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 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, ... I 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, ..., 0, 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, ... I 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
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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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
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, ... I 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:ABC Company provides a service to its clients. Each client has a job with a processing time of several
days. Once the process starts for a client's job, it must be carried out without any interruption. Each
client's job requires a certain number of operators in each day of its process. ABC must create a plan
for the 4 available clients' jobs for the next 5 days with minimum number of operators needed to
satisfy this demand. The processing time of the client's jobs and the number of operators each of them
needs in each day is given below. For instance, client 1 has a job that lasts for 2 days, and 2 and 3
operators are needed for days 1 and 2 of its execution.
Number of operators needed per day
Client
1
2
3
4
Processing time in
days
2
1
3
2
1
2
2
1
3
2
3
3
3
3
2
4
5
(a) Formulate an integer linear programming model to minimise the total operators needed.
Describe decision variables, objective function, and constraints properly.
(b) Solve the ILP formulated in part (a) using Excel Solver. What is the optimal solution and total
operators needed?
(c) Job 2 must start at least one day before job 3. For example, job 2 can start on day 1 and job 2
can start on days 2, 3, 4, or 5. Modify your model and add this condition.
(d) Solve the modified ILP formulated in part (c). Explain how the optimal solution is different
from part (b).
(e) If job 1 is started on day 1 then job 4 also must be started on day 1. Modify your model to
accommodate this condition.
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