Question

Problem # 14 Aggregate and Disaggregate Planning Hershey's collected the following data for 10 periods. It has been provided to determine the total cost of those periods. Use any kind of strategy to determine the cost. Initial Inventory: 200 Production in regular time: 80/person Production in overtime: 40/person Production by sub-contractors: 80/person Production cost in regular time: 100/unit Production cost in over time: 300/unit Production cost by sub-contractor: 400/unit Regular time available resources: 40 Inventory cost per unit per period: $200 Stock out cost per unit per period: $250 Hiring cost per additional resource: $500/person Lay off cost per additional resource: $350 2 Demand 3000 Period 1 4 6 7 9 10 3320 3350 3470 3200 3050 3400 3300 3010 3400

Answer 1

Following is the least-cost (i.e. optimal) strategy

Period	Demand	Workers	Overtime resources	SubC resources	Hire	Layoff	Ending inventory	Stockout	Regular production	Overtime production	Subcontract production	Prod + B.I - E.I + Stockout
0		40					200
1	3,000	35	0	0	0	5	0	0	2,800	0	0	3,000
2	3,320	41	0	0	6	0	0	40	3,280	0	0	3,320
3	3,350	42	0	0	1	0	10	0	3,360	0	0	3,350
4	3,470	43	0	0	1	0	0	20	3,440	0	0	3,470
5	3,200	40	0	0	0	3	0	0	3,200	0	0	3,200
6	3,050	38	0	0	0	2	0	10	3,040	0	0	3,050
7	3,400	42	0	0	4	0	0	40	3,360	0	0	3,400
8	3,300	41	0	0	0	1	0	20	3,280	0	0	3,300
9	3,010	38	0	0	0	3	30	0	3,040	0	0	3,010
10	3,400	42	0	0	1	0	0	10	3,360	0	0	3,400
Totals			0	0	13	14	40	140	32,160	0	0
Marginal costs					$500	$350	$200	$250	$100	$300	$400	Total cost
Cost					$6,500	$4,900	$8,000	$35,000	$3,216,000	$0	$0	$3,270,400

G K M A Overtime SubC Ending Regular Overtime Subcontract Period Demand Workers Hire Layoff Stockout Prod+B.I-E.I+Stockout inventory production production production resourcces resources 200 3 0 до - SUM( J4L 4 ) + H3-H4+14 -SUM(J5 L5 ) + H4-H5+I5 -SUM(J6: L6 ) + H5-H6+16 -C4 * 80 3000 0 0 0 0 D4*40 =E4 * 80 4 1 C3+F4-G4 - C5 80 5 2 3320 C4+F5-G5 0 40 D5 40 -E5*80 D6 40 6 3 3350 -C5+F6-G6 0 10 0 =C6 80 -E6*80 - =D7*40 -SUM(J7L7)+H6-H7+I7 3470 C6+F7-G7 0 1 0 0 20 C7 * 80 E7*80 7 4 -SUM(J8 LS ) + H7-H8+IS -SUM(J9L9 ) + HS-H9+I9 -C8 * 80 - C9* 80 D8*40 8 5 3200 C7+F8-GS 3 0 ES*80 0 -D9*40 9 6 3050 C8+F9-G9 0 10 E9*80 -C10*80 -C11*80 -C12*80 -C13*S0 E10 80 -C9+F10-G10 0 -C10+F11-G11 0 0 40 SUM(J10L10)+H9-H10+I10 10 7 3400 4 0 -D10*40 20 11 S 3300 0 1 0 -D11*40 E11 80 SUMJ11L11)+H10-H11+I11 SUMJ12L12)+H11-H12+I12 -SUMJ13L13)+H12-H13+ I13 E12 80 C11 F12-G12 0 30 12 9 3010 0 0 -D12*40 3400 0 13 10 -C11+F13-G13 0 0 1 0 10 -D13 40 E13 80 14 Totals 15 Marginal costs -SUMD4D13) -SUME4E13) =SUMF4F13)-SUM G4.G13)SUM(H4:H1=SUM14:113) =SUM(J4:J13) -SUM(K4K13) -SUML4L13) 500 100 300 400 350 200 250 Total cost -F14 F15 -G14 G15 - K14 "K15 =H14 "H15 I14 I15 J14 J15 -SUM(F16L16) 16 Cost =L14°L15

Set Objective: SM$16 ES To: OValue Of: 0 Min Max By Changing Variable Cells: $D$4:$I$13 ENS Subject to the Constraints: SF$4:$G$13=integer Add $M$4:$M$13 $B$4:$B$13 Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close