that it represents the physical structure of the GMC facility. Logic pertaining

to a particular department is contained in a box, such as the Food Service logic shown in Figure 5.

Departmental logic is placed in the model in a location representative of its real-life facility

location. Elevator nodes exist in the model as well and contain logic to allow transportation

objects to traverse floors. In addition, the model contains a node that represents the physical

location of each patient care unit. Finally, there exists a set of logic that represents any actions

taken once a material transport object reaches a location of interest. In total, the model includes

eight support services departments which perform pickup and delivery activities within GMC.

There are 19 inpatient units, 33 outpatient clinics, and 51 ancillary service departments across

eleven floors all of which are included in the model and accessed through a network of hallways

and elevators.

27

Figure 4. Simul8 Modeling Environment

Figure 5. Food Service Logic Modules

28

3.3.1 Modeling assumptions

Several assumptions were made in the development of the food delivery portion of the

model to facilitate model building while allowing for reliable results. The following list provides

the significant assumptions made:

1. The delivery host will mirror the cart usage; therefore, it will be assumed that if there

is a cart to be delivered to patients there will also be a host available to deliver it.

2. There are an unlimited number of delivery resources available; the model will profile

usage of these resources over time.

3. Only the process of delivering meals to patients will be modeled; the process of

collecting the empty trays from patients after they have finished their meal will not

be considered.

4. The scope of the food delivery model will be limited to the delivery process from the

time the food is prepared by the kitchen staff and placed on a cart to the time the

meal is delivered to the patient.

5. Only inpatient units that regularly receive meals delivered from the food service

kitchen will be included in the routing schedule.

The first assumption allows the model to track a single delivery resource representing

both the meal cart and delivery host. This assumption is considered valid because these two

resources must be available together to deliver meals. Therefore, the model will assume that the

number of carts is adequately matched to the number of delivery hosts staffed to deliver meals.

The second assumption allows the model to have access to a cart/delivery host at all

times. This eliminates the situation when a tray must wait for a cart/host before it can be sent for

delivery. By this assumption, the model allows for the analysis to demonstrate the number of

delivery resources required to prevent delays due to a lack of food carts or available delivery

29

hosts. In other words, it will allow for insight on the maximum required number of resources to

ensure that there are always sufficient delivery resources available.

The third and fourth assumptions pertain to the scope of this study. While this model will

only capture the meal delivery processes, a return process, which involves the patient’s empty

trays does take place in the real-world system. These two processes are currently considered

independently of one another and therefore will remain independent in this study, resulting in a

focus on the delivery of meals. In addition, because the process of preparing individual patient

meals is new to GMC, no current data exists to estimate the amount of preparation time required

for each meal. Therefore, the modeling process will not consider this aspect of the process, and

will focus on the routing and delivering of meals to patients.

Finally, the fifth assumption simply eliminates from the scope the delivery of any

meals/food to patients not regularly serviced by the food services department. Although there are

instances where the food service department prepares meals for patients outside its traditional

domain, the occurrence is considered sporadic, and therefore difficult to estimate.

30

Chapter 4

Analysis of Results

4.1 Introduction

This chapter describes the approach taken to analyze the on-demand food delivery system

at GMC. Eight scenarios were tested in the simulation model, each with a different combination

of system parameters. The results of the experiments allowed for confidence in the decision

making regarding operational system parameters based on how stakeholders value the affected

system performance measures.

4.2 Experimental Plan

This section outlines the experimental parameters and performance measures selected to

provide key insights into the food delivery system.

4.2.1 Performance Measures

Several performance measures were used to analyze the on-demand food delivery system,

as outlined in Table 4-1. The performance measures were determined based on stakeholder input.

The main objectives of the research were to understand resource needs to attain acceptable

service levels; therefore, the performance measures reflect these aspects of the food delivery

system model. The GMC Guest Services management team identified a goal delivery time of 45

minutes or less. This goal time specified by GMC includes the meal preparation time and

31

therefore the dispatch, routing, and delivery time should occur in less than 45 minutes to allow

time for the preparation.

To understand how long it takes for a meal to reach the patient from the time it has been

prepared in the kitchen, six performance measures were developed, namely, the service time

performance measure, wait time on cart before routing performance measure, and the percent

delivered beyond 25, 30, 35, and 40 minutes performance measures. A range of times was used

for the “percent delivered beyond” performance measures to allow for an understanding of

service levels depending on the realized food preparation time. By examining the performance

for the entire range, it will be possible to make a more informed decision once there is a better

understanding of how long it will take to prepare the food.

When considering resources, the delivery carts are a key aspect of the delivery model

and, therefore, three performance measures were created to estimate their utilization and the

efficiency with which they were used. Specifically, the cart utilization measure tracks the ratio of

average number of meals on a cart to the capacity of the cart when it leaves for delivery; a high

utilization will signify efficient use of the cart resource, while a low utilization will suggest that

the system is not getting the best use out of the resources available. Furthermore, the maximum

number of carts used over a day and the number of delivery trips made in a day represent how

efficiently the cart and host resources are used. Additional carts required, or a greater number of

delivery trips made, will require more host resources to accompany the extra carts needed. If

scenarios present an opportunity to make fewer trips with fewer carts, that will allow for savings

in resource expenditures.

32

Table 4-1. List of System Performance Measures (bold measures represent key performance measures)

Two performance measures were identified as key: Maximum number of carts used over

a day and Percent of meals delivered after 30 minutes. The maximum number of carts used over

a day was considered a key measure because it allows for an understanding of how many carts are

necessary to keep the system running at high performance. The percent of meals delivered

beyond 30 minutes was considered a key performance measure because it will provide insight

into the possibility of meeting the 45 minute service levels, provided a meal preparation time of

fifteen minutes of less. From this measure, the additional “percent delivered after” performance

measures can be used to understand how service will be affected if the preparation process

requires more or less time. This key performance measure simply gives a middle ground from

which to interpret the patient service level analysis. The pairing of these two key performance

measures is effective for decision making because it considers the balance between resource

usage and patient service levels.

System Performance Measures

Max Number of Carts Used Over a Day

Number of Delivery Trips Made in a Day

Cart Utilization

Service Time

Wait Time on Cart Before Routing

Percent Delivered after 25 minutes

Percent Delivered after 30 minutes

Percent Delivered after 35 minutes

Percent Delivered after 40 minutes

33

4.2.2 Experimental design

The simulation was run using eight different combinations of cart capacities and dispatch

timer settings. Table 4-2 contains each of the combinations tested and analyzed using the

simulation model.

Table 4-2. Experimental Scenarios

The cart capacity settings were chosen based on the available options of food carts for

purchase. The dispatch timer settings were chosen based on operational insight. Specifically,

consideration for the times to travel to and within the various zones was balanced against the need

to wait long enough for the cart to fill with a sufficient amount of meal trays for a given zone.

Given that some units can take more than four minutes to walk to and that hosts spend between

one and two minutes serving a meal to each patient, it was imperative that food not wait on the

cart so long as to compromise the ability to reach the patient in under 45 minutes from the time an

order is placed.

Data were collected on each scenario for a period of 30 days. This provided 30

independent replications to use for statistical analysis and comparison of the different scenarios.

95% confidence intervals were computed on each resulting performance measure using Student’s

t-distribution along with the assumption that the data are normally distributed.

ScenarioDispatch Time

(Minutes)

Cart Capacity

(Trays)

1 8 12

2 8 14

3 8 18

4 10 12

5 10 14

6 10 18

7 12 12

8 12 14

34

4.3 Results

Table 4-3 displays the resulting performance of the system under each combination of

parameters tested. The table contains averages and 95% confidence intervals for each

performance measure.

Table 4-3. Experimental Results

Minutes Cart Capacity Average 95% CI Average 95% CI Average 95% CI

8 12 17.22 (17.15, 17.29) 16.00 (15.83, 16.17) 242.60 (241.40, 243.80)

8 14 17.20 (17.13, 17.27) 15.93 (15.66, 16.21) 242.70 (241.39, 244.01)

8 18 17.23 (17.17, 17.29) 15.90 (15.72, 16.08) 243.23 (241.64, 244.82)

10 12 19.23 (19.16, 19.30) 14.63 (14.45, 14.82) 206.53 (205.36, 207.70)

10 14 19.31 (19.23, 19.38) 14.64 (14.46, 14.83) 205.00 (203.77, 206.23)

10 18 19.31 (19.23, 19.39) 14.37 (14.18, 14.55) 205.43 (204.39, 206.47)

12 12 20.97 (20.89, 21.04) 13.70 (13.53, 13.87) 179.60 (178.82, 180.38)

12 14 21.20 (21.11, 21.30) 13.27 (13.10, 13.43) 177.77 (176.79, 178.75)

Minutes Cart Capacity Average 95% CI Average 95% CI Average 95% CI

8 12 0.3613 (0.3597, 0.3629) 4.78 (4.77, 4.80) 10.24 (9.79, 10.69)

8 14 0.3086 (0.3068, 0.3105) 4.80 (4.78, 4.83) 10.13 (9.71, 10.55)

8 18 0.2399 (0.2387, 0.2412) 4.80 (4.78, 4.81) 10.14 (9.69, 10.59)

10 12 0.4235 (0.4210, 0.4259) 5.80 (5.82, 5.77) 19.11 (18.61, 19.61)

10 14 0.3660 (0.3640, 0.3681) 5.83 (5.81, 5.85) 19.61 (19.15, 20.07)

10 18 0.2850 (0.2835, 0.2864) 5.85 (5.83, 5.87) 19.06 (18.44, 19.68)

12 12 0.4878 (0.4856, 0.4899) 6.72 (6.69, 6.76) 27.22 (26.74, 27.70)

12 14 0.4238 (0.4217, 0.4260) 6.81 (6.78, 6.84) 29.1324 (28.67, 29.60)

Minutes Cart Capacity Average 95% CI Average 95% CI Average 95% CI

8 12 2.06 (1.83, 2.29) 0.1645 (0.104, 0.225) 0 (0, 0)

8 14 2.00 (1.78, 2.21) 0.1811 (0.131, 0.232) 0.003 (-0.003, 0.010)

8 18 2.10 (1.92, 2.29) 0.2471 (0.195, 0.299) 0.003 (-0.003, 0.010)

10 12 5.67 (6.02, 5.32) 0.9099 (0.792, 1.028) 0.061 (0.026, 0.095)

10 14 6.08 (5.78, 6.38) 1.2301 (1.080, 1.380) 0.117 (0.073, 0.161)

10 18 5.97 (5.59, 6.35) 1.2742 (1.098, 1.450) 0.199 (0.129, 0.270)

12 12 10.79 (10.41, 11.16) 2.4365 (2.258, 2.615) 0.231 (0.175, 0.288)

12 14 12.04 (11.58, 12.49) 3.1487 (2.845, 3.448) 0.434 (0.310, 0.558)

Parameters

Parameters

Parameters

Percent delivered after

35 min

Percent delivered after

30 min

Service Time Max Number of Carts Number of Delivery Trips

Cart UtilizationWait Time on Cart

Before Routing

Percent delivered after

25 min

Percent delivered after

40 min

35

Several trends are present in the data. First, as the dispatch timer increases, it is apparent

that the cart utilization and service time increase, while the maximum number of carts used over a

day, the number of delivery trips made, and the service level decrease. Additionally, the results

show that as the cart capacity increases, the cart utilization decreases. These trends reveal a broad

theme within the food delivery system: a trade-off exists between patient service and efficient use

of resources. The results also show that for any given scenario, dispatch to delivery time can take

between 17.15 and 21.3 minutes on average, leaving between 23.7 and 27.85 minutes to prepare

the meal for delivery. When focusing solely on patient service, the eight minute dispatch timer

provides the best performance in terms of percent of meals delivered beyond each of the time

intervals of interest. Finally, it is important to note that there were few instances where meals

were delivered beyond 40 minutes. These results suggest that given a reasonably efficient meal

preparation process, the 45 minute service time goal set by management is achievable and can be

further improved upon depending on which parameter settings are chosen and how much time the

meal preparation process requires.

A closer examination of the resulting cart utilization for each of the scenarios reveals that

a cart capacity of twelve meal trays provides the highest utilization for each of the three dispatch

timer settings. Table 4-4 shows the average number of carts filled to capacity for each of the

eight scenarios. The table demonstrates that when using a cart capacity of twelve trays, the cart

fills to capacity more often than when using a larger cart capacity, allowing for better use of the

resource. Furthermore, the results in Table 4-3 suggest that the cart utilization is the only

measure significantly affected by a change in cart capacity. For this reason, the three options

with a cart capacity of twelve trays and each of the three dispatch timer settings were given the

most consideration for recommendation. Visuals of the resource performance measures and

service performance measures for the twelve tray cart scenarios can be found in Figure 6 and

Figure 7, respectively. The trends in the two plots further emphasize the service-resource trade-

36

off discussed above. As the dispatch timer increases, the results show an improvement in the

efficient use of resources; however, the factors measuring patient service perform worse as the

timer length grows.

Table 4-4. Average Number of Carts Filled to Capacity for Each Scenario

Figure 6. Resource Performance Measures Plot for Twelve Tray Cart Scenarios

Dispatch Timer Cart Capacity

Average Number

of Carts Filled to

Capacity

8 12 1.13333

8 14 0

8 18 0

10 12 5.6667

10 14 0.93333

10 18 0

12 12 12.5667

12 14 4.367

16.00

242.60

36.1306 14.63

206.53

42.3489 13.70

179.60

48.7761

0.00

50.00

100.00

150.00

200.00

250.00

300.00

Max Number of Carts Number of Delivery Trips Cart Utilization (as apercentage)

Resource Performance Measures 12 Tray Carts

8 Minutes 10 Minutes 12 Minutes

37

Figure 7. Service Performance Measures Plot for Twelve Tray Cart Scenarios

Figure 7 can also provide assistance in planning for food preparation times. Logically, as

preparation time increases, the time to available to dispatch, route, and deliver meals decreases.

From Figure 7, it becomes clear that the service level quickly decreases as more preparation time

is required. For example, if meals only require five minutes to prepare, the percent of meals

delivered after 40 minutes is between 0 and 0.231% depending on the dispatch timer setting. This

means that greater than 99% of meals will achieve the order-to-delivery time goal of 45 minutes.

By contrast, if food preparation takes twenty minutes, the percent of meals delivered after 25

minutes suggests that between 10.24 and 27.22% of meals may be delivered beyond the 45

minute goal because it becomes much more unlikely that meals can be dispatched, routed, and

delivered in less than 25 minutes.

Whereas the previous results provided insight into the maximum number of carts used

over a given day, it does not provide insight into how often those maximum numbers of carts are

in use throughout the day. Figure 8 provides a visual representation of this information. For each

17.22

4.78

10.24

2.06 0.1645 0

19.23

5.80

19.11

5.67

0.9099 0.061

20.97

6.72

27.22

10.79

2.4365 0.231

0.00

5.00

10.00

15.00

20.00

25.00

30.00

Service Time Wait Time onCart Before

Routing

Percentdelivered after

25 min

Percentdelivered after

30 min

Percentdelivered after

35 min

Percentdelivered after

40 min

Service Performance Measures 12 Tray Carts

8 Minutes 10 Minutes 12 Minutes

38

dispatch timer setting, the chart provides a profile of the percent of time a given number of carts

is in use throughout a day. While, for example, the eight minute dispatch timer experiences a

count of seventeen carts in use for a period of time in a day, it is for less than 0.01% of the time

that food services is delivering meals to patients. This again emphasizes the trade-off between

resources and service: a balance must be struck between the need to have a cart available to

deliver food, and the acceptable limit of time that a meal may take longer to be delivered because

it is waiting for a cart.

Figure 8. Cart Usage Profile Plot for each Twelve Tray Cart Scenario

Figure 9 displays yet another view of the delivery resource data analyzed for each of the

three twelve tray cart scenarios. This plot shows the average maximum number of carts in use

throughout the meal delivery operation hours for each dispatch timer setting. In any given hour,

more carts are in use throughout the system with the eight minute dispatch timer, and the least

number of carts are in use with the twelve minute dispatch timer. Additionally, three peaks are

visible in the plot around traditional meal times (8am, 12pm, and 6pm). Although the number of

39

carts available for use throughout the day will likely remain constant, the number of delivery

hosts staffed throughout the day will depend on meal order demand. This plot suggests that host

staffing levels should be increased around traditional meal times and can be cut back during the

off-peak hours. The use of part-time hosts may be useful to accommodate these peaks in demand.

Figure 9. Average Number of Carts in Use throughout a Day for all Twelve Tray Cart Options

4.4 System Limitations

The logic and simulation modeling undertaken for this research has proven valuable in

providing insight into the operational abilities and trade-offs of the on-demand food delivery

system; however, it is important to outline the limitations of the system to allow for appropriate

use of the data. Specifically, resource assumptions and the scope of the model must be taken into

consideration when using the results for operational decision making.

0

2

4

6

8

10

12

14

16

18

Av

era

ge

Nu

mb

er

of

Ca

rts

In U

se

Hour

Average Number of Carts in Use Throughout a Day

12 Tray Carts

8 Minutes 10 Minutes 12 Minutes

40

As mentioned in Section 3.3.1, the model represents delivery hosts in the same way it

represents delivery carts: if there is a cart ready for delivery, it is assumed there will be a host

available to route it. While this assumption will still allow for insight into the needs of both

delivery cart resources as well as host resources, it does not account for the human factors

associated with delivery hosts. There are no shifts or break schedules incorporated into the

model, and, therefore, additional hosts may be required to account for employee downtime during

breaks and shift changes.

4.5 Recommendations

Based on the results of the eight scenarios tested and analyzed in the simulation model, it

is recommended that GMC purchase carts with a capacity of twelve trays for use in the food

delivery system. This will allow for the best cart utilization as compared with the fourteen and

eighteen tray carts. Choosing the twelve tray carts will also not greatly affect the patient service

levels when compared with the other options, as seen in Table 4-4. The timer on the carts with

larger capacity expires more often before the cart is full and therefore service time is not affected

because the carts leave for delivery regardless of how full they are.

When choosing the dispatch timer, it is imperative to consider whether any sacrifice can

be made in patient service to save in resource expenditures. Furthermore, it is important to

consider how service will be affected with the realization of longer or shorter meal preparation

times. If meal delivery beyond 45 minutes cannot be tolerated, it is recommended that an eight-

minute dispatch timer be used. This will help ensure that even with food preparation time

incorporated into the system, meals will more likely be delivered under the 45 minute time

constraint. If some sacrifice in service is acceptable, a ten-minute dispatch timer will provide a

better balance between efficient use of resources and patient service levels, provided meals take

41

fifteen minutes or less to prepare. This is shown through the lower number of delivery trips and

lower number of carts (and hosts) needed throughout the day while serving only 5.67% of meals

beyond 45 minutes (given a 15-minute meal preparation time). If meals take longer than fifteen

minutes to prepare, it is recommended that an eight-minute dispatch timer be used to keep the

patient order-to-delivery time under 45 minutes; however, as shown in the results, as much as

10.24% of meals will be delivered late in this scenario.

42

Chapter 5

Conclusions and Future Research

This research has demonstrated the use of simulation modeling to make informed

operational decisions for a new on-demand delivery system at Geisinger Medical Center in

Danville, PA. The simulation model has captured the dispatch, routing, and delivery process of

hot meals to inpatients, reflecting the system performance that can be expected given eight

different operational strategies. The operational strategy that allowed for the best balance

between resource utilization and patient service levels utilized delivery carts with a capacity for

twelve trays, and a dispatch timer setting of ten minutes, provided a meal preparation time of less

than fifteen minutes. The results suggest that this policy will allow for approximately 94.3% of

patients to receive their meals within 45 minutes of placing an order. If meals are expected to

take more than fifteen minutes to prepare, a policy using delivery carts with a capacity for twelve

trays and a dispatch timer setting of eight minutes will provide the best patient service levels of

89.67% percent of meals delivered within 45 minutes of placing an order, at the cost of less

efficient use of resources. The results also provide an expectation for the number of carts

needed, as well as information to assist planning for host staffing levels depending on the

operational policy chosen. Finally, the results confirm that segregating the hospital facility into

three spatial zones allows for efficient delivery service to patients.

There are several opportunities for future research involving the on-demand food delivery

model. The simulation model, in particular, presents many opportunities for expansion. For

example, host resources can be modeled independently from delivery carts. This would allow for

the inclusion of employee breaks and shift changes to better represent the staffing needs of host

resources to meet desired service levels. Additionally, estimates regarding meal preparation time

could lead to the ability to incorporate this process into the model. This would provide a better

43

estimate around patient service time from order to delivery of meals because it could incorporate

the variability inherent in the meal preparation process.

GMC has initially decided to operate the on-demand delivery process between the hours

of 6:30am and 9:30pm. It is common, however, for patients to be admitted later in the evening

and need to eat a meal. Further analysis of admissions data could help validate that the current

operating hours are best-suited to accommodate the majority of patients requiring meals

throughout the day, or may suggest that an adjustment in operation hours would better serve the

needs of patients. In addition, once the on-demand delivery system has been implemented,

additional data can be collected on the patient meal order distribution to ensure that the model

still accurately reflects the actual events of the system.

Finally, this research has shown the operational insight provided by simulation modeling

for the food delivery process. This work can be expanded to help design an efficient process for

the return of dirty trays to the kitchen. Currently, GMC’s food service operational policies dictate

that the return of dirty trays be a separate process using separate resources and separate routing

schedules. Vehicle routing research suggests that these two processes may be combined to create

efficiencies. By incorporating the return process into the model, alternative return strategies can

be tested, including those that take advantage of the food carts and delivery hosts who are

currently returning empty handed to the kitchen after delivering meals. Exploring these

alternative strategies may result in opportunities to make both the delivery and return processes

more efficient.

44

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