Reference no: EM13230946
The purpose of this simulation project is to provide you with an opportunity to use the POM-QM for Windows software to solve a linear programming problem and perform sensitivity analysis.
POM-QM for Windows software
For this part of this project, you will need to use the POM software:
- Read Appendix IV of the Operations Management (Heizer & Render, 2011) textbook.
- Install and launch the POM-QM for Windows software and from the main menu select Module, and then Linear Programming.
Note: You can retrieve the POM-QM for Windows software from either the CD-ROM that accompanied your Heizer and Render (2011) textbook.
- Program the linear programming formulation for the problem below and solve it with the use of POM. (Refer to Appendix IV from the Heizer and Render (2011) textbook.)
Note: Do not program the non-negativity constraint, as this is already assumed by the software.
For additional support, please reference the POM-QM for Windows manual provided in this week's Learning Resources.
Individual Project problem
A firm uses three machines in the manufacturing of three products:
- Each unit of product 1 requires three hours on machine 1, two hours on machine 2 and one hour on machine 3.
- Each unit of product 2 requires four hours on machine 1, one hour on machine 2 and three hours on machine 3.
- Each unit of product 3 requires two hours on machine 1, two hours on machine 2 and two hours on machine 3.
The contribution margin of the three products is £30, £40 and £35 per unit, respectively.
Available for scheduling are:
- 90 hours of machine 1 time;
- 54 hours of machine 2 time; and
- 93 hours of machine 3 time.
The linear programming formulation of this problem is as follows:
Maximise Z = 30X1 + 40X2 + 35X3
3X1 + 4X2 + 2X3 <= 90
2X1 + 1X2 + 2X3 <= 54
X1 + 3X2 + 2X3 <= 93
With X1, X2, X3 >= 0
- What is the optimal production schedule for this firm? What is the profit contribution of each of these products?
- What is the marginal value of an additional hour of time on machine 1? Over what range of time is this marginal value valid?
- What is the opportunity cost associated with product 1? What interpretation should be given to this opportunity cost?
- How many hours are used for machine 3 with the optimal solution?
- How much can the contribution margin for product 2 change before the current optimal solution is no longer optimal?
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