Question

Q2. Supply Chain Management

(a) Suppose you are a print house manager for newspapers. Your cost is 20 cents per newspaper and you charge the retailer 80 cents per newspaper. The retailer sells to customers at $1 per newspaper. Any unsold newspaper is returned to you for full refund of the wholesale price. Demand for newspapers is normally distributed with mean 50 and standard deviation 9. How many newspapers should you print? (4 points)  

(b) The retailer would like to “induce” you to print more newspapers. Therefore, the retailer agrees to “pay-back” unsold newspapers at price $2 cents per newspaper. How many newspapers will you print? What pay-back price should the retailer offer to induce you to print the quantity that maximizes the combined profit of you and the retailer? (4 points)  

Answer 1

(a)

Cost of underage, Cu = 0.80 - 0.20 = 0.60
Cost of overage, Co = 0.20 - 0 = 0.20 (note that the salvage value is zero as the retialer pays nothing for the unsold copies)

So, newsvendor critical ratio = Cu / (Co + Cu) = 0.6 / (0.2+0.6) = 0.75

Corresponding z value = 0.6745

Optimal printing quantity, Q = 50 + 0.6745*9 = 56 units

(b)

Cost of underage, Cu = 0.80 - 0.20 = 0.60
Cost of overage, Co = 0.20 - 0.02 = 0.18

critical ratio = Cu / (Co + Cu) = 0.6 / (0.18+0.6) = 0.77

Corresponding z value = 0.7388

Optimal printing quantity, Q = 50 + 0.7388*9 = 56.6 units i.e. 57 units

----------------------

Selling price in the market, Sp = 1
Puchace cost of the retailer, Pc = 0.8
Salvage value, Sv = 0
Variable cost of the producer, Vc = 0.2

Use th following formula to find the optimum 'buy-back' price, b

b = Sp - (Sp - Pc)*(Sp - Sv) / (Sp - Vc) = 1 - (1 - 0.8)*(1 - 0) / (1 - 0.2) = 0.75

So, the optimum 'pay-back' price is (Pc - b) = 0.80 - 0.75 = 0.05 i.e. 5 cents

****Please please please LIKE THIS ANSWER, so that I can get a small benefit, Please****