Chopra/Meindl 4/e
CHAPTER NINE
Case Questions
1. Which option delivers the maximum profit for the supply chain: Sandra’s plan,
Bill’s plan, or no promotion at all?
The bottom-line results for the three plans are:
Bill’s plan
$49,380,240
Sandra’s plan $48,972,440
No Promotion $47,664,204
Slightly different results can be obtained if all decision variables are declared as
integers.
The plans for the three approaches follow:
The original plan
Month
Beginning Inventory
Regular Production
Overtime
Production
Max OT Production
Overtime Cost
Subcontract
Subcontract Cost
Total Production
July
50000
90240
0
August
40240
90240
0
September
20507
109440
0
October
77
179840
0
November
2
274560
0
December
24663
275200
0
22560
$0
0
$0
90240.0
22560
$0
27
$486
90267.0
27360
$0
130
$2,340
109570.0
44960
$0
85
$1,530
179925.0
68640
$0
101
$1,818
274661.0
68800
$0
137
$2,466
275337.0
Demand
100000
110000
130000
180000
250000
300000
Ending Inventory
Holding Cost
Backorder
Stockout Cost
40240
$160,960
0
$0
20507
$82,028
0
$0
77
$308
0
$0
2
$8
0
$0
24663
$98,652
0
$0
0
$0
0
$0
Work Force
Regular Time Cost
Number Hired
Hiring Cost
Number Laid Off
Layoff Cost
141
$338,400
0
$0
159
$795,000
141
$338,400
0
$0
0
$0
171
$410,400
30
$90,000
0
$0
281
$674,400
110
$330,000
0
$0
429
$1,029,600
148
$444,000
0
$0
430
$1,032,000
1
$3,000
0
$0
Chopra/Meindl 4/e
Sandra’s Plan
Month
Beginning Inventory
Regular Production
Overtime Production
Max OT
Overtime Cost
Subcontract
Subcontract Cost
Total Production
July
50000
161280
75
40320
$1,688
123
$2,214
161478
August
111478
161280
0
40320
$0
123
$2,214
161403
September
162881
161280
73
40320
$1,643
63
$1,134
161416
October
297
161280
0
40320
$0
81
$1,458
161361
November
35658
219520
76
54880
$1,710
113
$2,034
219709
December
80367
219520
24
54880
$540
89
$1,602
219633
Demand
100000
110000
324000
126000
175000
300000
Ending Inventory
Holding Cost
Backorder
Stockout Cost
111478
$445,912
0
$0
162881
$651,524
0
$0
297
$1,188
0
$0
35658
$142,632
0
$0
80367
$321,468
0
$0
0
$0
0
$0
Work Force
Regular Time Cost
Number Hired
Hiring Cost
Number Laid Off
Layoff Cost
252
$604,800
0
$0
48
$240,000
252
$604,800
0
$0
0
$0
252
$604,800
0
$0
0
$0
252
$604,800
0
$0
0
$0
343
$823,200
91
$273,000
0
$0
343
$823,200
0
$0
0
$0
$1,294,614
$1,258,538
$608,765
$748,890
$1,421,412
$825,342
Monthly Costs
Chopra/Meindl 4/e
Bill’s plan
Month
Beginning Inventory
Regular Production
Overtime
Production
Max OT
Overtime Cost
Subcontract
Subcontract Cost
Total Production
July
50000
186880
0
August
136880
186880
0
September
213760
186880
0
October
270640
186880
0
November
277520
187520
0
December
40
210560
0
46720
$0
0
$0
186880
46720
$0
0
$0
186880
46720
$0
0
$0
186880
46720
$0
0
$0
186880
46880
$0
0
$0
187520
52640
$0
0
$0
210560
Demand
100000
110000
130000
180000
465000
210000
Ending Inventory
Holding Cost
Backorder
Stockout Cost
136880
$547,520
0
$0
213760
$855,040
0
$0
270640
$1,082,560
0
$0
277520
$1,110,080
0
$0
40
$160
0
$0
600
$2,400
0
$0
Work Force
Regular Time Cost
Number Hired
Hiring Cost
Number Laid Off
Layoff Cost
292
$700,800
0
$0
8
$40,000
292
$700,800
0
$0
0
$0
292
$700,800
0
$0
0
$0
292
$700,800
0
$0
0
$0
293
$703,200
1
$3,000
0
$0
329
$789,600
36
$108,000
0
$0
Monthly Costs
$1,288,320
$1,555,840
$1,783,360
$1,810,880
$706,360
$900,000
Monthly Sales
$5,000,000
$5,500,000
$6,500,000
$9,000,000
$20,925,000
$10,500,000
2. How does the answer change if a discount of $10 must be given to reach the same
level of impact that the $5 discount received?
Both plans suffer from the additional discount; Bill’s plan on a percentage basis is
a slightly larger decline than Sandy’s.
Bill’s plan
$46,969,480 – a decline of $2.4 million
Sandra’s plan $46,867,040 – a decline of $2.1 million
From a production floor perspective, Bill’s plan switches to a virtually level labor
force with a shortfall of 40 units made up by subcontracting in the last month.
Sandra’s plan also features greater labor stability with far less subcontracting until
December, when 200 units are subcontracted.
3. Suppose Sandra’s fears about increasing outsourcing costs come to fruition and
the cost rises to $22/unit for subcontracting. Does this change the decision when
the discount is $5?
Chopra/Meindl 4/e
Sandra’s plan rings up $48,903,800 by laying off 43 workers in July, hiring 75 in
November and another 3 in December, and subcontracting 200 units in December.
Bill’s plan results in a profit of $49,966,611 and has significant fluctuations in the
labor pool; 174 workers are laid off in July, 103 and 206 are hired back in
September and October respectively. Overtime production exceeds subcontracting
production throughout the planning period.