The University of Wisconsin Milwaukee Business Administration 478-Supply Chain Analytics Midterm 01 Oct. 8 at 9 PM Note 1: This is a take-home exam and you have 48 hours to finish and submit it to the assigned dropbox. Note 2: For some questions you may need to write an algebraic model and solve them using excel. Please submit a.doc file for your answer and excel file for each question. NOTE 3: This is an exam please Do every question on you own Note 4: For some questions you may need to use SolverTable for sensitivity analysis, please make sure that you have it installed on your machine. Note 5: There are 5 questions, but you need to choose and answer only 4 questions. If you would like to answer all 5 questions, I consider the 4 questions that you receive top grade for and the extra will be considered as Bonus point. Therefore, you may receive 120/100. - 1 -
1) Suppose you are a director of a library at a college and responsible for scheduling and staffing. The library is open for 24 hours and you determined that the minimum required personnel as follows: Time of the day Minimum number of staff required Midnight 4 AM 5 4 AM 8 AM 4 8 AM 12 PM 6 12 PM 4 PM 8 4 PM 8 PM 10 8 PM - Midnight 6 Note that the schedule can be cyclic meaning that the pattern can repeat each week. As a manager you want to hire two types of staff: full-time and part-time. The fulltime employee must work for 8 consecutive hours and will be paid $14 per hour. The part-time can work only for one 4-hour period during each day and will be paid $10/hour. There is another requirement: during each hour period, there must be at least one full time employee on duty for each part-time employee hired for that period. a. Develop a linear program for this staffing problem that minimizes cost? b. Solve your linear model using Excel and submit your spreadsheet model and the results. How many full-time and part-time employees are required? What is the minimum cost? - 2 -
2) Consider a corporation that produces three types of bookcases: standard, narrow, and wide. The production of each bookcase requires three types of processes: trimming, shaping and assembly. Each type requires the following processing time (in hours per unit) Standard Narrow Wide Capacity Trimming 0.3 0.2 0.4 200 Shaping 0.4 0.3 0.5 200 Assembly 0.5 0.5 0.5 600 Contribution to profit $8 $12 $14 a. Develop a linear program for this production planning problem. b. What are the optimal production quantity for each bookcase? What is the optimal profit? Submit your spreadsheet model and the results. c. Show reduced cost for each variable and shadow price for each constraint? Explain what each value represent. - 3 -
3) A food company is planning to introduce a trail mix as new product. The ingredients include seeds, raisins, flakes and two kinds of nuts. Each ingredient contains certain amount of vitamin, minerals, protein, and calories. The new product should have certain amount of the nutrition listed above. As a management scientist you are asked to develop a linear program that determines the optimal product ingredients at the minimum cost. The parameters of the problem are shown in the table below. What are your binding constraints? Submit your spreadsheet model and the results. Explain the relationship between binding constraint(s) and the respective shadow prices. Grams/pound Seeds Raisins Flakes Pecans Walnuts Nutritional requirement Vitamins 16 20 12 30 15 20 Minerals 7 9 4 8 2 15 Protein 2 6 14 1 3 15 Calories 500 400 190 350 475 700 Cost per $5 $7 $6 $8 $9 pound - 4 -
4) NewAge Pharmaceutical produces a drug called NasaMist from four different chemicals. For today demand, the company must produce 1000 pounds of the drug. There are three active ingredients in the drug: A, B, and C. By weight, at least 8% of the drug must consist of A, at least 4% of B, and at least 2% C. At least 100 pounds of chemical 2 must be used. The cost per pound of each chemical and the amount of each active ingredient in one pound of each chemical are as follows Ingredient/ lb of chemical Cost/ lb of A B C Chemical Chemical 1 0.03 0.02 0.01 $8 Chemical 2 0.06 0.04 0.01 $10 Chemical 3 0.10 0.03 0.04 $11 Chemical 4 0.12 0.09 0.04 $14 a. Determine the cheapest way of producing today s batch of NasaMist. Submit your spreadsheet model and the results. b. Determine reduced costs and shadow prices and explain how shadow price affect the constraints and the objective function. c. Use SolverTable to see how much the percentage of requirement of A is really costing NewAge. Let the percentage required vary from 5% to 14%. - 5 -
5) Budget Auto produces inexpensive cars. Each is sold for $7900. The raw material in a car costs $5000. Labor time and robot time are needed to produce cars. A worker can do the needed labor on, at most, 100 cars per month; a robot can complete the needed work on, at most, 200 cars per month. The company currently has four workers. Each worker receives a monthly salary of $6000. It costs $2500 to hire a worker and $1000 to fire a worker. Hired workers are fully productive during the month they are hired. Robots must be bought at the beginning of month 1 at the cost of $15000 per robot. The demand for cars are known and listed in the table below. At the end of each month, the company incurs a holding cost of $200 per car. How can the company maximize the profit earned during the next six months? Submit your spreadsheet model and the results. Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Demand 400 500 600 800 700 600-6 -