Scenario 3 A firm is weighing three capacity alternatives: small, medium, and la
ID: 346600 • Letter: S
Question
Scenario 3
A firm is weighing three capacity alternatives: small, medium, and large job shop. Whatever capacity choice is made, the market demand for the firm's product can be "moderate" or "strong." The probability of moderate market demand is estimated to be 0.4; the probability of strong market demand is estimated to be 0.6. The anticipated profits are as follows:
a. Small job shop: moderate market demand = $24,000; strong market demand = $54,000.
b. Medium job shop: moderate market demand = $20,000; strong market demand = $64,000.
c. Large job shop: moderate market demand = -$2,000; strong market demand = $96,000.
Referring to Scenario 3 above, your director wants to increase the probability of moderate market demand to 0.5, without changing any other probabilities (i.e., he wants to keep the probability of strong market demand at 0.6). What should you do?
recalculate the EMV for the Medium job shop and report the revised (in any) recommended decision
politely inform your director that this is not possible; the sum of all probabilities for market demand needs to equal 1
recalculate the EMV for the Small job shop and report the revised (in any) recommended decision
recalculate the EMV for the Large job shop and report the revised (in any) recommended decision
collectively recalculate all EMVs and report the revised (in any) recommended decision
Explanation / Answer
Three capacity options for the firm = "small", "medium", "large"
The probability of moderate market demand = 0.4
The probability of strong market demand = 0.6
The estimated profits from Small job shop, moderate market demand = $24,000
The estimated profits from Small job shop, strong market demand = $54,000.
The Estimated Monetary Value for small job shop = 0.4*24000+0.6*54000 = $ 42000
The estimated profits from Medium job shop, moderate market demand = $20,000
The estimated profits from Medium job shop, strong market demand = $64,000.
The Estimated Monetary Value for Medium job shop = 0.4*20000+0.6*64000 = $ 46400
The estimated profits from Large job shop, moderate market demand = -$2,000
The estimated profits from Large job shop, strong market demand = $96,000.
The Estimated Monetary Value for Large job shop = 0.4*(-2000)+0.6*96000 = $ 56800
From the above scenario we see that from the value of the EMV's , the recommended decision would be to opt for a large job shop as it has a greater chance of success.
If we assume the probability of moderate market demand to be 0.5, then as the total probability of all future events that may occur has to be equal to 1. Thus the probability of strong market demand would also be 0.5. In such a case the EMV's for the three cases of different sized job shops would be as follows-
The revised Estimated Monetary Value for small job shop = 0.5*24000+0.5*54000 = $ 39000
The revised Estimated Monetary Value for Medium job shop = 0.5*20000+0.5*64000 = $ 42000
The revised Estimated Monetary Value for Large job shop = 0.5*(-2000)+0.5*96000 = $ 47000
Although the market demand is not possible to control on its own, it can be seen from the revised values of the EMV's that although they are much closer, still the value of the EMV for large job shop is the highest. In such a case too, the recommended decision would be to opt for large job shop.
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