Play Time Toy Company1
Play Time Toy faces a highly seasonal pattern of sales. In the past, Play Time has
used a seasonal production schedule, where the amount produced each month
matches the sales for that month. Under this production plan, inventory is
maintained at a constant level. The production manager, Thomas Lindop, is
proposing a switch to a level, or constant, production schedule. This schedule
would result in significant savings in production costs but would have higher
storage and handling costs, fluctuating levels of inventories, and would also
have implications for financing. Jonathan King, president of Play Time Toy, has
been reviewing pro forma income statements, cash budgets, and balance sheets
for the coming year under the two production scenarios. Table 1 shows the pro
forma analysis under seasonal production, and Table 2 shows the pro forma
analysis under level production.
Greg Cole, chief financial officer of Play Time, prepared the two tables. He
explained that the pro forma analyses in Tables 1 and 2 take fully into account
the 11% interest payments on the unsecured loan from Bay Trust Company and
the 3% interest received from its cash account. An interest charge of 11%/12 on
the balance of the loan at the end of a month must be paid the next month.
Similarly, an interest payment of 3%/12 on the cash balance at the end of a
month is received in the next month.
The inventory available at the end of December 1990 is $530,000 (measured in
terms of cost to produce). Mr. Cole assumed that this inventory represents a sales
value of $530,000/0.651667 = $813,300.
The inventory and overtime costs in Tables 1 and 2 are based on the cost
information developed by Mr. Lindop. This information is summarized in Table
3.
Mr. Cole further explained how the cost information was used in the pro forma
analyses. For example, in Table 1, the production in August is $1,458,000. The
overtime cost in August is therefore calculated to be $61,000 (=0.15 x (1,458,000 1,049,000)). Play Time uses LIFO (last-in, first-out) accounting, so overtime costs
From Practical Management Science (2nd ed., Winston and Albright, 2001 Duxbury Press, p.
490-492; Case 9.1).
1
are always charged in the month that they occur.2 The annual overtime cost for
the seasonal production plan is $435,000. In Table 2, under level production,
finished goods worth $5,164,000 are in inventory at the end of July. The
inventory cost for the month is $20,000 (=0.07/12 x (5,164,000 - 1,663,000)). The
annual inventory cost for the level production plan is $100,000.
Mr. Lindop felt that a minimum of $813,300 of inventory (measured in terms of
sales value, or $530,000 measured in terms of cost to produce) must be kept on
hand at the end of each month. This inventory level represents a reasonable
safety stock, required since orders do not occur uniformly during a month.
Mr. King was impressed at the possible increase in profit from $237,000 under
the seasonal production plan to $373,000 under level production. While studying
the pro forma projections, Mr. King realized that some combination of the two
production plans might be even better. He asked Mr. Lindop to try to find a
production plan with a higher profit than the seasonal and level plans.
Mr. Lindop proceeded to develop a spreadsheet-based linear programming
model to maximize annual net profit.
Questions
Note: Mr. Lindop's model is contained in the file playtime.xls. The spreadsheet is
ready to be optimized, but it has not been optimized yet.
1.
Run the optimization model in the file playtime.xls. What is the
optimal production plan? What is the optimal annual net profit? How
does this optimal production plan compare to the seasonal and level
production plans?
2.
Suppose that Play Time's bankers will not extend any credit over $1.9
million — in other words, the loan balance in any month cannot
exceed $1.9 million. Modify the spreadsheet model to take into account
this restriction. What is the optimal production plan in this case? What
is the optimal annual net profit?
3.
Annual profit is a measure of reward for Play Time Toy. The
maximum loan balance is a measure of risk for the bank. Construct a
trade-off curve between optimal annual profit and the maximum loan
balance.
This assumes that overtime production is used only to satisfy current demand and not to build
up inventory.
2
B60.2350
2
Prof. Juran
Table 1: Seasonal Production (Annual net profit = 237)
Production (sales value)
Inventory (sales value)
INCOME STATEMENT
Net sales
Cost of goods sold
Materials & regular wages
Overtime wages
Gross profit
Operating expenses
Inventory cost
Profit before int & taxes
Net interest payments
Profit before taxes
Taxes
Net profit
BALANCE SHEET
Cash
Accts receivable
Inventory
Net P/E
Total Assets
Accts payable
Notes payable
Accrued taxes
Long term debt
Equity
Total liab & equity
B60.2350
Actual
Dec 1990
850
813
Actual
Dec 1990
175
2,628
530
1,070
4,403
255
680
80
450
2,938
4,403
Jan
108
813
Jan
108
Feb
126
813
Feb
126
Mar
145
813
Mar
145
Apr
125
813
Apr
125
May
125
813
May
125
Projected for 1991
June
July
Aug
125
145
1,458
813
813
813
June
July
Aug
125
145
1,458
Sept
1,655
813
Sept
1,655
Oct
1,925
813
Oct
1,925
Nov
2,057
813
Nov
2,057
Dec
1,006
813
Dec
1,006
Total
9,000
70
0
38
188
0
(150)
10
(160)
(55)
(106)
82
0
44
188
0
(144)
2
(146)
(50)
(97)
94
0
51
188
0
(137)
1
(138)
(47)
(91)
81
0
44
188
0
(144)
1
(146)
(50)
(96)
81
0
44
188
0
(144)
2
(146)
(50)
(97)
81
0
44
188
0
(144)
2
(147)
(50)
(97)
1,079
91
486
188
0
298
7
290
99
192
1.254
131
539
188
0
351
18
333
113
220
1,340
151
565
188
0
377
19
359
122
237
656
0
350
188
0
162
19
144
49
95
5,865
435
2,700
2.256
0
444
86
358
122
237
Feb
1,365
234
530
1,070
3,199
38
0
(24)
450
2,736
3,199
Mar
1,116
271
530
1,070
2,987
44
0
(151)
450
2,644
2,987
Apr
934
270
530
1,070
2,804
38
0
(232)
450
2,548
2,804
May
808
250
530
1,070
2,658
38
0
(282)
450
2,452
2,658
Projected for 1991
June
July
Aug
604
450
175
250
270
1,603
530
530
530
1,070
1,070
1,070
2,454
2,320
3,378
38
44
437
0
0
408
(363)
(411)
(324)
425
425
425
2,355
2,263
2,431
2,454
2,320
3,378
Jan
782
958
530
1,070
3,340
32
0
25
450
2.832
3,340
3
94
0
51
188
0
(137)
2
(140)
(48)
(92)
950
61
447
188
0
259
3
256
87
169
Sept
175
3,113
530
1.070
4,888
497
1,600
(256)
425
2,623
4,888
Oct
175
3,580
530
1,070
5,355
578
1,653
(143)
425
2,843
5,355
Nov
175
3,982
530
1,070
5,757
617
1,656
(21)
425
3,080
5,757
Total
9,000
Dec
175
3,063
530
1,070
4,838
302
966
(4)
400
3,175
4,838
Prof. Juran
Table 2: Level Production (Annual net profit = 373)
Production (sales value)
Inventory (sales value)
INCOME STATEMENT
Net sales
Cost of goods sold
Materials & regular wages
Overtime wages
Gross profit
Operating expenses
Inventory cost
Profit before int & taxes
Net interest payments
Profit before taxes
Taxes
Net profit
BALANCE SHEET
Cash
Accts receivable
Inventory
Net P/E
Total Assets
Accts payable
Notes payable
Accrued taxes
Long term debt
Equity
Total liab & equity
B60.2350
Actual
Dec 1990
850
813
Actual
Dec 1990
175
2,628
530
1,070
4,403
255
680
80
450
2,938
4,403
Jan
750
1,455
Jan
108
Feb
750
2,079
Feb
126
Mar
750
2,684
Mar
145
Apr
750
3,309
Apr
125
May
750
3,934
May
125
Projected for 1991
June
July
Aug
750
750
750
4,559
5,164
4,456
June
July
Aug
125
145
1,458
Sept
750
3,551
Sept
1,655
Oct
750
2,376
Oct
1,925
Nov
750
1,069
Nov
2,057
Dec
750
813
Dec
1,006
Total
9000
70
0
38
188
0
(1501
10
(160)
(55)
(106)
82
0
44
188
2
(147)
3
(149)
(51)
(99)
94
0
51
188
6
(143)
2
(146)
(50)
(96)
81
0
44
188
10
(154)
5
(159)
(54)
(105)
81
0
44
188
13
(158)
10
(168)
(57)
(111)
81
0
44
188
17
(161)
15
(177)
(60)
(117)
1,079
0
576
188
11
377
32
346
118
228
1,254
0
671
188
4
478
37
441
150
291
1,340
0
717
188
0
529
31
498
169
329
656
0
350
188
0
162
22
141
48
93
5,865
0
3,135
2,256
100
779
214
565
192
373
Apr
175
270
2,157
1,070
3,672
225
704
(240)
450
2,533
3,672
May
175
250
2,564
1,070
4,059
225
1,259
(297)
450
2,422
4,059
Jan
556
958
948
1,070
3,533
225
0
25
450
2,832
3,533
Feb
724
234
1,355
1,070
3,383
225
0
(25)
450
2,734
3,383
Mar
175
271
1,749
1,070
3,265
225
108
(155)
450
2,637
3,265
4
94
0
51
188
20
(158)
21
(179)
(61)
(118)
Projected for 1991
June
July
175
175
250
270
2,971
3,365
1,070
1,070
4,466
4,880
225
225
1,900
2,493
(389)
(450)
425
425
2,305
2,187
4,466
4,880
950
0
508
188
16
304
26
277
94
183
Aug
175
1,603
2,904
1,070
5,752
225
3,087
(355)
425
2,370
5,752
Sept
175
3,113
2.314
1,070
6,672
225
3,693
(269)
425
2,599
6,672
Oct
175
3,580
1,549
1,070
6,374
225
2,953
(119)
425
2,890
6,374
Nov
175
3,982
697
1,070
5,924
225
2,005
50
425
3,218
5,924
Total
9,000
Dec
175
3.063
530
1,070
4,838
225
836
66
400
3,311
4,838
Prof. Juran
Play Time Cost Information

Gross margin. The Cost of goods sold (excluding overtime costs) is 65.1667% of
sales under any production schedule. Materials costs are 30% of sales. All other
non-materials costs, including regular wages but excluding overtime wages, are
35.1667% of sales.

Overtime cost. Running at capacity but without using any overtime, the plant
can produce $1,049,000 of monthly sales. Units produced in excess of this
capacity in a month incur an additional overtime cost of 15% of sales. (The
monthly production capacity of the plant running on full overtime is $2,400,000
of sales. Since November has the maximum level of projected sales at $2.057.000,
the capacity on full overtime should never pose a problem.)

Inventory cost. The plant has a limited capacity to store finished goods. It can
store $1,663,000 worth of sales at the plant. Additional units must be moved and
stored in rented warehouse space. The cost of storage, handling, and insurance of
finished goods over this capacity is 7% of the sales value of the goods per year, or
7%/12 per month.
B60.2350
5
Prof. Juran