Question

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $30 each from its Asian supplier. Unfortunately, at the time of order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally distributed with mean of 3,600 and standard deviation of 1,200. Teddy Bower sells these parkas at $70 each. Each unsold parka has a salvage value of $18. Now suppose Teddy Bower found another supplier in the U.S. that can produce parkas very quickly but at a higher price than Teddy Bower’s Asian supplier. Hence, in addition to parkas from Asia, Teddy Bower can buy an unlimited quantity of additional parkas from this American supplier at $50 each after demand is known.

a) Given the opportunity to order from the American supplier at $50 per parka after demand is known, what order quantity from its Asian supplier now maximizes Teddy Bower’s expected profit, i.e., optimal first order quantity?

b) Given the order quantity in part a), what is Teddy Bower’s expected profit? [Hint: expected profit = maximum profit – mismatch cost, where maximum profit = (p-c)* ??]

Answer 1

Cost of shortage Cs= 70-30 =40

Cost of overage Co= 30-18 =12

Service level = Cs/Cs+Co = 40/12+40 = 0.7692

z value for Service level = 0.74

Optimum stocking level = mu+ z x SD

= 3600+1200 ( 0.74) = 4488

Expected lost sales = sigma x L(z) = 1200 x 0.132 =158.4 =158

Expected sales = mean - expected loss sales = 3600-158 =3442

Expected leftover inventory = Q - expected sales

= 4488-3442 = 1046

Expected profit = expected sales ( price-cost) + leftover inventory ( salvage value-cost)

= 3323 x40 - 1046 x( 12) = 132920 -12552 =120368