Owens Corning Fiberglas $($OCF$)$ makes several types, weights, and widths of Fiberglas mats from chopped strands of fibreglass for boat hulls on two production lines in a plant$\mathrm{.}4$

Aggregate planning for OCF involves choosing a certain number of shifts $($one to four shifts, or$,$ equivalently, $40,80,120,$ or $160$ hours of operation per week$),$ depending on forecast demand. MPS is determined by optimization, minimizing product changeover, production, and inventory costs. Product changeover takes between $0\mathrm{.}5$ hour and $1$ hour, and is sequence dependent, taking longest for fibreglass type change, and least for width change. Changeover cost includes loss of profit, direct labour, and mat waste.

For simplicity, we will consider only one production line and two products: light $(0\mathrm{.}75$ ounces$/$sq$.$ ft$,76$ inches wide$),$ and heavy $(1\mathrm{.}5$ ounces$/$sq$.$ ft$,76$ inches wide$)$ mats. The forecast for the next eight weeks for light mats is $110,000$ pounds, and for heavy mats is $120,000$ pounds. Given the aggregate plan, the line can make $370,000$ pounds of light or $185,000$ pounds of heavy mats during each of the next eight weeks. Instead of optimization we will use the economic production quantity $($EPQ$)$ for each mat.

A$)$ If product changeover cost from heavy to light is $$1,100$ and from light to heavy is $$1,500,$ holding cost rate is $12$ percent per year, price of light mats is $$0\mathrm{.}75$ per pound, price of heavy mats is $$0\mathrm{.}50$ per pound, and demand occurs $50$ weeks a year, calculate the EPQ for each product.

B$)$ If there are $230,000$ pounds of light and $240,000$ pounds of heavy mats on hand, determine which product will run out first.

C$)$ Using the above results and safety stocks of $110,000$ pounds of light and $120,000$ pounds of heavy mats, plan production of the two products so that neither product's projected on hand dips below its safety stock level and their production lot sizes are as close to their EPQ as possible. That is$,$ if light mats will be short, interrupt the production of heavy mats $($at the end of the week$)$ and start making light mats.