A company with a very large machine shop wants to determine the machines that will be dedicated to the production of n s

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A Company With A Very Large Machine Shop Wants To Determine The Machines That Will Be Dedicated To The Production Of N S 1 (104.4 KiB) Viewed 14 times

A company with a very large machine shop wants to determine the machines that will be dedicated to the production of n similar products. Assume that there are m different machines capable of producing each of these products, but the production times of these machines might be different. Let ti be the unit production time of product i at machine j for i=1,..,n and j=1,...,m. The demand for product i is denoted by d; for i=1,...,n. Assume that the whole demand for each product should be produced by a single machine, i.e. each product will be assigned to one machine. 1. (3.5pt) Assume that the goal of the company is to find product-machine assignments such that the total production time of the products is minimized. Formulate this problem as an IP. Clearly define the decision variables and write down the mathematical model. 2. (2.5pt) Assume that the goal of the company is to minimize the maximum (total) production time for any product. Modify the model developed in the previous item for this case. If you need additional variables, clearly define them. 3. (3pt) Assume that the absolute difference between the running times of machines 1 and 2 cannot be greater than A time units. Write down the constraint(s) for modelling this requirement. If you need additional variables, clearly define them. 4. (1pt) Assume that each machine can process at most 3 different products. Write down the constraint(s) for modelling this requirement.