ACold Inc is a frozen food distributor with 10 warehouses across the country. Iv

Question

ACold Inc is a frozen food distributor with 10 warehouses across the country. Ivan Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery to ACold’s customers. Since the warehouse carries hundreds of different products, Ivan decided to study one. He picked Caruso’s Frozen Pizza (CFP). Average daily demand for CFPs is normally distributed with a mean of 383 and a standard deviation of 160. Since ACold orders at least one truck from their supplier each day, ACold can essentially order any quantity of CFP it wants each day. In fact, ACold’s computer system is designed to implement an order-up-to policy for each product. Ivan notes that any order for CFPs arrives 5 days after the order. a. Suppose an order-up-to level of 2442 is used. What is the expected on-hand inventory? Use Table 14.1 and round to nearest integer. b. Suppose an order-up-to level of 2533 is used. What is the expected on-order inventory? Round your answer to the nearest integer. c. Suppose an order-up-to level of 1917 is used. What is the in-stock probability? Use Table 14.1. Round your answer to one decimal. d. Suppose ACold wants a 0.92 in-stock probability. What should the order-up-to level be? Use Table 14.1. Round your answer to the nearest integer.

Explanation / Answer

This is basestock inventory model

a) Average demand over l+1 period = 410*(4+1) =2050

SD of demand over l+1 period = 154*(4+1) = 344.35

Order upto level = 2493

z = (2493-2050)/344.35 = 1.2865

Corresponding to z, value of I(z) taken from the table = 1.3334  (value determined using interpolation)

Expected on-hand inventory = I(z) = 344.35*1.3334 = 459

b) Expected on order inventory = Average daily demand * lead time (l) = 410*4 = 1640

c) Order upto level, S = 2061

z = (2061*2050)/344.35 = .0319

Expected inventory on hand, V = I(z) = 344.35*0.416 = 143

Expected backorder =  µ - (S - V) = 2050 - (2061 - 143) = 132

Stock-in probability = 1 - backorder/expected daily demand = 1 - 132/410 = 0.678

d) For 0.93 stock-in probability, z = 1.48 (taken from the table)

Order upto level, S = 2050 + 1.48*344.35 = 2560

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