linear programming model to compute an optimal production policy
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Part I
During the next four months Shoeco must meet, on time, the following demands for pairs of shoes: 300 in month 1; 500 in month 2; 100 in month 3; and 100 in month 4. At the beginning of month 1, 50 pairs of shoes are on hand, and Shoeco has three workers. A worker is paid $1500 per month. Each worker can work up to 160 hours a month before he or she receives overtime. A worker may be required to work up to 20 hours of overtime and is paid $25 per hour for overtime. It takes four hours of labor and $5 of raw material to produce a pair of shoes. At the beginning of each month workers can be hired or fired. Hiring costs are $1600 per worker and firing costs are $2000 per worker. At the end of each month, a holding cost of $30 is charged for each pair left in inventory. Production in a given month can be used to meet that months demand. Use LP to determine an optimal production and labor policy.
Part II
Assuming backlogs are allowed and that it costs $25 for each pair backlogged, adjust the above model to include that aspect.
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Solution Summary
The solution presents explanations and calculations to arrive at an optimal production policy.
Solution Preview
The key to this problem is realizing that there are two variables to solve: the number of workers and the number of hours of overtime. Solver accommodates allowing two variables. Here is the set-up in excel. Look at the formulas in the cells to get a grasp of ...
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