Linear Optimization

OR/MATH 441

MPL Project— Pharmaceutical Clinical Trial Distribution

Fall, 2016

A pharmaceutical company, named “LongerLife”, plans to deliver clinical trials to three different clinics

(C1, C2, and C3). The trials are used for the emergency treatments so LongerLife must fulfill all

requirements. LongerLife has 3 deliver trucks. Each truck can ship 200 trials per trip. Depending on the

distance between LongerLife and its clinics, the shipping cost may be different. Usually, it takes a week

to deliver, i.e., if we decide to deliver in Week 1, the clinic will receive the trials in Week 2 and the truck

will be available in Week 2. Each clinic has a dedicated space for holding the left-over trials. The holding

cost per trial is around ten cents per week. To simplify the question, LongerLife can produce as many

trials as we want in any week. Currently, LongerLife just delivers the trails when the clinics don’t have

any inventory on hand. Due to the high shipping cost and the frequent out of stocks, LongerLife requests

our help. The company has provided the following data. Please use the optimization skills learned in

OR/MATH 441 and help LongerLife improve the distribution plan.

The demand data is as follows.

Weeks 1 2 3 4 5 6 7 8 9 10

C1 0 0 220 70 60 150 30 130 60 70

C2 0 150 30 50 50 10 450 100 50 80

C3 0 50 160 40 200 170 0 30 30 120

The shipping cost may depend on the distance. The following data is the shipping cost per round trip.

C1 C2 C3

Shipping cost per round trip($)

150 200 250

The space in the clinics is shown in the following table.

C1 C2 C3

Inventory Limitation 225 150 100

Please provide a report to manager that answers the following:

I. Formulate the problem to determine the distribution in order to minimize the total cost.

Please provide a mathematical description of the model.

II. Follow the formulation in Part I and solve this problem using MPL as a Mixed Integer

optimization problem. Please provide the .mpl file and any accompanying data files on

blackboard. I need machine-readable code so that I can run the problem.

III. If we fix the truck deliver plan (not including the amount of trials in each trip), the problem

will become a linear optimization problem. Please comment on the sensitivity of the

solution you obtained in part II. to changes in cost coefficients.

IV. Please comment on the sensitivity of the solution you obtained in Part III, i.e., to changes in

the constraint data, e.g., to increase the inventory limitation.

V. Given this analysis, what is your recommendation to the company?

VI. (Open question) The actual demand data may not be known when we optimize. In

LongerLife, the actual demand may have +10% or -10% variation. The manager would like to

also consider this factor in the optimization model. Do you have any suggestion? How do we

do?

General Rules for Final Project:

Due: Thursday, Dec 8, 2016, at 3:10 pm

• Please provide the following items.

(1) One page of executive summary.

(2) Project description (no more than three pages).

(3) MPL files.

• Grading policy: The instructor will grade the project based on the following criteria.

(1) Correctness (60%, including I. and II.: Do you help the company correctly?

(2) Business Insights (30%, including III. IV. and V.): Could you provide some suggestions to the

company?

(3) Creativity (10%, part VI.): What and how do you propose the future plan for the company?

• Team grading policy: You can evaluate your teammate. If you are not satisfied with your

teammate, you can send me an email before the midnight of Dec 8 (Thursday) with your reason and

suggestion of the penalty (less than or equal to five points), his/her project score will be calculated

accordingly. For example, if the project score is 90, Student 1 suggests a 3-point penalty to Student 2

and Student 3 suggests a 5-point penalty to Student 2. Student 2 will get 82 in the project.

• If you have questions about the project, contact us, preferably by e-mail ([email protected]

and [email protected]).