MPL Project- Pharmaceutical Clinical Trial Distribution
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?