The Lee Air Conditioning Company is considering purchase of a special shipment o

Question

The Lee Air Conditioning Company is considering purchase of a special shipment of portable air conditioners from Japan. Each unit will cost Lee $800 and be sold for $1250. Lee does not want to carry over surplus air conditioners to the following year. Thus, all supplies will be sold to a wholesaler, Paul & Company, who has agreed to take all surplus units for $500 per unit. The probability distribution for air conditioners is shown below:

(a) What are Lee’s optimal order quantity and the expected profit?

(b)If Lee has surplus then Paul & Company agreed to take all surpluses from Lee for $500 per unit plus a fixed charge of $200 (e.g., Lee’s pay Paul & Company $200 fixed charge & receive from Paul & Company the surplus times $500). What is the expected profit if Lee ordered 8 air conditioners from Japan?

Demand 5 6 7 8 9 Estimated Probability 0.3 0.15 0.25 0.15 0.15

Explanation / Answer

The demand function is as follows:

Lost profit per unit = $1,250 - $800 = $450

Salvage loss per unit = $800 - $500 = $300

Therefore the critical ratio or the comulative probability for order quantity = 300/(300+450) = .4

Therefore the optimum order quantity is 7 (lowest comulative probability > critical ratio) and the expected profit ($2,587.5) is calculated as follows:

(b) In case Lees pay $200 to Paul & company as a fixed charge, the same needs to be added for calculation of salvage loss for Lee in case of surplus. The expected profit ($2,372.5) if Lee ordered 8 air conditioners is worked out as follows:

Prob(demand>) 1 0.7 0.55 0.3 0.15 Demand 5 6 7 8 9

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