Consider a toy retailer with warehouses in St. Louis and Kansas City, Missouri. The warehouses stock an identical popular toy delivered to stores in the two cities. Assume a warehouse serves only stores in its city. Weekly demand for St. Louis is normally distributed with mean 2,000, and standard deviation 400 (that is N(μ = 2,000, σ = 400)). Weekly demand for KansasCity is distributed N(μ = 2,000, σ = 300). We assume that the two cities are far enough apart so that demand in the two cities is independent.The following parameters are seen by both warehouses:Replenishment lead time in weeks ~ N(μ = 2, σ = 0.1);Fixed shipping cost of replenishment: $500;Cost per toy: $10; andHolding cost per toy 20 percent of toy’s value per year.How many toys should each location order at a time and when should they reorder if they want a 99 percent cycle service level? What if they pool the two locations?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 54P
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Consider a toy retailer with warehouses in St. Louis and Kansas City, Missouri. The warehouses stock an identical popular toy delivered to stores in the two cities. Assume a warehouse serves only stores in its city. Weekly demand for St. Louis is normally distributed with mean 2,000, and standard deviation 400 (that is N(μ = 2,000, σ = 400)). Weekly demand for Kansas
City is distributed N(μ = 2,000, σ = 300). We assume that the two cities are far enough apart so that demand in the two cities is independent.
The following parameters are seen by both warehouses:
Replenishment lead time in weeks ~ N(μ = 2, σ = 0.1);
Fixed shipping cost of replenishment: $500;
Cost per toy: $10; and
Holding cost per toy 20 percent of toy’s value per year.
How many toys should each location order at a time and when should they reorder if they want a 99 percent cycle service level? What if they pool the two locations?

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