Linear Programming Decision Making – Lab TWO
In last week’s homework we concentrated on linear programming as a deterministic decision making tool. The example however was not relevant in today’s working world (too simple). This lab should provide a much more relevant exercise; determining the product mix to maximize profit over an extended planning horizon, with multiple products and multiple workstations (or locations).
Consider an organization that produces three products (X,Y and Z) and has available 4 workstations (A,B,C and D). The production time (in minutes) per unit produced varies from workstation to workstation (due to different manning levels) as shown below:
A B C D
Product X 5 7 4 10
Y 6 12 8 15
Z 12 14 9 17
Similarly the profit contribution (contribution to fixed costs) per unit produced varies as a function of the workstation it is produced on, given the age and quality of the specific workstation.
A B C D
Product X 10 8 6 9
Y 18 20 15 17
Z 15 16 14 17
We are going to consider a two week planning horizon. The following number of hours are available per workstation per week.
Workstation Week One Week Two
A 30 50
B 40 30
C 35 20
D 45 35
The demand for each product are given below in each week and a total for both weeks (i.e., you must “hit” all 3 minimums)
Product Week One Week Two Total For Both Weeks
Minimum Minimum Minimum
X 80 120 220
Y 150 120 300
Z 120 90 220
1 – Provide a mathematical formulation,
2 – Provide the Excel file for the A,b and F matrices and also a screen shot of your inputs in the Word Doc.
3- Screen shot of Matlab results and Matlab script.
4 – A brief interpretation of the results.
5 – What would the revised solution be if Workstation A hours were increased 25%.
6 – What would you change to increase profits at least 20%?
7- Consider any problem you are interested in; provide the following:
A – A brief description of the problem (one paragraph or less)
B – What is the goal to maximize or minimize? (one or two sentences)
C – What are the proposed decision variables?
D – Mathematical Formulation
E – What problems do you foresee with application of this technique?
8 – Brief comment about the appropriateness of this technique in your career path.
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