Posted: February 4th, 2016

Product Unit Cost Quantity Product Cost Vendor Total Vendor Capacity Vendor A 1 $12 $0 0 600 Vendor A 2 $10 $0 Vendor B 1 $13 $0 0 1,000 Vendor B 2 $11 $0 Vendor C 1 $14 $0 0 800 Vendor C 2 $10 $0 Product 1 Order Totals 0 Demand 1,000 Total Cost Product 2 0 800 $0

A store purchases two products (Product 1 and Product 2) that it stocks from three different vendors (Vendor A, Vendor B and Vendor C). The suppliers have limited capacity, and no one supplier can meet all of demand of Acme Mexico City. In addition, the vendors charge different prices for the products as shown in the table below:

Vendor’s Price
Product A B C
1 $12 $13 $14
2 $10 $11 $10

Each vendor has a limited capacity in terms of the total number of products it can supply. However, as long the store provides sufficiently advanced orders, each supplier can devote its capacity to product 1, product 2, or any combination of the two products, if the total number of units ordered is within its capacity. Vendor capacities are as follows.

Vendor A B C

Capacity 600 1000 800

The demand at the store is 1000 units of product 1 and 800 units of product 2 .

The purchasing manager wants to determine an optimal – ie, a lowest-cost – buying plan that would determine how many (>= 0) of each product should be bought from each vendor. To help the purchasing manager:

1) Develop an LP model for the above problem.

The following is a sample model showing a partial starting setup:

Product Unit Cost Quantity Product Cost Vendor Total Vendor Capacity
Vendor A 1 $12 $0 0 600
Vendor A 2 $10 $0
Vendor B 1 $13 $0 0 1,000
Vendor B 2 $11 $0
Vendor C 1 $14 $0 0 800
Vendor C 2 $10 $0
Product 1 Order Totals 0 Demand 1,000 Total Cost
Product 2 0 800 $0

2) Solve the developed LP model using Solver.