A company wishes to plan its production with seasonal demands over a 12-month pe

Question

A company wishes to plan its production with seasonal demands over a 12-month period. The monthly demandof theproduct is100,000 unitsduring the monthsof October, November, and December; 10,000 units during the months of January, February, March, and April; and 30,000 units during the remaining months. Suppose that the unit product cost is $5.00, provided that it is manufactured from the beginning of Janurary to end of June. From July to end of December, the unit costs are reduced to $4 because of the installation of an improved manufacturing system. The total units that can be manufactured during any particular month cannot exceed 120,000 for Jan-Sept, and 150,000 for Oct-Dec. The inventory cost per unit during any month is $0.20. Assume that the item is perishable and can only be stored for future sales by at most two months. For example, an item produced in beginning of January can be sold in January and February, but not in March.

1. Formulate the production scheduling problem so that the total cost of production and inventory is minimized.

2. Write the model using Xpress or another software.

(Has to be soft-coding)

Explanation / Answer

Particuler January February March April May June July August September October November December Demand            10,000            10,000            10,000            10,000            30,000            30,000            30,000            30,000            30,000         1,00,000         1,00,000         1,00,000 Cost                       5                       5                       5                       5                       5                       5                       4                       4                       4                       4                       4                       4 Inventoy cost 0.2 Capicity        1,20,000        1,20,000        1,20,000        1,20,000        1,20,000        1,20,000        1,20,000        1,20,000        1,20,000         1,50,000         1,50,000         1,50,000 Production quanity I each month                     -              10,000            10,000            10,000            30,000            30,000            30,000            30,000            30,000         1,00,000         1,00,000         1,10,000              2,000 50000 50000 50000 150000 150000 120000 120000 120000 400000 400000 400000 Total Cost      20,12,000 Total quaniy produced        4,90,000 Total Demand        4,90,000 Cost per Unit                 4.11 Note Since product perishes in 2 months, it is suggested to produce 10,000 additional quanit in December and carry forward the same for Next year January.

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