The Aggregate Planning Problem.
Emily's Cookie Company makes a variety of chocolate chip cookies in their plant in Chicago. Based on orders received and forecasts ofbuying habits, it is estimated that the demand for the next four months is 850, 1,260, 510,and 980, expressed in thousands of cookies. Each worker can produce 308 cookies per day.Assume that the number of workdays in each of the next four months is 20 days. There arecurrently 100 workers employed, and there is no starting inventory of cookies. Workers arepaid $5500 per month. The cost of hiring one worker is $150; the cost of firing one workeris $200; the cost of holding one cookie in inventory for one month is 8 cents. Backlogs(stockouts) are permitted only in months 1 through 3, at a cost of 20 cents per cookie permonth, and backorders must be filled the following month; no backlogs are permitted atthe end of month 4. Emily can subcontract up to 20,000 cookies per month at a cost of$300 per thousand cookies. At the end of month 4, there must be at least 10,000 cookies in inventory.
Using Microsoft Excel, solve:
a) as a linear programming problem.
b) as a mixed integer programming problem, where all variables representing theworkforce size per period (Wt), the number of employees hired at the beginning of each period (Ht), and the number of employees laid off at the beginning of each period (Lt)must be integers.