Chapter 9 - Chapter 9 Planning Supply and Demand in the...

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Chapter 9: Planning Supply and Demand in the Supply Chain: Managing Predictable Variability We define a comprehensive set of decision variables that are utilized in problems 9-1 to 9-3 depending on the problem context. Decision Variables: H t = # of workers hired in month t (t = 1,..,12) L t = # of workers laid-off in month t (t = 1,..,12) W t = # of workers employed in month t (t = 1,..,12) O t = # of hours of overtime in month t (t = 1,..,12) I t = # of units held in inventory at the end of month t (t = 1,..,12) C t = # of units subcontracted in month t (t = 1,..,12) P t = # of units produced in month t (t = 1,..,12) Parameters: D t = # of units demanded in time period t (t = 1,…12) Problem 9-1 : Minimize = = = = + + + 12 1 12 1 12 1 12 1 40 3 22 2400 i t i t i t t t P I O W Subject to: Inventory constraints: 12 ,.., 1 , 1 = = - + - t D I P I t t t t 4000 12 0 = = I I Overtime constraints: 12 ,..., 1 , 0 20 = - t W O t t Production constraints: 12 ,... 1 , 0 160 2 = - - t W O P t t t Workforce constraints: 12 ,..., 0 , 250 = = t W t (a) Worksheet 9-1 provides the solution to this problem and the corresponding aggregate plan. The total cost of the plan is $16,820,000
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(b) From the table below we can see that it is better to promote in April than in July, as the profit is slightly higher. Price=$125 Total Cost r r r No promotion Promotion (April) Promotion (July) Total Cost = $16,820,000 $17,059,400 $17,367,300 Total Revenue = $28,500,000 $28,916,625 $29,198,750 Profit = $11,680,000 $11,857,225 $11,831,450 Profit increase = $177,225 $151,450 (c) If a sink is sold at $250, then the profit associated with promotion in July is higher than in April. So, as the product margin increases it is more beneficial to offer the discount in high demand period. Price= $250 Total Cost r r r No promotion Promotion (April) Promotion (July) Total Cost = $16,820,000 $17,059,399.94 $17,367,299.95 Total Revenue = $57,000,000 $57,833,250 $58,397,500 Profit = $40,180,000 $40,773,850.06 $41,030,200.05 Profit increase = $593,850.06 $850,200.05 Problem 9-2 : We now include hiring and layoff costs in the model. Note that the workforce level constraints also change. Minimize = = = = = = + + + + + 12 1 12 1 12 1 12 1 12 1 12 1 40 3 22 2400 2000 1000 i t i t i t t t t t t t P I O W F H Subject to: Inventory constraints: 12 ,.., 1 , 1 = = - + - t D I P I t t t t 4000 12 0 = = I I Overtime constraints: 12 ,..., 1 , 0 20 = - t W O t t Production constraints: 12 ,... 1 , 0 160 2 = - - t W O P t t t
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Workforce constraints: 12 ,..., 1 , 0 1 = = + - - - t L H W W t t t t 250 0 = W (a) Total Cost = $ 16,571,000 Total Revenue = $ 28,500,000 Profit = $ 11,929,000 Period Productio n 0 $ 1 20,000 2 20,000 3 20,000 4 20,000 5 20,000 6 20,000 7 20,000 8 20,000 9 20,000 10 18,000 11 15,000 12 15,000 (b) Promotion in July is better. Profit increases to $218,900.1 Total Cost r r r No promotion Promotion (April) Promotion (July) Total Cost = $16,571,000 $16,794,500 $17,050,850 Total Revenue = $28,500,000 $28,916,625 $29,198,750 Profit = $11,929,000 $12,122,125 $12,147,900 Profit increase= 0 $193,125.1 $218,900.1 (c)
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