SEEM 3060
Linear/Integer program formulation and python problem solving
Direction:
For each of the following problem:
A. Formulate the corresponding linear/integer program. Explain the meaning of each
variable and each constraint in your short report.
B. Based on Google OR-Tools, write a python program to solve the formulated problem.
Print the source code of your program, and screen capture the output of your program.
Explain the answer in your short report.
C. Please write your report in a clear and professional manner, like the way you would
communicate (in writing) with your boss. You can assume that your boss took SEEM3060 several years ago, i.e. you can assume that he/she knows the basics of operations research.
D. Confidential peer evaluation will be conducted. Instruction for the peer evaluation will be provided right after the final exam of this course. Each student is requested to submit his/her confidential peer evaluation by a deadline (to be announced right after the final exam of this course).
1. To use your Christmas vacation in a worthwhile manner, you have decided to help your uncle repairing his farm house in a remote island off Sai Kung. Your uncle’s neighbor has given you thirty sheets of plywood, each sheet of the size 10 ft ¡Á 10 ft.
To repair the farm house, you need twenty sheets of plywood in the shape of circle of 5-ft diameter, as well as fifteen sheets of plywood in the shape of rectangles of 4 ft ¡Á 6 ft.
From geometry you have learned in high school, you know that you can cut a sheet of 10 ft ¡Á 10 ft plywood in the following ways:
It will cost you $20 to cut a circle, and $15 to cut a rectangle. The price includes all the necessary cuts and does not depend upon which way the shape is cut. On the other hand, you can purchase a circle of 5-ft diameter at the cost of $45, and a rectangle of 4 ft ¡Á 6 ft at the cost of $30.
You would like to minimize the cost of obtaining (via cutting and/or purchasing) the 20 sheets of the circle plywood and the 15 sheets of the rectangular plywood. Being environmentally minded, your uncle also requires you that all this cutting will not result in more than 30% of wastage. (For example, in the second cutting pattern
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shown in the preceding figure, 4% of the plywood is wasted, when you cut 4 sheets of 4 ft ¡Á 6 ft rectangle off a 10 ft ¡Á 10 ft plywood.)
Formulate an integer program for the problem. Then write a python program to solve it.
2. As an intern of the Micron Medical Equipment Retail Corporation, you are asked to solve the following problem: The customer requirements for a best-selling electronic microscope for the coming four months are 2 units (Jan. 2021), 4 units (Feb. 2021), 2 units (March 2021) and 3 units (April 2021) respectively.
Your company needs to place orders to get these units from a supplier. The cost of placing an order is $4,000. The cost per unit is $10,000. The inventory holding cost is $300 per unit per month. Also, an order for delivery can only be made at the start of each month.
For example, if you place an order to have 6 units to be delivered at the start of Jan. 2021 (hence satisfying the demands for both Jan. and Feb.), and another order to have 5 units to be delivered at the start of March (satisfying the demands for both March and April), then the total cost would be:
$4,000 + 6 units x $10,000/units + 4 units x 1 month x $300/(unit¡¤month) + $4,000 + 5 units x $10,000/units + 3 units x 1 month x $300/(unit¡¤month)
In short, for the start of each month, you need to decide whether you should make an order for delivery, and if you do decide to make an order for delivery, how many units to order.
Formulate an integer program, so that you can minimize the total cost while being able to satisfy the customer demand. Then write a python program to solve it.
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