next up previous contents
Next: Discussion. Up: Production over Time Previous: Problem Description


The decisions seem to be how many of each computer to produce in each period at regular time, how many to produce at overtime, and how much inventory to carry in each period. Let's denote our time periods t = 1,2,3,4. Let tex2html_wrap_inline995 be the number of notebooks produced in period t at regular time and tex2html_wrap_inline999 be the number of notebooks produced in period t at overtime. Finally, let tex2html_wrap_inline1003 be the inventory at the end of period t.

Look at the first quarter: how are these variables restricted and related?

Clearly we need tex2html_wrap_inline1007 and tex2html_wrap_inline1009 . Now, anything that starts as inventory or is produced in the period must either be used to meet demand or ends up as inventory at the end of period 1. This means:


For period 2, in addition to the upper bounds, we get the constraint


For period 3, we get


and for period 4 (assuming no inventory at the end):


Our objective charges 2000 for each x, 2200 for each y, and 100 for each i:


Michael A. Trick
Mon Aug 24 14:40:57 EDT 1998