The Hickory Flat Sawmill $($HFS$)$ makes four kinds of lumber in one mill. Orders come from a variety of lumber companies to a central warehouse. Whenever the warehouse hits the reorder point, an order is placed to HFS$.$ Pappy Red, the sawmill manager, has set the lot sizes to be run on the mill on the basis of historical demands and common sense. The smallest amount made is a lot of $1,000$ board$-$feet $(1kbf).$ The time it takes to process a lot depends on the product, but the time does not vary more than $25$ percent from the mean. The changeover time can be quite long depending on how long it takes to get the mill producing good product again. The shortest time that anyone can remember is $2$ hours. Once it took all day $(8$ hours$).$ Most of the time it takes around $4$ hours. Demand data and run rates are given in Table $15\mathrm{.}10.$ The mill runs productively $8$ hours per day, $5$ days per week $($assume $4\mathrm{.}33$ weeks per month$).$

The lot sizes are $50$ of the knotty $110,34$ for the clear $14,45$ for the clear $16,$ and $40$ for the rough plank. Lots are run on a first$-$come, first$-$served basis as they arrive from the warehouse. Currently the average response time is nearly $3$ weeks $(14\mathrm{.}3$ working days$).$