Sample_quiz2_solutions

# Month working days net demand production required

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backorders are allowed, and all demand is met during the six months. Month Working days Net Demand Production Required workers Hiring/ Layoffs Workforce Cost Holding Cost Backorder Cost Production Cost July 21 760 935 10 Layoff 2 \$ 16,000 \$ 1,225 \$ - \$ 327,250 August 22 990 935 10 \$ 16,000 \$ 840 \$ - \$ 327,250 September 21 840 935 10 \$ 16,000 \$ 1,505 \$ - \$ 327,250 October 23 1040 935 10 \$ 16,000 \$ 770 \$ - \$ 327,250 November 19 1290 935 10 \$ 16,000 \$ - \$ 8,575 \$ 327,250 December 20 690 935 10 \$ 16,000 \$ - \$ - \$ 327,250 Grand Total 5610 Total Cost \$ 5,200 \$ 96,000 \$ 4,340 \$ 8,575 \$ 1,963,500 \$ 2,077,615 (c) Which of the two solutions above would you recommend to L-Print Management? Justify your answer. The level strategy is cheaper, and has far less layoffs, although we do have a shortage of 245 units for one month (November). If the \$35 is a true reflection of the shortage cost, then we should go with the level strategy. 17

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(d) Formulate the aggregate planning problem for L-Print as a linear programming model assuming no backordering is allowed. Be sure to define all variables and include all of the required constraints. Define: H t = # hires, beginning of pd. t L t = # layoffs, beginning of pd. t WF t = # workers in pd. t X t = production, pd. t I t = inventory, end pd. t D t = net demand pd. t WD t = working days, pd. t Min 6 6 6 6 1 1 1 1 2000 2600 1600 7 t t t t t t t t H L WF I = = = = + + + I t -1 + X t = D t + I t , t = 1, …, 6, WF t = WF t -1 + H t L t , t = 1, …, 6, X t 5 WD t * WF t , t = 1, …, 6 X t H t , I t , L t , WF t 0, t = 1, …, 6. 18
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