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Case: PRODUCTION AT MARQUIP

Marquip Manufacturing produces heads for engines used in the manufacture of trucks. The

production line is highly complex, and it measures $900$ feet in length. Two types of engine

heads are produced on this line: the P$-$Head and the H$-$Head. The P$-$Head is used in heavy

duty trucks and the H$-$Head is used in smaller trucks. Because only one type of head can be

produced at a time, the line is set up to manufacture either the $P-$Head or the $H-$Head, but not

both. Changeovers are made over a weekend; costs are $$500$ in going from a setup for the $P-$

Head to a setup for the H$-$Head, and vice versa. When set up for the P$-$Head, the maximum

production rate is $100$ units per week and when set up for the H$-$Head, the maximum

production rate is $80$ units per week.

Marquip just shut down for the week after using the line to produce the P$-$Head. The manager

wants to plan production and changeovers for the next eight weeks. Currently, Marquip's

inventory consists of $125P-$Heads and $143H-$Heads. Inventory carrying costs are charged at

an annual rate of $19\mathrm{.}5$ percent of the value of inventory. The production cost for the $P-$Head is

$$225,$ and the production cost for the $H-$Head is $$310.$ The objective in developing a

production schedule is to minimize the sum of production cost, plus inventory carrying cost,

plus changeover cost.

Marquip received the following requirements schedule from its customer $($an engine

assembly plant$)$ for the next nine weeks:

Safety stock requirements are such that week$-$ending inventory must provide for at least $80$

percent of the next week's demand.

Question:

Prepare a report for Marquip's management with a production and changeover schedule for

the next eight weeks. Be sure to note how much of the total cost is due to production, how

much is due to inventory, and how much is due to changeover.

$($Note: Provide all relevant details of the mathematical models used for your analysis$)$