ISyE 3104: Introduction to Supply Chain Modeling: Manufacturing and Warehousing Instructor : Spyros Reveliotis Spring 2006 Solutions for Homework #3 Problem set

25000 x₁₂ + 45000 x₂₂ ≥ 100000 …….. (2)

30000 x₁₃ + 45000 x₂₃ ≥ 100000 …….. (3)

x₁₁ + x₁₂ + x₁₃ ≤ y₁ …….. (4)

x₂₁ + x₂₂ + x₂₃ ≤ y₂ …….. (5)

y₁, y₂ integers …….. (6)

x_ij ≥ 0, for i = 1, 2, j = 1, 2, 3 …….. (7)

1. 
   The objective is set to minimize the total cost, which is the sum of products of the leasing cost and the units to be leased for each technology.
   
2. 
   The decision variables (changing cells) are x_ij and y_i.
   
3. 
   There are four sets of constraints.
   
   1. 
      Non-negativity of technology dedicated to each product family.(Constraint 7)
      
   2. 
      For each technology, the capacity dedicated to each product family is less than or equal to the units leased. (Constraints 4, 5)
      
   3. 
      Integrality of leasing quantity. (Constraint 6)
      
   4. 
      For each product, the dedicated capacity is adequate to meet its demand. (Constraints 1 to 3)
      

The optimal solution is found to be leasing 2 units of technology 1, and 5 units of technology 2. The screenshots and answer report are as follow: