Outsourcing Decisions
Suppose that you are the Manager of the Purchasing Department in a manufacturing company. Currently, you are trying to outsource one of the raw materials (a steel pipe) required for manufacturing your product. Specifically, you know that you need to purchase and ship exactly 5,000 units of steel pipe each week to the manufacturing plant. There are four possible suppliers that you can purchase and ship the steel pipes from. Each supplier has different purchase costs per unit of steel pipe and different shipping costs due to their distances. Furthermore, each supplier has limited weekly supply of steel pipes. The table below summarizes the following data:
- The distance of each supplier to the manufacturing plant (in miles)
- The purchase cost charged by each supplier per steel pipe ($ per unit of steel pipe)
- The weekly supply capacity of each supplier (units of steel pipe)
- The transportation cost charged by the supplier for shipping one unit of steel pipe per mile ($ per steel pipe per mile)
As the purchasing manager, you want to minimize the total cost of weekly steel pipe supply to the manufacturing plant, which includes weekly purchase costs and weekly transportation costs. To do so, you need to determine how many units of steel pipe to ship weekly from each supplier (assume that you can purchase and ship fractional number of steel pipes from the suppliers). While doing so, you need to consider the following:
- Weekly transportation cost should not exceed 80% of the total weekly cost
- Since suppliers 3 and 4 are closer to the manufacturing plant, you want the total steel pipes purchased and shipped weekly from suppliers 3 and 4 to be more than or equal the total steel pipes purchased and supplied weekly from suppliers 1 and 2
- Since you want to build good relations with your suppliers, you want to purchase and ship at least 250 units of steel pipe from each supplier each week
- You want to purchase and ship at least 2 units of steel pipe from supplier 1 for each unit of steel pipe you purchase and ship from supplier 4
In this problem, you are asked to formulate the above outsourcing problem mathematically as a linear model. To do so, define your decision variables, objective and express your objective function and constraints in terms of your decision variables, and combine everything to get the final formulation.