*FIND THE FOLLOWING:

- Objective function 1 (total transportation costs)

- Objective function2 (total opening costs of plants)
- balance constraint (enough raw material should be sent from the supplier to each plant)

- The capacity constraint of plants

- The capacity constraint of supplier

- Demand satisfaction constraint
 

Q1) A company has a contract with several retailer to satisfy the demand of a specific product. For this reason, the manager of the company decided to establish some plants in some candidate locations. The final product is made using raw materials that can be provided by a set of supplies. The following figure shows a schematic overview of the corresponding supply chain network. MIMAMON suppliers Notations: indices: 1 k m { e parameters: by 01 Cim da Cjx Given the notations defined below, formulate a two objective mathematical model to minimize the total transportation costs and the total opening cost of plants in a way that the demand of retailers is satisfied. Write your model in an algebraic form in the table given on the next page. Iml/ Yjk Cmij plants by 0 index for suppliers (i=1,2,....) index for plants (-1.2...) index for retailers (k=1,2,....K) index of raw materials (m=1,2,....) decision variables: production capacity of plantj opening cost of plant/ supply capacity of supplier i for raw material m demand of retailer k cik retailers k dz number of raw materials of type m required for manufacturing a single product transportation cost of sending one unit of raw material m from supplier (to plant/ transportation cost of sending one unit of product from plant / to retailer k number of raw materials of type m sent from supplier ( to plant/ number of products to be transported from plant/ to retailer k =1 if plant j is opened: 0 otherwise