General Algebraic Modeling System

INDR262 - Term Project #2 Consider the two-echelon multi-commodity facility location problem. We are given a set V1 of suppliers, a set V2 of potential warehouses, a set V3 of demand points, and a set K of products. The capacity of supplier i∈V1 for product k∈K is qik units and the demand of customer r∈V2 for product k∈K is drk units. The unit cost of shipping from supplier i ∈ V1 to warehouse j∈V2 for product k∈K is Cijk and the unit cost of transportation from warehouse j∈V2 to demand point r∈V3 for product k∈ K is C’jrk. The minimum and maximum activity levels (uj) at potential warehouse j∈V2 is z-j and z+j , respectively. The cost of operating warehouse j∈ V2 is given by fj + gjuj. Suppose that the demand of each demand point for each product is divisible, i.e., a demand point can receive its demand for each product from many warehouses. Consider the following instance of this kind of problem. We have only one type of product. There are five potential suppliers labeled 1,2,…,5 , five warehouses labeled 1,2,…,5 and six demand points labeled 1,2,…,6 . The capacities of suppliers are given by 40, 20, 45, 30 and 28 respectively. The fixed costs of operating the warehouses are given by 200, 170, 100, 95, and 60, respectively. The demands of the demand points are given by 22, 26, 24, 23, 22, and 15, respectively. The unit transportation costs from supplier i to warehouse j and from warehouse j to demand point r are given by the following functions: Cij 1 2 3 4 5 1 2 2 2 3 3 2 2 2 2 3 3 3 2 2 2 3 3 4 4 4 4 2 2 5 4 4 4 2 2 C’jr 1 2 3 4 5 6 1 2 2 2 3 3 3 2 2 2 2 3 3 3 3 2 2 2 3 3 3 4 4 4 4 2 2 2 5 4 4 4 2 2 2 Minimum and maximum activity levels for warehouses are as following: warehouse Z-j Z+j 1 10 30 2 8 32 3 7 31 4 9 29 5 11 28 Management wants to operate just three warehouses. On the other hand the cost is important for management. Formulate the problem as a linear programing problem. -What are the decision variables? - What are the constraints? Explain clearly. a. Solve the problem using GAMS -You should import parameters from an excel file. Also, you should export the results to an excel file for all the remaining parts of the question. b. Suppose that you do not necessarily have to satisfy the demand of each customer. However for each customer r∈V3 there is a penalty cost Pr of each unit of unmet demand but management need to ensure that at least 80% of demand of each customer should be satisfied due to service level requirement. Pr is stated in following table: Demand point r Pr 1 190 2 190 3 90 4 100 5 95 6 180 Solve the problem using GAMS. You should import parameters from an excel file. Also, you should export the results to an excel file for all the remaining parts of the question. c. Suppose that management has decided to operate warehouse 2 and 5 definitely because they have very good locations. Solve the problem using GAMS. You should import parameters from an excel file. Also, you should export the results to an excel file for all the remaining parts of the question. *You are supposed to use DISPLAY function in your GAMS code. NOTE: In this project you have to send your gms file and a word document which includes your results and model. Your results should include the value of all of the decision variables and objective functin. Also in the word file, you have to CLEARLY indicate your decision variables. DO NOT forget to add comments to your GAMS code. Please use Winzip or Winrar and name your file as (INDR262_Project_YourGroupNumber).