Example 1
Given the needed data for definite strategy:
1- Forecast or demand for each month,
2- Production days for each month,
345678-
No. of Workers (work force size also called labor),
Regular Worker payroll and over time payroll = $ ,
Hiring labor cost and layoff labor (firing) cost = $ ,
Carrying inventory cost per time , beginning inventory value and storage cost,
Unit production cost = $,
Subcontract cost or expenses = $
month
Demand
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
1
220
90
210
396
616
700
378
220
200
115
95
260
Production
days
2
22
18
21
22
22
20
21
22
20
23
19
20
Total
3500
250
Dem. Per day
(d/d)
3
220/22=10
5
10
18
28
35
18
10
10
5
5
13
Cum. prd.
Days
4
22
22+18=40
40+21=61
83
105
125
146
168
188
211
230
250
Cumulative
Demand
5
220
220+90=310
310+…=520
916
1532
2332
2610
2830
3030
3145
3240
3500
a- To draw the graph between cum. Demand and time: cum. production days(between the last two
columns ), the average production requirement must be first calculated:
Average production requirement = total demand / total prod. Days = 3500/250 = 14 units/day.
1
b- To draw the histogram graph between the cum. Demand and production days (or the cumulative
prod. Days )
c- Plan 1- Level Strategy with stockpile inventory plan:
month
Demand
1
Produc
tion
days
2
Prod. Quantity
per day(14
units)
3
Jan.
220
22
14x22=308
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Total
90
210
396
616
700
378
220
200
115
95
260
3500
18
21
22
22
20
21
22
20
23
19
20
250
14x18=252
294
308
308
280
294
308
280
322
266
280
3500
Max. Inventory = 900 units , and
Inventory
(prod. demand)
308-220
= +88
+162
+84
- 88
- 308
- 420
- 84
+ 88
+ 80
+ 207
+ 171
+ 20
Ending
Inventory
Balance
88
88+162=250
250+84=334
334-88=246
- 62
- 482
- 566
-478
- 398
-191
- 20
0
Max. Shortage = - 566 units
Average inventory balance= 5513 / 12 = 459.4 = 460 units.
The carrying cost / year = $ 20% of average inventory value.
= ( % x unit cost )x (aver. Inventory)
The storage costs (based on max. inv. at any one time) = $ 0.90 / unit cost.
= (% x maximum inventory value)
2
Ending
Inventory
Balance with
566 on first
month
566+88=654
645+162=816
900
812
504
84
0
88
168
375
546
566
5513
Max. inventory
Max. shortage
Inventory cost = carrying cost + storage cost
= 0.20 x 460 x $ 100 + $ 0.90 x 900 = $ 10010
d-
Plan 2- Chase strategy with Varying Employment( by hiring and firing labor) :
= $ 12000 (as given). You have to check and continue the solution…
Demand
Production
days
1-Jan.
2-Feb.
3-Mar.
4-Apr.
5-May
6-Jun.
7-Jul.
8-Aug.
1
220
90
210
396
616
700
378
220
2
22
18
21
22
22
20
21
22
Prod.
Quantity per
day(10 units)
3
220
180
210
220
220
200
210
220
9-Sep.
-10Oct.
11-Nov.
12-Dec.
200
115
95
260
20
23
19
20
200
230
190
200
Total
3500
250
2500
workers
needed
Labor
hiring
Labor
firing
(start #10 )
12
8
11
12
12
10
11
12
10
13
9
10
Cost of
hiring and
lay off
workers
+12
-4
+3
+1
0
-2
+1
+1
-2
+3
-4
+1
e- Plan 3- mixed strategy with subcontract: level strategy with subcontract
- Production rate = 10 units/ day
- Unit production cost = $ 100,
- Subcontract cost or expenses= $ 107 …. So
(The marginal unit cost= unit cost of subcontract - unit cost produced at home)= $ 107- $
100
= $ 7 per unit
The carrying cost / year = $ 20% of average inventory value.
month
Demand
Production
days
Jan.
Feb.
Mar.
Apr.
May
Jun.
1
220
90
210
396
616
700
2
22
18
21
22
22
20
Prod. Quantities
per day(10 units)+3
Inventory
To carry
220
180
210
220
220
200
0
+ 90
0
- 176
-396
-500
3
Cost of
subcontract
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
378
220
200
115
95
260
21
22
20
23
19
20
210
220
200
230
190
200
Total
3500
250
2500
-168
0
0
+ 115
+ 95
-60
Total production quantity = 2500 units (also you can calculate it as : total production days 250 X 10
units per day).
Number of needed units to cover all demands = total demand – annual production
= 3500 – 2500 = 1000 units as shortage to be covered by subcontract.
Inventory cost / unit /month= 0.20 X $ 100 / 12 = $ 1.67
90 units X 2 months X $ 1.67
115-60 =55 units X 6 month X $ 1.67
60 units X 2 month X $ 1.67
95x5 x1.67
Sum
$ 300.6
$ 551.1
$ 200.4
$ 793.23
$ 1844
The marginal cost = 1000 X 7 = $ 7000
The total cost of plan 3, includes inventory cost + marginal cost = $ 1844 + $ 7000= $ 8844
(With no storage cost ).
f- Plan 4 - mixed strategy with overtime: level with overtime:
month
Demand
Product
-ion
days
Jan.
Feb.
Mar.
Apr.
may
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
1
220
90
210
396
616
700
378
220
200
115
95
260
2
22
18
21
22
22
20
21
22
20
23
19
20
Prod.
Quantity
per day(10
units)
3
220
180
210
220
220
200
210
220
200
230
190
200
Total
3500
250
2500
4
Inventory
available
Cumulative
inventory
0
+ 90
0
- 176
-396
-500
-168
0
0
+ 115
+ 95
-60
-86
115
210
150
workers
needed
for
overtime
9
40
50
17
-
overtime
payroll
$
Example 2: Given data
Hiring cost = $ 200/worker
Firing cost = $ 100/worker
Regular pay = $ 5000/worker/month
Overtime pay = 1.5 times of regular pay
Backorder cost = $20/unit (based on end of month storage)
Productivity = 10 unit /worker/month
Workforce size = 20 workers
Beginning inventory = 0
inventory carrying cost = $ 10/unit/month (based on the end of month).
To solve this example, for level strategy , where production rate is constant.
Solution:
month
Demand
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
1
100
150
250
400
250
50
90
160
260
390
240
60
Total
2400
Production
rate
2
200
200
200
200
200
200
200
200
200
200
200
200
Inventory
start
0
100
150
100
-100
-150
0
110
150
90
-100
-140
Inventory
At end of
month
100
150
100
-100
-150
0
110
150
90
-100
-140
0
Inventory
Carry cost
1000
1500
1000
2000
3000
1100
1500
900
2000
2800
7000
Production rate= 2400/12= 200 units per month.
To estimate worker size needed = 200 units/10 prody. = 20 workers
Total payment for 20 workers = 20 x $ 5000 x 12 months = $ 1200000
Cost of backorders = $ 9800
Inv. Carrying cost = $ 7000
Total annual plan (1)cost = 1200000 + 7000 +9800 = $ 1216800
5
Backorder
cost
9800
2 chase strategy : when production equal demand, with hiring and firing:
Beginning workforce size = 20 workers
month
Demand
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
1
100
150
250
400
250
50
90
160
260
390
240
60
Total
2400
Work force
size
2
10
15
25
40
25
5
9
16
26
39
24
6
# hiring
Hiring cost
# firing
Firing cost
5
10
15
1000
2000
3000
10
1000
15
20
1500
2000
15
18
1500
1800
Labor pay roll
= no. of labor x
payment
50000
75000
125000
200000
125000
25000
45000
80000
130000
195000
120000
30000
7800
1200000
4
7
10
13
800
1400
2000
2600
12800
Total inventory cost = $ 0
Total backlog = $ 0
Total hiring cost = $ 12800
Total firing cost = $ 7800
Total wages = 1200000
Overtime cost = $ 0
Total annual plan (2) cost = $ 122600
3- mixed strategy with overtime and idle time:
* To match demand by producing the exact quantities.
* Constant labor size=20 workers.
- Productivity = 10 unit /worker/month.
- Beginning inventory = 0 units.
6
month
Demand
Work force
size
Needed
workforce
# Labor
overtime
# Labor
idle time
Labor
Regular pay
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Total
100
150
250
400
250
50
90
160
260
390
240
60
2400
20
20
20
20
20
20
20
20
20
20
20
20
10
15
25
40
25
5
9
16
26
39
24
6
5
20
5
6
19
4
-
10
5
100000
100000
100000
100000
100000
100000
100000
100000
100000
100000
100000
100000
1200000
15
11
4
14
Total regular payroll cost = $ 1200000
Total overtime cost = $ 442500
Total annual plan (3) cost = $ 1642500
The best strategy the company should consider is plan (1)
7
Cost of
overtime
37500
150000
37500
45000
142500
30000
442500