The production manager of a manufacturing company has to devise a production plan for item AK102 for the next four months. The item is to be produced at most once monthly; because of capacity limitations the monthly production may not exceed 10 units. The cost of one setup for any positive level of production in any month is $10.
The demand for this item is uncertain and varies from month to month; from past experience, however, the manager concludes that the demand in each month can be approximated by a Poisson distribution with parameter λn (n shows the month to which the distribution refers).
Inventory is counted at the end of each month and a holding cost of $10 is charged for each unit; if there are stock outs, a penalty of $20 is charged for every unit out of stock. There is no initial inventory and no outstanding back-orders; no inventory is required at the end of the planning period. Assume that the production lead time is short so that the amount released for production in one month can be used to satisfy demand within the same month. What is the optimal production plan, assuming that the optimality criterion is the minimum expected cost? Assume that λ1= 3, λ2 = 5, λ3 = 2, λ4 = 4 units.