MARGINAL ANALYSIS

It is difficult to develop the conditional profit table when there are a large number of scenarios and possible actions. The marginal analysis approach sidesteps an unmanageable conditional profit table. We will illustrate the procedure and its advantages through the following example.

Example 

 

The fresh from the fields, vegetable and fruit wholesalers buys, produce and then sells to retailers. Currently, green peas are available. The wholesaler pays Rs.200 per box of peas. A box sold on the same day fetches Rs.300, otherwise it has a salvage value of Rs.50. Historical data has established the following demand for green peas.

Number of boxes	21	22	23	24	25	26	27	28
Probability	0.07	0.08	0.10	0.11	0.29	0.20	0.09	0.06

The wholesaler has decided to stock the optimal number of boxes based on the expected profit criterion.

Let us solve the problem using the conditional profit table. Note that the profit generated by the sale of one box is Rs.100 and the loss incurred on an unsold box is Rs.150.00.

Conditional Profit Table

Stocking level	Daily Demand								Expected profit
	21 (0.07)	22 (0.08)	23 (0.10)	24 (0.11)	25 (0.29)	26 (0.20)	27 (0.09)	28 (0.06)
21 22 23 24 25 26 27 28	2100 1950 1800 1650 1500 1350 1200 1050	2100 2200 2050 1900 1750 1600 1450 1300	2100 2200 2300 2150 2000 1850 1700 1550	2100 2200 2300 2400 2250 2100 1950 1800	2100 2200 2300 2400 2500 2350 2200 2050	2100 2200 2300 2400 2500 2600 2450 2300	2100 2200 2300 2400 2500 2600 2700 2550	2100 2200 2300 2400 2500 2600 2700 2800	2100.00 2182.50 2245.00 2282.50 2292.50 2230.00 2117.50 1982.50

From the table, we see that the optimal stocking level is 25 (which generates the maximum expected profit of Rs.2,292.50).

As it can be seen, this approach is tedious and the conditional profit table is bound to become unmanageable.

 

Posted Date: 9/15/2012 2:26:48 AM | Location : United States

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