MBA 675 Week 10 HW

Order 1 2 3 4 5 Order Due Date (hours from now) 1 6 10 12 Order 2 5 3 8 2 3 3 15 18 1 4 1 9 20 3 5 0 7 21 4 The due dates reflect the need for the order to be at its next operation. 5 B. Comment on the performance of the two rules relative to these measures. Order 2 5 4 1 3 Chapter 10, Problems #18- in addition to developing scheduling rules based on FCFS and EDD develop scheduling rules for shortest processing time (SPT) and Slack using the definition of Slack at the start of this assignments document. In addition to evaluating the average flow time and average lateness, also evaluate the average early time. The Hickory Company manufactures wooden desks. Management schedules overtime every weekend to reduce the backlog on the most popular models. The automatic routing machine is used to cut certain types of edges on the desktops. The following orders need to be scheduled for the routing machine: Time since order arrived (hours ago) Estimated Machine Time (hours) A. Develop separate schedules by using the FCFS and EDD rules. Compare the schedules on the basis of average flow time and average past due hours. After calculations, the SPT has the shortest late time and the highest early time. Hickory company should use the SPT schedule for the most efficiency.

First Come First Serve (FCFS) Start Est. Machine Time (hrs.) Finish time Due Time Past Late Time Time Since Order Arrival Flow Time Early Hours 0 10 10 12 0 6 16 2 10 3 13 8 5 5 18 0 13 15 28 18 10 3 31 0 28 9 37 20 17 1 38 0 37 7 44 21 23 0 44 0 11 29.4 0.4 Avg. Late Time Earliest Due Date (EDD) Start Est. Machine Time (hrs.) Finish time Due Time Past Late Time Time Since Order Arrival Flow Time Early Hours 0 3 3 8 0 5 8 5 3 10 13 12 1 6 19 0 13 15 28 18 10 3 31 0 28 9 37 20 17 1 38 0 37 7 44 21 23 0 44 0 10.2 28 1 Avg. Late Time Shortest Processing Time (SPT) Start Est. Machine Time (hrs.) Finish time Due Time Past Late Time Time Since Order Arrival Flow Time Early Hours 0 3 3 8 0 5 8 5 3 7 10 21 0 0 10 11 10 9 19 20 0 1 20 1 19 10 29 12 17 6 35 0 29 15 44 18 26 3 47 0 8.6 24 3.4 Avg. Late Time FCFS 12.9 FCFS 31.5 1.1 EDD 16.125 EDD 34.375 1.125 SPT 15.90625 SPT 34.21875 1.40625 Avg. Flow Time Avg. Early Time Avg. Flow Time Avg. Early Time Avg. Flow Time Avg. Early Time

Ingredients Almonds 180 6 8% 6% $ 0.28 Walnuts 190 4 2% 6% $ 0.38 Peanuts 170 7 0% 4% $ 0.12 Decision Variables: Almonds Walnuts Peanuts 0.28 0.38 0.12 Capacity X1(calories) 0 0 0 <= 720 Capacity X2(protein 0 0 0 >= 20 Capacity X3 (Calcium %ADR) 0.15 0.15 0.15 >= 0.15 Capacity X4 (Iron % ADR) 0.2 0.2 0.2 >= 0.2 Objective: Minimize costs: .28A+.38W+.12P Constraints: Calories: 180A+190W+170P <= 720 Protein: 6A+4W+7P<=20 Calcium: .08A+.02W+0P >= 0.15 Iron: .06A+.06W+.04P >= 0.2 C= Calories (per oz) Grams of protein (per oz.) % ADR of Calcium (per oz.) % ADR of Iron (per oz.) Cost (per oz.)

Variable Almonds Walnuts Peanuts SUM Sign RHS Ounces 0.5 0.5 1 - - - Min. Pacakge Cost $ 0.14 $ 0.19 $ 0.12 - - - Solution B satisfies the new constraints Calories (per oz.) 180 190 170 - - - Calories 90 95 170 355 <= 720 Grams (per oz.) 6 4 7 Protein 3 2 7 12 >= 20 ADR Calcium 8% 2% 0% ADR Iron 6% 6% 4% % of Calcium 4% 1% 0% 5% >= 15 % of Iron 3% 3% 4% Total Ounces 0.5 0.5 1 2 = 4 Total Almonds 0.5 0.5 >= 0.5 Total Walnuts 0.5 0.5 >= 0.5 Total Peanuts 1 1 >= 1 B. The marketing department at Nutmeg insists that each package should contain at least 0.5 ounce of almonds, at least 0.5 ounce of walnuts, and no more than 1 ounce of peanuts. Does the solution developed for part (a) satisfy these new constraints? If not, use linear programming to find a solution that includes these marketing requirements. What is the new cost of raw materials?

Consider each of the following statements independently, and state whether it is true or false. Explain each answer. B. The capacity of machine B can be reduced to 280 hours without affecting profits. C.If machine C had a capacity of 115 hours, the production output would remain unchanged. A. If the price of hat 3 were increased to $11.50, it would be part of the optimal product mix. Hint: Hat 3 is represented by and its optimal value currently is 0, which means that it is not to be produced (and not part of the optimal product mix). False- the reduced cost for X3 is $7, this would mean that you would want to increase the price to maxamize profits. Selling hat 3 for $11.50 would not yeild enough profits. True- the lower bound value is 265, the current solution has slack of 135 hours. Reducing capacity to to 280 does not affect the schedule and has the same overall profit. (15 hours of slack time available if this did happen) False- The upper bound limit is 120, meaning the capacity is over 115 which is less than the upper bound limit. Shadow price could be used in this scenario, the production output would change to utilize the increased capacity.

Product B. Solve yo Alpha Beta Delta Gamma Price $ 350.00 $ 320.00 $ 400.00 $ 500.00 Material Cost $ 50.00 $ 40.00 $ 125.00 $ 150.00 Weekly Demand (in units) 100 60 50 80 20 0 40 10 25 20 0 50 0 20 60 30 Alpha= Beta= Delta= Gamma= Alpha Beta Delta Gamma Supplement D, Problems #23 – works parts a), b) and d) and for d) only set-up the formulation for this part but you do not need to solve it. On a) the demand is the maximum demand Supertronics, Inc., would like to know how the firm’s profitability is altered by product mix. Currently, product mix is determined by giving priority to the product with the highest per-unit contribution margin (defined as the difference between price and material cost). Details on the Supertronics product line, including processing time at each workstation, follow: (in min) (in min) (in min) A. Assume that Supertronics has 5,500 minutes of capacity available at each workstation each week. Develop a linear program to define the production mix that maximizes contribution margin. D. How wo already com

Perform an ethical analysis using the concepts presented in the Week Nine Assignments document What is th What are the two most critical issues that must be addressed in this Ethical Dilemma? Ethical Dilemma #2 Scheduling people to work second and third shifts (evening and “graveyard”) is a problem in almost every 24-hour company. There can be potentially dangerous issues on the night shift. In addition, ergonomic data indicate the body does not respond well to significant shifts in its natural circadian rhythm of sleep. There are also significant long-run health issues with frequent changes in work and sleep cycles. Consider yourself the manager of a nonunion steel mill that must operate 24-hour days, and where the physical demands are such that 8-hour days are preferable to 10- or 12-hour days. You and your employees have spent much time and energy developing an employee empowerment work environment. Your empowered employees have decided that they want to work weekly rotating shifts. That is, they want a repeating work cycle of 1 week 7 A.M. to 3 P.M, followed by a second week from 3 P.M. to 11 P.M., and the third week from 11 P.M. to 7 A.M. You are sure this is not a good idea in terms of both productivity and the long-term health of the employees. If you do not accept their decision, you undermine the work empowerment program, generate a morale issue, and perhaps. More significantly, generate a few more votes for a union. Answer the following questions:Perform an ethical analysis using the concepts presented in the Week Nine Assignments document. What are the two most critical issues that must be addressed in this Ethical Dilemma? What is the ethical position and what would you do? Things to consider: 1. Define the conflict and identify the higher-order values involved 2. Identify the stakeholders 3. Identify the options you can reasonly take 4. Identify the potential cnsequences of your options The ethical dilemma at hand revolves around two crucial issues: employee health and safety, and organizational productivity and efficiency. Firstly, the well-being of the employees is a significant concern, as working rotating shifts, particularly night shifts, can disrupt their natural sleep patterns, leading to fatigue, reduced alertness, and potential safety hazards in a physically demanding steel mill environment. Secondly, there is a potential impact on productivity and efficiency, as significant shifts in work schedules can result in decreased concentration, fatigue-related errors, and overall performance decline, hindering the mill's operational effectiveness. To address this ethical dilemma, it is important for the manager to find a balance between employee preferences and the long-term interests of both the individuals and the organization. This involves considering alternative solutions that prioritize employee health and safety while maintaining productivity levels. Open and transparent communication with the empowered employees is crucial to understand their concerns and collaboratively reach a mutually beneficial resolution. By actively addressing these critical issues, the manager can navigate the ethical dilemma, uphold the work empowerment program, foster a positive work environment, and ensure the well-being and productivity of the employees. The ethi employe As the m 1. Gathe of rotati 2. Foster perspec input. 3. Educa understa them m 4. Explo empowe rotation 5. Priori indicate alternati In summ open dia environm

he ethical position and what would you do? ical position in this scenario is to carefully balance employee well-being and organizational productivity. It involves considering the potential risks to ee health and safety posed by rotating shift schedules, while also acknowledging the importance of maintaining operational effectiveness. manager in this situation, my proposed course of action would be as follows: er Relevant Information: I would thoroughly research and analyze scientific studies, expert opinions, and industry best practices regarding the effects ting shift schedules on employee health, safety, and productivity. This knowledge would inform my decision-making process. r Open Dialogue: I would actively engage in open and honest conversations with the empowered employees to gain a deep understanding of their ctives, concerns, and reasons for advocating for a rotating shift schedule. This dialogue would demonstrate my willingness to listen and value their ate and Inform: Using the research findings, I would transparently share information with the employees to provide them with a comprehensive anding of the potential risks associated with rotating shifts. By raising awareness about the impact on long-term health and safety, I would help make informed decisions regarding their work schedules. ore Alternative Solutions: Together with the employees, I would collaboratively explore alternative scheduling options that offer flexibility and erment while mitigating the negative consequences of rotating shifts. This proactive approach could involve considering modified shift patterns, job ns, or innovative solutions that strike a balance between employee preferences and their well-being. itize Health and Safety: Ultimately, the well-being and safety of the employees would be my top priority. If the scientific evidence overwhelmingly es that rotating shifts pose significant risks, I would transparently communicate these concerns to the employees. In such cases, I would propose tive schedules that prioritize their long-term health and safety while ensuring the organization's operational efficiency. mary, my ethical stance would prioritize employee health and safety while also considering the productivity needs of the organization. By fostering alogue, sharing information, exploring alternative solutions, and making decisions that strike a balance, I would strive to maintain a positive work ment, preserve the principles of the empowerment program, and safeguard the well-being of the employees in the best possible way.