Question

Use Table 13.4. Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain: Teddy Bower forecasts that its demand is normally distributed with mean 2100 and standard deviation 1200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity (and also doesn't collect a tax benefit for the donation). If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method. What is the probability this parka turns out to be a "dog", defined as a product that sells less than half of the forecast? Use Excel. (Round your answer to 4 decimal places.) How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? Use Table 13.4 and the round-up rule c. If Teddy Bower orders 3000 parkas, what is the in-stock probability? Use Excel. (Round your answer to 4 decimal places.) d, If Teddy Bower orders 3000 parkas, what is expected leftover inventory? Use Table 13.4 and the round-up rule. (Round your answer to 2 decimal places.) e. If Teddy Bower orders 3000 parkas, what is expected sales? (Round your answer to 2 decimal places.) f. If Teddy Bower orders 3000 parkas, what is expected profit? Round your answer to 2 decimal places.) How many parkas should Teddy Bower order to ensure a 98.5% in-stock probability? how many parkas should Teddy Bower's order? Use Table 13.4 and the round-up rule.

Answer 1

Answer Cost of overordering Co Date: --1/6/2019 Purchase cost Salvage value = $10 0 $10 - $22- $10 $12 Cost of underorder Cu Selling price Purchase cost 12/ (12+10) 12/22 0.545 Critical ratio Cu / (Co+Cu) (a) Half of the forecast 2100/2 1050 PX 1050) NORM.DIST(1050, 2100, 1200, TRUE) 19.07% (b) For max expected profit, The ordered quantity should be such that Z will be equal to NORMSINV(0.545) = 0.11 Order quantity = Q 2100 Z x 1200 2100 0.11 x 1200 2232 + -

(g) For In-stock probability 0.985 Z NORMSINV (0.985) = 2.17 Order quantity 2100 Z x 1200 2100 2.17 x 1200 4704

3000(as given) so, Z = (3000 - 2100) / 1200 = 0.75 L(Z) Loss function corresponding to Z 0.75 is equal to 0.131 Expected Lost Sales, L(Q) L(Z) x SD 0.131 x 1200 157.2 Expected Sales, S(Q) Mean Demand L(Q) 2100 - 157.2 1942.8 Expected Left Over Inventory, V(Q) = Q - S(Q) 3000 1942.8 Expected profit = Cu x S(Q)+ Cox V(Q) 12 x 1942.8 - 10 x 1057.2 = S12,742 1057.2 = Stockout probability 1 - NORSDIST(Z) = 1 - NORSDIST(0.75) 22.7%

(3000-2100)/1200 0.75 e) For 3000 units, z value For z-0.75, corresponding L(z)= 0.1312 (taken from standard normal table) Expected lost sales (L) o*L(z) 1200*0.1312 = 157 - Expected Sales,S = u-L 2100 - 157 = 1943 Expected unsold inventory, V = Q - S 3000 - 1943 1057