Question

A company needs to open new warehouses to distribute products to the customers in two different regions. The company has to decide where to open warehouses and in which capacity should be preferred for them. Past data shows that average daily demand of customers are 1000 units for the customers in region 1 and 1200 units for the customers in region 2. There are two possible locations to open a warehouse. The daily equivalent setup cost of opening a warehouse at location alternative A requires $1,000 for a warehouse with delivery capacity of 1000 units per day and it requires $1,500 for a warehouse with delivery capacity of 2200 units per day. The daily equivalent setup cost of opening a warehouse at location alternative B is $550 for a warehouse with a maximum capacity of 1200 units per day. Delivery costs are as follows: $1 from a warehouse located at A to the customers in region 1; $1.5 from a warehouse located at A to the customers in region 2; $1.5 from a warehouse located at B to the customers in region 1; $1 from a warehouse located at B to the customers in region 2. Develop a linear mathematical model for minimizing total daily equivalent cost of distribution system

Answer 1

Linear Programming model is as follows:

Let A1 = 1, if a warehouse is opened at location A with delivery capacity of 1000 units per day, otherwise A1 = 0

A2 = 1, if a warehouse is opened at location A with delivery capacity of 2200 units per day, otherwise A2 = 0

B = 1, if a warehouse is opened at location B with delivery capacity of 1200 units per day, otherwise B = 0

Xij be the quantity to be shipped from warehouse at location i to region j, where i={a,b} and j={1,2}

Minimize 1000A1+1500A2+550B+1Xa1+1.5Xa2+1.5Xb1+1Xb2

s.t.

Xa1+Xa2-1000A1-2200A2 <= 0

Xb1+Xb2-1200B <= 0

Xa1+Xb1 = 1000

Xa2+Xb2 = 1200

Xij >= 0

A1, A2, B = {0,1}

--------------------

Solution using LINGO is as follows:

Result:

Total cost = $ 3,750