A company faces a firm schedule of delivery commitments for a product over the next six months. The production cost varies by month due to anticipated changes in materials costs. The company's production capacity is 100 units per month on regular time and up to 15 additional units per month on overtime.
Table 1 contains delivery requirements and production costs by month. The cost of carrying an unsold unit in stock is $2 per month. The problem for the company is to determine the number of units to produce in regular time and overtime each month to meet requirements at minimum cost. The firm has no units at the beginning of month 1 and wishes to have no units on hand at the end of month 6.
|Cost per unit in regular time ($)||30||30||32||32||31||32|
|Cost per unit in overtime ($)||35||35||37||37||36||37|
Table 1: Requirement and costs
|Number of units at the beginning of month 1||0|
|Number of unit at the end of the moth 6||0|
|Maximal month production in regular time||100 units|
|Maximal month production in overtime||15 units|
|Cost of unsold unit month stocking||2 $ per unit and month|
Table 2: Production and stocking characteristics