$1.(4$ pts$-1$ point each part$)$ Specialty Coffee Shop uses $4$ pounds of a specialty tea weekly; each pound costs $$18.$ Carrying costs are $$1\mathrm{.}2$ per pound per week because space is very scarce. It costs the firm $$8$ to prepare an order. Assume the basic EOQ $$applies$.$ Assume $52$ weeks per year, closed on Mondays.

$($a$)$ How many pounds should Specialty $$order at a time?

$($b$)$ What is total annual cost $($excluding item cost$)$ of managing this item on a cost$-$minimizing basis?

$($c$)$ In pursuing lowest annual total cost, how many orders should Specialty place annually?

$($d$)$ How many days will there be between orders $($assume $312$ operating days$)$ if Specialty practices EOQ behavior?

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WORK:

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ANSWERS:

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Formula used

Answer

a

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c

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d

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$2.(2$ pts$)$ Consider a product with a daily demand of $500$ units, a setup cost per production run of $$100,$ a daily holding cost per unit of $$0\mathrm{.}20,$ and an annual production rate of $219,000$ units. The firm operates and experiences demand $365$ days per year. Suppose that management mistakenly used the basic EOQ model to calculate the batch size instead of using the production order quantity model. How much money per year has that mistake cost the company if any?

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$3.(2$ points$)$ The Winfield Distributing Company has maintained an $80\%$ service level policy for inventory of string trimmers. Mean demand during lead time is $150$ trimmers, and the standard deviation during lead time is $50$ trimmers. The annual cost of carrying one trimmer in inventory is $$6.$ The area salespeople have recently told Winfield's management that they could expect a $$400$ improvement in profit $($based on current figures of cost per trimmer$)$ if the service level were increased to $99\%.$ Is it worthwhile for Winfield to make this change?

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$4.(4$ pts$)$ An airport is trying to balance where to place the three subgroups $($local $($A$),$ regional $($B$),$ and national $($C$))$ for an airline. The distance between terminals and the number of trips that travelers make between subgroups for flight connections per day are listed. Find the assignment that minimizes the distance travelers must walk if you assigned A to Terminal $2,$ B to $3$ and C to $1.$

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Airline

A

B

C

Trips to A

$--$

$60$

$90$

Trips to B

$90$

$--$

$70$

Trips to C

$60$

$40$

$--$

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Terminal

$1$

$2$

$3$

Distance to Terminal $1$

$--$

$3000$

$5000$

Distance to Terminal $2$

$3000$

$--$

$7000$

Distance to Terminal $3$

$5000$

$7000$

$--$

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$5.(8$ pts$,2$ points each part$)$ You have been asked to balance a flow shop assembly operation to achieve an output rate of $150$ units per eight$-$hour day. Task times and precedence relationships are shown in the table below.

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Task

Predecessor$($s$)$

Duration $($minutes$)$

A

$--$

$1\mathrm{.}4$

B

$--$

$0\mathrm{.}8$

C

A$,$ B

$0\mathrm{.}4$

D

$--$

$1\mathrm{.}8$

E

$--$

$0\mathrm{.}4$

F

C

$3\mathrm{.}0$

G

E$,$ F

$2\mathrm{.}0$

H

D$,$ G

$1\mathrm{.}2$

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$($a$)$ Draw the precedence diagram.

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$($b$)$ Determine the desired cycle time.

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$($c$)$ Determine the theoretical minimum number of stations needed.

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$($d$)$ Balance this line using the smallest processing time heuristic.

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$($e$)$ What is the efficiency of the line obtained in part d$?$