8. Cabot Appliances, a retail chain, is trying to decide what size order it shou
ID: 348763 • Letter: 8
Question
8. Cabot Appliances, a retail chain, is trying to decide what size order it should place with its supplier of room air conditioners. Room air conditioner sales are highly sea- sonal, and the number of units sold is very dependent on summer weather patterns Cabot places one order per year. Reorders are impractical after the selling season begins to develop. Although the actual sales level cannot be known for sure, Cabot analyzes past selling seasons, long-term weather reports, and the general state of the economy. The following probabilities of various sales levels are then estimated: Sales Unit 300 750 1200 1450 1550 Probability 0.2 0.2 0.35 0.15 0.1 A unit has a delivered price to Cabot of $320 and it is priced to customers at $400. Air conditioners unsold at the end of the season are discounted to $300, which clears them from inventory. Purchases can be made only in increments of 250 units, with a 500-unit minimum order a. Assuming no inventory is to be carried to the next year, what single order size should be placed?Explanation / Answer
A)
8.
The inventory management model to be used here is Single-Period Model.
Cost per unit = $ 320.
Revenue per unit = $ 400.
Salvage value per unit = $ 300.
Excess cost, Ce = Cost per unit – Salvage value per unit = 320 – 300 = $ 20.
Shortage cost, Cs = Revenue per unit - Cost per unit = 400 – 320 = $ 80.
Service Level, SL = Cs / (Cs + Ce) = 80 / (80 + 20) = 80 / 100 = 0.8
Sales unit
Probability
Cumulative Probability
300
0.2
0.2
750
0.2
0.4
1,200
0.35
0.75
1,450
0.15
0.90
1,550
0.1
1.00
Total
1.00
a.
To achieve a service level of at least 80%, number of air conditioners that has to be ordered by Cabot Appliances in a single order = 1,500 (since Cumulative Probability exceeds Service Level when the demand is equal to 1,450 air conditioners and purchases can be made only in increments of 250 units).
Sales unit
Probability
Cumulative Probability
300
0.2
0.2
750
0.2
0.4
1,200
0.35
0.75
1,450
0.15
0.90
1,550
0.1
1.00
Total
1.00
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