A store is considering how many current model smart phones to order given a new

Question

A store is considering how many current model smart phones to order given a new model is soon to be released next month. The probability distribution of demand for the current model of smart phone is normal with a mean of 1200 units and a standard deviation of 350. The current smart phone retails for $1400 each and costs S1000 each to purchase. The total cost of a shortage is estimated to be $1400 per smart phone. Any unsold smart phones at the end of the month will be sold at the discounted price of $775 per smart phone (i) How many current smart phones should be ordered to minimise the expected total cost given that only one order may be placed? (i) The supplier is offering her an order of 1 760 units of the current model at a reduced purchase price of $900 and any unsold smart phones will be returned to the supplier for a rebate (instead of being sold at a discount instore next month). If both the shortage cost and selling price remain the same, what rebate per smart phone will make the 1 760 units optimal? Using Inventory Models to Solve the Question

Explanation / Answer

(i) Shortage or Underage cost, Cu = 1400

Overage cost, Co = purchase cost - discounted sale price = 1000 - 775 = 225

To minimize the expected total cost, Critical ratio = Cu/(Cu+Co) = 1400/(1400+225) = 0.8615

z value = NORMSINV(0.8615) = 1.087

Number of smartphones to be order = Mean demand + z*stdev = 1200+1.087*350 = 1580

(ii) For order quantity of 1760, z = (1760-1000)/350 = 2.17

Probability = NORMSDIST(2.17) = 0.985

Shortage cost remains same, so Cu = 1400

Critical ratio = Cu/(Cu+Co) = 0.985, Solving the above equation for Co, we get

Co = 21.32

Rebate per smartphone = 21.32

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