Quantitative techniques for Aggregate Aggregate Planning Process
Pure Strategies
Mixed Strategies
Linear Programming
Transportation Transportation Method
Other Quantitative Techniques
Dr T SAMPATH KUMAR, ASSOCIATE
1
Mixed Strategy
•
Combination of Level Production and Chase Demand strategies
•
Examples of management policies
•
no more than x% of the workforce can be laid off in one quarter
inventory levels cannot exceed x dollars
Many industries may simply shut down manufacturing during the low demand season and schedule employee vacations during that time
Dr T SAMPATH KUMAR, ASSOCIATE
2
Graphical method In graphical method, cumulative demand values and cumulative production capacities are plotted on the same graph, to identify the gap between demand and production capacity during different periods. In this method, cost data is not taken in to account.
Dr T SAMPATH KUMAR, ASSOCIATE
3
Graphical method (problem 1) ABC corporation has developed a forecast for a group of items that has the following demand pattern. Quarter
Demand
Cumulative demand
1
270
270
2
220
490
3
470
960
4
670
1630
5
450
2080
6
270
2350
7
200
2550
8
370
2920
Dr T SAMPATH KUMAR, ASSOCIATE
4
Graphical method (problem 1) Plot the demand as a histogram. Determine the production rate required to meet average demand and plot the average demand forecast (Production rate) on the graph. Plot the actual cumulative forecast requirements over time and compare them with the available average forecast requirements. Indicate the excess inventories and backorders on the graph
Dr T SAMPATH KUMAR, ASSOCIATE
5
Graphical method 800 670
700 600 470
500
450 370
400 300
270
Average demand
270 220
Demand
200
200
100 0
1
2
3
4
5
6
7
8
Periods (Quarters) Dr T SAMPATH KUMAR, ASSOCIATE
6
Graphical method
3500 3000
2920 2550
2500
2350 2080
2000
Cumulative demand
1630
1500 1000
960
500
490 270
0 1
2
3
4
5
6
7
Dr T SAMPATH KUMAR, ASSOCIATE
8
7
Preparation of inventory balance (Problem 2) The monthly inventory balance required for a organization is tabulated. With constant work force, no idle time or over time, no back order, no use of subcontract an no capacity adjustments. Determine, only by following a plan of letting the inventory to absorb all fluctuations in demand. Month
Forecast
Production @ 16 /day
January February March April May June July August September October
220 90 210 396 616 600 375 780 265 775
353 288 336 352 352 320 336 320 368 304
November
325
320
December
Dr T SAMPATH175 KUMAR, ASSOCIATE
320
8
Preparation of inventory balance (Problem 2) Now imagine, that the organization has determined that to follow a plan of meeting demand by varying the size of work force would result in hiring and layoff cost estimated at Rs.22,000. If the cost of producing each unit is Rs.100, the carrying costs/per annum are 20% of average inventory value and storage cost are Rs.9/unit, which plan result in lower cost: varying inventory or varying employment (hiring/layoff)?
Dr T SAMPATH KUMAR, ASSOCIATE
9
Preparation of inventory balance Forecast
Production @ 16 /day
Ending inventory balance
January
220
353
353-220=133
133+1003=1136
353/16=22
February
90
288
288+133=421 421-90=331
331+1003=1334
288/16=18
March
210
336
457
1460 (Max)
21
April
396
352
413
1416
22
May
616
352
149
1152
22
June
600
320
-131
872
20
July
375
336
-170
833
21
August
780
320
-630
373
20
September
265
368
-527
476
23
October
775
304
-998
5
19
November
325
320
-1003
0
20
December
175
320
-858
145
20
Average inventory
9202/12=766.83
Month
Dr T SAMPATH ASSOCIATE MaxKUMAR, Inventory
Ending balance No. of with 1003 on Jan working days
1460
10
Preparation of inventory balance Solution:
1. Carying cost = Avg. Inventory ×Unit Production cost×Carrying cost/annum Carying cost = Rs.766.8 ×100×0.2 = Rs. 15,336 Storage cost = Storage cost/unit ×Max. Inventory Storage cost = Rs.9×1460 = Rs.13,140 Total cost = Carying cost + Storage cost = Rs.28,476 2. Hiring / lay offcost = Rs.22,000
Conclusion:
So, hiring and layoff is the better option in this cost structure.
Dr T SAMPATH KUMAR, ASSOCIATE
11
Heuristic method In heuristic method, a list of pure strategies and mixed strategies are generated and evaluated in terms of cost and finally a pure strategy or a mixed strategy with the minimum total cost is selected for implementation.
Dr T SAMPATH KUMAR, ASSOCIATE
12
Pure strategies Various pure strategies are •
Vary the work force size
•
Changing the inventory levels
•
Subcontracting
Dr T SAMPATH KUMAR, ASSOCIATE
13
Pure strategies (Problem 3) The forecast for a group of items is reproduced as shown in previous table of graphical method. 1.
Suppose that the firm estimates that it costs Rs.150 per unit to increase the production rate, Rs.200 per unit to decrease the production rate, Rs. 50 per unit per quarter to carry the items on inventory and Rs.100 per unit if subcontracted. Compare the cost incurred if pure strategies are followed.
Dr T SAMPATH KUMAR, ASSOCIATE
14
Quarter
Demand
Cumulative Demand
1
270
270
2
220
490
3
470
960
4
670
1630
5
450
2080
6
270
2350
7
200
2550
8
370
2920
Dr T SAMPATH KUMAR, ASSOCIATE
15
1) Plan I – varying the work force size:Work force will be varied to meet the actual demand. (ie) During the period of low demand, the company must fire employees (or) During the period of high demand, the company must hire employees. Table – Varying the workforce size to meet the demand Quarter Demand Compare
1
270
2
220
3
Cost of increasing the
Cost of Decreasing
Total cost of
(eg.)
production level
the production level
Plan
2-1,
(hiring)
(firing)
so on
(x150)
(x 200) -
-
-
-50
-
50x200 =10,000
10,000
470
250
250x150 = 37,500
-
37,500
4
670
200
200x150 = 30,000
-
30,000
5
450
-220
-
220x200 = 44,000
44,000
6
270
-180
-
180x200 = 36,000
36,000
7
200
-70
-
70x200 = 14,000
14,000
8
370
170
170x150 = 25,500
-
Total cost of Plan I Dr T SAMPATH KUMAR, ASSOCIATE
25,500 1,97,000 16
2) Plan II – Changing Inventory levels: The company set the average demand as its production capacity to this average demand To avoid shortages, 255 units is added from the beginning of period 1 Table – Cost calculation for changing Inventory levels Qua Demand Cumulativ Production
Cumulative
rter
e Demand level
Inventory
Adjusted
Cost of
production
Inventory
holding
level
with 255
Inventories
(min) 0
1
2
3
4
5 = 4-2
6 = 5+255
7 = 6x Rs.50
1
270
270
365
365
95
350
17,500
2
220
490
365
730
240
495
24,750
3
470
960
365
1095
135
390
19,500
4
670
1630
365
1460
-170
85
4,250
5
450
2080
365
1825
-255(min) 0
0
6
270
2350
365
2190
-160
95
4750
7
200
2550
365
2555
5
260
13,000
8
370
2920
365
2920
0
255
12,750
2920/8 = 365
Total cost of Plan II Dr T SAMPATH KUMAR, ASSOCIATE
96,500 17
3) Plan III – subcontracting Some firms may be interested in setting up its regular time capacity to its minimum value and meet the rest of the demand using subcontracting. The cost of such a plan was calculated. 200 minimum is set as production level. Table – Cost calculation for subcontracting Quarter
Demand
Production units
Subcontract units
Incremental
1
2
3 = 1-2
subcontracting cost at Rs. 100/unit 4 = 3x 100
1
270
200
70
70x100 = 7000
2
220
200
20
2000
3
470
200
270
27,000
4
670
200
470
47,000
5
450
200
250
25,000
6
270
200
70
7000
7
200 (min)
200
0
0
8
370
200
170
17,000
Total cost of plan III Dr T SAMPATH KUMAR, ASSOCIATE
1,32,000 18
Conclusion: •
Plan – Total cost I
- 1,97,000
II -
96,500
III -
1,32,000
Plan II has the least cost (ie) Changing Inventory levels.
Dr T SAMPATH KUMAR, ASSOCIATE
19
