CrossChek Sporting Goods• CrossChek Sporting Goods is a manufacturer of sporting

goods, including golf clubs, hockey equipment, bats, balls and all things related to sports.

• A significant portion of CrossChek’s operations involve the process of procurement of components and materials from suppliers, through to the manufacturing of sporting goods for distribution. CrossChek’s sporting products are then sold direct to consumers, as well as to retail outlets.

• For the business to be profitable, a number of operations need to be optimized:

Manufacturing• Consider two high-end hockey sticks, A and B. $150 and

$200 profit are earned from each sale of A and B, respectively. Each product goes through 3 phases of production.• A requires 1 hour of work in phase 1, 48 min in phase 2, and 30 min

in phase 3.• B requires 40 min, 48 min and 1 hour, respectively.

• Limited manufacturing capacity: • phase 1 1000 total hours• phase 2 960• phase 3 1000

• How many of each product should be produced? • Maximize profit• Satisfy constraints.

New Product Lines• Each year CrossChek decides which new baseball bats

and gloves it will market. Consider that each new bat is expected to generate $150K for the year, while each new glove generates $200K.

• Each new offering requires time for marketing (bats 20 hrs, gloves 30 hrs), which is limited to a total of 200 hrs.

• Each product also has storage space requirements (bats 300 sq ft, gloves 400 sq ft), which is limited to 3000 sq ft.

• How many new lines of bats and gloves should be offered?

Scheduling Product Production

Activity Description Predecessor Time (days)

A Planning -- 5

B Club Head Design A 4

C Club Head Manufacturing B 8

D Shaft Assembly A 7

E Grip Attachment D 1

F Club Head Assembly C, D 4

G Balancing E, F 5

Inventory Optimization• CrossChek acts as a distributor for “Joe Buck Signature”

footballs. Demand for this particular type of football varies from 30-60 units per day. Each unit sold yields $20 profit. The holding and opportunity costs of each unit totals $1 per day. What is our optimal inventory level? If there is a fixed cost of $200 associated with each order CrossChek makes with its supplier, at what point should we place orders? How much should we order?

Processing Orders• CrossChek gets requests-for-quotes at a rate of about 15

per hour. Each of these requests is individually assessed by a sales clerk, who then answers with a quote. Each clerk earns a wage of $17 per hour, and the average profit earned by CrossChek is $28 per request. It takes a clerk an average of 15 minutes to answer a request for a quote, and it is found that the probability of a sale is 25% if a quote is given within an hour, dropping by 5% after each additional hour. What is the optimal number of clerks to employ?

Evolution• Consider new products A, B and C. If CrossChek is

successful in persuading its retail partners to carry A, it expects to make $500K profit. Otherwise, it stands to lose about $100K. For B, make $400K or lose $50K, and for C make $300K or break even.

• It expects A, B and C to be successful with probabilities, of 30%, 40% and 50%, respectively.

• Also, if A is successful, it plans to roll out a “CrossChek Special” version of the product, which will make an additional profit of $50K with 70% probability.

• Which product should they produce?

Multi-Criteria Decision Making• Consider other factors, in the above scenario, such as the

extra (unpaid) time that several employees will need to invest, as well as the possibility of low employee moral if the new product fails. CrossChek may even need to consider layoffs, which may damage public image. This factor will need to be included in the analysis.

Course Project• Create a fictional business similar to that above, and

determine optimal processes and decisions for the business using management science techniques learned in class. Students will work in teams (of 4 or 5). Teams will submit a report as well as give a presentation.

What is Management Science?• The science of managerial decision-making. A systematic

approach to:• modeling processes• clarifying constraints and objectives• defining the alternative strategies • evaluating potential courses of action

• Often referred to as “operations research” or “operational research” (UK)

Decision Making• Central to management science• Process:

• 1. Define the problem• 2. Identify the alternatives• 3. Determine the criteria• 4. Evaluate the alternatives and select

Models• Representations of objects, situations, scenarios, etc.,

used to monitor the effects associated with various inputs.• A model car may be used to assess the effects of different

test crashes.• A mathematical model may be used to compute how

aerodynamics reduce wind resistance, and thus improve overall gas mileage

• More simply a mathematical model can be used to compute CrossChek’s profits from sales of a particular hockey stick:

P = 150x

Models• Mathematical models usually contain

• an objective (what to do)• constraints (the rules that must be followed).

• Example objective: maximize profit for the week ($150 per unit).

• Example constraint: maximum of 40 hours for production (each unit takes 8 hours).

Model Inputs• Controllable inputs are those over which we have

influence (in this case X), and are also referred to as decision variables. The decision alternatives are the different values for these inputs or variables. The optimal alternative is the set of input values that• is feasible (i.e. satisfies the constraints)• best meets the objective

• Uncontrollable inputs are those over which we have no influence

Modeling Example• CrossChek would like to set up displays in some of its

retail stores for two new lines of hockey sticks. The company has designated two employees to work 8 hours each on setting up these displays. They need to figure out the optimal number of stores in which to set up each display.

• It is expected that each display of the first stick will bring in $3K in new profit, the second $2K

• It takes employee 1 4 hours to set up each display for the first type of stick

• Each display for the second type of stick requires 1 hour from employee 1 and 2 hours from employee 2.

Back to CrossChek Manufacturing• Consider two high-end hockey sticks, A and B. $150 and

$200 profit are earned from each sale of A and B, respectively. Each product goes through 3 phases of production.• A requires 1 hour of work in phase 1, 48 min in phase 2, and 30 min

in phase 3.• B requires 40 min, 48 min and 1 hour, respectively.

• Limited manufacturing capacity: • phase 1 1000 total hours• phase 2 960• phase 3 1000

• How many of each product should be produced? • Maximize profit• Satisfy constraints

Linear Programming• This particular model is a linear programming model, or

linear program.• A mathematical model in which the objective and the

constraints are described using linear functions (functions in which each variable appears in a separate term and is raised to the first power. A function with n variables will create a line in n-dimensional space).

• “Programming” is not meant in the sense of computer programming, but rather that (optimal) decisions must be made within the model. Thus the act of describing and solving a decision problem with linear objective and constraint functions is referred to as linear programming.

LINDO