A Multiperiod Scheduling Example

PM Computers assembles its own brand of personal computers from component parts it purchases overseas and domestically. PM sells most of its computers locally to different departments at State University as well as to individuals and businesses in the immediate geographic region.

PM has enough regular production capacity to produce $160$ computers per week. It can produce an additional $50$ computers with overtime. The cost of assembling, inspecting, and packaging a computer during regular time is $$190.$ Overtime production of a computer costs $$260.$ Furthermore, it costs $$10$ per computer per week to hold a computer in inventory for future delivery. PM wants to meet all customer orders, with no shortages, to provide quality service. PM$\text{'}$s order schedule for the next $6$ weeks is as follows:

$\backslash$table$[[$Week$,$Computert rders$],[1,105],[2,170],[3,230],[4,180],[5,150],[6,250]]$

PM Computers wants to determine a schedule that will indicate how much regular and overtim production it will need each week to meet its orders at the minimum cost. The company wants $n$ inventory left over at the end of the $6-$week period.