A company is planning production for the next 4 quarters and wants to minimize the cost of
Question:
A company is planning production for the next 4 quarters and wants to minimize the cost of production. The production cost, demand, and production capacity vary from quarter to quarter as shown in Table 1 below. The maximum amount of inventory that can be held is 100 units, and management wants to keep at least 50 units on hand at all times. The quarterly per unit inventory holding cost is 4% of the unit production cost for the same quarter. There are currently 50 units in inventory, and the company wants to produce at no less than one half of its maximum capacity in any quarter.
(Quarter on top row i.e., 1, 2, 3, 4)
Table 1. Input Data for Production Planning Problem
Let Xi = number of units produced in quarter i, i = 1, ?, 4 and
Yi = beginning inventory for quarter i, i = 1, ?, 4
Write the algebraic formulation of this optimization problem, such that total production costs are minimized. Be sure to include the objective function and all necessary constraints. (Hint: You should have 12 constraints in addition to the non-negativity constraints.)
Create a spreadsheet model for this scenario and use Solver to find the optimal solution. Be sure to highlight the number of units produced and the total production cost.
Managing Operations Across the Supply Chain
ISBN: 978-0078024030
2nd edition
Authors: Morgan Swink, Steven Melnyk, Bixby Cooper, Janet Hartley