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In the fashion retail industry transshipment is the flow of the products from a retail location to another one to satisfy the demand at the receiver location. Sender only sends a product if it has excess inventory to its demand and it occurs to rebalance the inventory among retail locations. Assume that there is a retailer with I stores. There are O products nominated for transshipment. The available inventory rio, i = 1,2, ..., I, o = 1,2, ..., 0, and demand levels dio, i = 1,2, ..., I, o = 1,2, ..., O, for all stores are known. Moreover, the sales prices of these products are known and are the same in all stores, po, 0 = 1,2, ... 0. There is a transportation cost when a product is sent from a store to another, Cij, i, j = 1, 2, ... D which is independent for the type of the product. Assume that if a product o is transshipped from store i, all its available inventory, i.e., rio, must be sent to a single store, thus, partial transshipment is not allowed. However, a store can receive the same product from different stores. (a) Formulate a mixed integer linear programming model to maximise the total profit. Describe decision variables, objective function, and constraints properly. (b) Now assume that all stores have a capacity on the number of products that they can transship. Modify your model to accommodate this extra condition.

In the fashion retail industry transshipment is the flow of the products from a retail location to another one to satisfy the demand at the receiver location. Sender only sends a product if it has excess inventory to its demand and it occurs to rebalance the inventory among retail locations. Assume that there is a retailer with I stores. There are O products nominated for transshipment. The available inventory rio, i = 1,2, ..., I, o = 1,2, ..., 0, and demand levels dio, i = 1,2, ..., I, o = 1,2, ..., O, for all stores are known. Moreover, the sales prices of these products are known and are the same in all stores, po, 0 = 1,2, ... 0. There is a transportation cost when a product is sent from a store to another, Cij, i, j = 1, 2, ... D which is independent for the type of the product. Assume that if a product o is transshipped from store i, all its available inventory, i.e., rio, must be sent to a single store, thus, partial transshipment is not allowed. However, a store can receive the same product from different stores. (a) Formulate a mixed integer linear programming model to maximise the total profit. Describe decision variables, objective function, and constraints properly. (b) Now assume that all stores have a capacity on the number of products that they can transship. Modify your model to accommodate this extra condition.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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a mixed integer linear programming question

In the fashion retail industry transshipment is the flow of the products from a retail location to another one to satisfy the demand at the receiver location. Sender only sends a product if it has excess inventory to its demand and it occurs to rebalance the inventory among retail locations. Assume that there is a retailer with I stores. There are O products nominated for transshipment. The available inventory rio, i = 1,2, ..., I, o = 1,2, ..., 0, and demand levels dio, i = 1,2, ..., I, o = 1,2, ..., 0, for all O, stores are known. Moreover, the sales prices of these products are known and are the same in all stores, po, o = 1,2, ... 0. There is a transportation cost when a product is sent from a store to another, Cij, i, j = = 1, 2, ... D which is independent for the type of the product. Assume that if a product o is transshipped from store i, all its available inventory, i.e., rio, must be sent to a single store, thus, partial transshipment is not allowed. However, a store can receive the same product from different stores. (a) Formulate a mixed integer linear programming model to maximise the total profit. Describe decision variables, objective function, and constraints properly. (b) Now assume that all stores have a capacity on the number of products that they can transship. Modify your model to accommodate this extra condition.
Transcribed Image Text:In the fashion retail industry transshipment is the flow of the products from a retail location to another one to satisfy the demand at the receiver location. Sender only sends a product if it has excess inventory to its demand and it occurs to rebalance the inventory among retail locations. Assume that there is a retailer with I stores. There are O products nominated for transshipment. The available inventory rio, i = 1,2, ..., I, o = 1,2, ..., 0, and demand levels dio, i = 1,2, ..., I, o = 1,2, ..., 0, for all O, stores are known. Moreover, the sales prices of these products are known and are the same in all stores, po, o = 1,2, ... 0. There is a transportation cost when a product is sent from a store to another, Cij, i, j = = 1, 2, ... D which is independent for the type of the product. Assume that if a product o is transshipped from store i, all its available inventory, i.e., rio, must be sent to a single store, thus, partial transshipment is not allowed. However, a store can receive the same product from different stores. (a) Formulate a mixed integer linear programming model to maximise the total profit. Describe decision variables, objective function, and constraints properly. (b) Now assume that all stores have a capacity on the number of products that they can transship. Modify your model to accommodate this extra condition.
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