412-Krooks-HW3

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University of Massachusetts, Amherst *

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412

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Business

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Apr 3, 2024

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Problem 1 (10 points) In reference to the first model in Lecture 4, Ajax’s managerial accounting group has recomputed the net profit figures as follows: Each Alpha sold yields a net profit of $385, each Beta sold yields a net profit of $545, and each Gamma sold yields a net profit of $635. In addition, the manager of the test facilities has improved A-line testing procedures so that each Alpha requires 0.85 hour, whereas each Beta requires 0.65 hour. Testing a Gamma laptop still requires one hour. Finally, the production manager has hired additional personnel and there are now 2250 hours available each week for assembly of the three computers. 120 hours and 48 hours are respectively available on the A-line and the C-line for testing purposes each week. 1. Write an optimization model where the number of laptops assembled is integer (“whole numbers”). Provide an optimal solution using AMPL. Copy/paste your .mod file at the end of your solution. Objective function: Max. 385MA + 545MB + 635MC Constraints: A-line: 0.85MA + 0.65MB < 120 C-line: MC < 48 Labor hours: 10MA + 15MB + 20MC < 2250 ampl: reset; ampl: model 412/ajax3.mod; ampl: option solver cplex; ampl: solve; CPLEX 22.1.1.0 : optimal solution; objective 82920 3 dual simplex iterations (2 in phase I) ampl: display MA, MB, MC; MA = 54 MB = 114 MC = 0 ajax3.mod: var MA >= 0; var MB >= 0; var MC >= 0; maximize Profit: 385*MA + 545*MB + 635*MC; subj to aline: .85*MA + .65*MB <= 120; subj to c2: MC <= 48;
subj to c3: 10*MA + 15*MB + 20*MC <= 2250; 2. Which capacities would you consider expanding to generate further profits? Which would not change your optimal solution even if they were expanded? a. I would consider improving the capabilities of the C-line. The productivity of the A-line was improved and more labor hours were added giving the ability to produce more of both the Alpha and Beta models. Considering the Gamma model would yield the highest profit, I would want to expand on the C-line capabilities and possibly add more labor hours. 3. Management would like to make sure that at least 20 Gammas are produced because of some ongoing contract. Revise your model. What is a new optimal solution with this additional requirement? Objective function: Max. 385MA + 545MB + 635MC Constraints: A-line hours: 0.85MA + 0.65MB < 120 C-line hours: MC < 48 Gamma production: MC > 20 Labor hours: 10MA + 15MB + 20MC < 2250 Ampl solver: ampl: model 412/ajax3a.mod; ampl: option solver cplex; ampl: solve; CPLEX 22.1.1.0 : optimal solution; objective 81988 3 dual simplex iterations (2 in phase I) ampl: display MA, MB, MC; MA = 96 MB = 56 MC = 20 Problem 2 (10 points) Read the article entitled "Matching Supplies to Save Lives" under Lecture 5. In about no more than two pages, discuss: 1. The managerial problem/challenges encountered. a. It was noted that the two areas needing the most improvement were yields and inventories. Product availability was a big dilemma that contributed to the challenge of both yields and inventories. The size of a pig heart valve is not able to be determined until it is processed and the variability of the size of pig hearts is due to some uncontrollable factors. This can be anything from the pig’s breed to its food. The unpredictability and the variability of the sizes
of the pig hearts contributed largely to the inventory and distribution sectors of American Edwards Laboratories. The company experienced shortages in certain valve sizes and a surplus in others. 2. The solution approach proposed and its data requirements. a. The solution approach proposed was a linear programming optimization model. It was meant to assist in determining the optimum quantity of hearts to be ordered from the company’s vendors based on data from previous distributions. The data required for this model included procurement, processing and inventory costs, heart valve sales, raw heart supply by vendor, and vendor heart valve size distributions and yields. In order for the model to work properly, data had to be collected on all incoming valves, the valve source, and its final status. 3. The financial impact as well as the impact on business processes and people involved. a. Before the implementation of the optimization model, American Edwards Laboratories was spending nearly $80,000 every month on excess inventory. In the first three months, excess costs were reduced to less than $10,000 per month resulting in annual savings of over $1 million. The implementation of the model gave production managers more control and the ability to forecast more accurately. With more accurate forecasting, shortages were identified well in advance which gave the opportunity to the company to implement corrective measures. 4. Might there be a typo in some of the constraints presented in the appendix? a. The demand constraints should be written as follows: i. .3X a + .1X b > 100 ii. .5X a + .6X b > 300 iii. .2X a + .3X b > 250
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