Problem $11-10$

Refer to Solved Problem $1$ in the textbook. A manager is attempting to put together an

aggregate plan for the coming nine months. She has obtained a forecast of expected

demand for the planning horizon. The plan must deal with highly seasonal demand;

demand is relatively high in perlods $3$ and $4$ and again in perlod $8,$ as can be seen from

the following forecasts:

The department now has $20$ full$-$time employees, each of whom can produce $10$ units of

output per perlod at a cost of $$6$ per unit. Inventory carrying cost is $$5$ per unit per

perlod, and backlog cost is $$10$ per unit per perlod. The manager is considering a plan

that would involve hiring two people to start working in perlod $1,$ one on a temporary

basis who would work only through perlod $5.$ This would cost $$500$ in addition to unit

production costs. Refer to this plan as Plan A$.$

Prepare two additional aggregate plans. For plan B$,$ hire one more worker at a cost of

$$200.$ Make up any shortfall using subcontracting at $$8$ per unit, with a maximum of $20$

units per perlod $($l$.$e$.,$ use subcontracting to reduce back orders when the forecast

exceeds regular output$).$ Note that the ending inventory in perlod $9$ should be zero.

Therefore, Total forecast $-$ Total output $=$ Quantity subcontracted. An additional

constraint is that back orders cannot exceed $80$ units in any perlod. For plan C$,$ assume

no workers are hired $($so regular output is $200$ units per perlod instead of $210$ as in plan

B$).$ Use subcontracting as needed, but no more than $20$ units per perlod.

a$.$ Compute the total cost of each plan. $($Omlt the $"$$$"$ sign In your response.$)$

b$.$ Which plan has the lowest cost?

A

$B*$

C