EXAMPLE $2-4$

Recall the hardware supply warehouse from the previous example. Now, rather than delivering $1,000$ units of a specialized fastener to a local manufacturing company each week, the company has contractually committed to delivering a different number of units each week for $10$ weeks:

$\backslash$table$[[$Week$,1,2,3,4,5,6,7,8,9,10],[$Demand$,500,700,1,000,800,900,500,300,400,800,1,100]]$

Each time the warehouse places an order for these items from its supplier, an ordering and transportation fee of $$20$ is charged to the warehouse. The warehouse pays $$1\mathrm{.}00$ for each fastener and charges the local firm $$5\mathrm{.}00$ for each fastener. Annual holding cost is $25$ percent of inventory value. or $$0\mathrm{.}25$ per year $($which works out to about $$0\mathrm{.}005$ per week$).$ The warehouse manager would like to know how much to order for each of the $10$ weeks.

This question can be answered using the tools of mathematical optimization, and it turns out that it is optimal to order in weeks units$),$ units$),$ and $9(1,900$ units$).$ The total cost of this strategy is $$7,099\mathrm{.}43.$ By way of comparison, a strategy of ordering every week to meet demand in that week costs $$7,200,$ ordering every other week costs $$7,116\mathrm{.}83,$ and ordering in the first week to meet all $10$ weeks of demand will cost $$7,174\mathrm{.}33.$