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INDE6620 Optimization and Applications

Question:
A company wants to manufacture five products over a 2-year (24 months) planning horizon. Table below provides the revenue (i.e., selling price) for each product. The table also presents the number of worker-hour to produce one unit of each product.

 Product Selling Price (1st yr.) Selling Price (2st yr.) Worker-hour to produce one unit A 1100 1200 11.5 B 1100 1200 12 C 1100 1200 12 D 1100 1200 12.5 E 1100 1200 11.5

The table below provides the maximum demand for each period, which are expected to be similar for all the products: Month

 Month 1 2 3 4 5 6 7 8 9 10 11 12 YEAR 1 210 225 240 255 350 350 400 450 450 360 265 180 YEAR 2 215 230 245 260 305 355 405 455 365 270 200 185

The company has a commitment to produce and ship 80% of the maximum demand for each period. The company has 75 workers available. Each worker can work for 160 hours per month. Each worker costs \$33 per hour (including benefits). Overtime is allowed with the cost of 50\$ per hour (including benefits). The manger is also allowed to hire and lay off workers if necessary. The costs of hiring a new worker in the first year and the second year are estimated to be \$2600 and \$2800, respectively. The costs to lay-off a worker in the first year and the second year are estimated to be \$1400 and \$1600, respectively. Moreover, the manager is allowed to keep and use inventory.

The company expects the holding costs to be \$9 for one period (per item) and remains constant over the planning horizon for all the products.

a) Define all the variables and list all your assumptions.
b) Develop the mathematical formulation to maximize the profit.
c) Find the optimal solution. Enough detail and associated computer files should be provided.
d) Suppose that the production manager is allowed to modify the cost elements. What would be your cost-saving suggestion?