The Theory of Constraints

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5.1 The Theory of Constraints

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Q: Consider the following problems in which four jobs must each be processed on two machines starting with Machine A and then going to Machine B. The following processing times are available (in hours): Job Processing Time Machine A Processing Time Machine B A 1 5 B 8 2 C 3 9 D 7 7 What is the minimum makespan for this group of jobs? Depict it graphically using a Gantt chart.

Q: The Dean's office is interested in determining the percentage of students receiving A's in their study tour classes. The results of three classes are summarized in this table: Observation Period A Grade Other Grade Observations Monday 26 3 23 Tuesday 25 0 25 Wednesday 15 1 16 Total 66 4 70 The Assistant Dean wants a 98 percent confidence level and a degree of precision of + 0.04. How many more observations are needed?

Q: A single-sampling plan by attributes is needed for a purchased component. Table G.1 is appended to this exam. Sample size = 80 Acceptance number (c) = 1 Acceptance quality level (AQL) = 0.02 Lot tolerance proportion defective (LTPD) = 0.06 Given the preceding information draw the AOQ curve and determine the AOQL.

Q: Jackson Sheds has four different warehouse configurations under study, ranging from four warehouses to seven warehouses (only integer values). Each warehouse has a capacity of 200 units and costs $200 to maintain over the course of a year. Demand can range from 1,000 units per year up to 2,000 units in increments of 250 units. If the system warehouse capacity is sufficient to handle the year's demand, then the per unit cost is $2 per unit, but if the warehouse capacity is insufficient, the per unit cost for each unit in excess of system capacity is $3 per unit. The likelihood for each possible demand is shown in the table. Likelihood 0.1 0.2 0.3 0.3 0.1 Demand 1,000 1,250 1,500 1,750 2,000 Which warehouse configuration is best for Jackson Sheds?

Q: Jackson Sheds has four different warehouse configurations under study, ranging from four warehouses to seven warehouses (only integer values). Each warehouse has a capacity of 400 units and costs $200 to maintain over the course of a year. Demand can range from 1,000 units per year up to 2,000 units in increments of 250 units. If the system warehouse capacity is sufficient to handle the year's demand, then the per unit cost is $2 per unit, but if the warehouse capacity is insufficient, the per unit cost for each unit in excess of system capacity is $5 per unit. The likelihood for each possible demand is shown in the table. Likelihood 0.1 0.2 0.3 0.3 0.1 Demand 1,000 1,250 1,500 1,750 2,000 Which warehouse configuration is best for Jackson Sheds?

Q: Jackson Sheds has four different warehouse configurations under study, ranging from four warehouses to seven warehouses (only integer values). Each warehouse has a capacity of 300 units and costs $200 to maintain over the course of a year. Demand can range from 1,000 units per year up to 2,000 units in increments of 250 units. If the system warehouse capacity is sufficient to handle the year's demand, then the per unit cost is $2 per unit, but if the warehouse capacity is insufficient, the per unit cost for each unit in excess of system capacity is $5 per unit. The likelihood for each possible demand is shown in the table. Likelihood 0.1 0.2 0.3 0.3 0.1 Demand 1,000 1,250 1,500 1,750 2,000 Which warehouse configuration is best for Jackson Sheds?

Q: A national firm has beef jerky processing facilities in Locations 1, 2, 3, and 4. They ship to central distributors (represented as A, B, C, and D) handling four regions of the country. The per-unit shipping costs between each possible combination of locations are shown in the following table. A B C D 1 $5 $10 $5 $4 2 $3 $4 $4 $3 3 $8 $6 $8 $2 4 $2 $3 $5 $9 The processing facility locations are capable of monthly production (in tons) as follows: Location 1: 600 Location 2: 350 Location 3: 475 Location 4: 850 The central distributors have firm commitments for the following quantities: Distributor A: 650 Distributor B: 725 Distributor C: 400 Distributor D: 500 What is the lowest-cost shipping arrangement that can be made between the plant locations and distributors and what is the annual shipping cost?

Q: The VP of Finance studied the printing costs at the university and knew it was time for bold, decisive action. The annual fixed cost of printing at the school was $850,000 and the per-page cost was one cent. Fortunately, his brother-in-law happened to own a company that would lease the printers to the university for only $600,000. The only issue to be decided was what the per-page cost would be for the leased printers. On average, the university had been printing about 10,000,000 pages per year. What would a break-even per-page printing cost be given the average printing volume?

Q: Complete the following MPS Record

Q: Consider the MPS, BOM, and inventory data shown. Master Production Schedule: The following table shows the MPS start quantities for the next 10 weeks. Finished Item A 1 2 3 4 5 6 7 8 9 10 Finished Item A MPS Start 20 40 30 20 40 Bill of Material: - Item A uses 2 each of component D, 1 each of component C and 2 each of subassembly B. - Subassembly B uses 2 each of component E. Selected Inventory Data: Item Lot Sizing Rule Lead Time Scheduled Receipts On-Hand B L4L 1 40 in period 1 C POQ = 3 2 40 D FOQ = 250 1 100 E L4L 2 160 in period 2 Construct the MRP schedule using the preceding information.

Q: Job Process Time (days) Due Time (days) Days Since Arrival A 2 7 12 B 8 16 9 C 4 4 8 D 10 17 5 E 5 15 3 F 12 18 2 Use the information in the preceding table and sequence the six jobs using FCFS and EDD. The jobs are listed in the order of their arrival. Calculate the average flow time and average past due. It is now time zero.

Q: A retailer experiences a seasonal demand pattern for its services. Labor requirements over a typical six-month period follow. Period 1 2 3 4 5 6 Requirement 7 8 9 11 12 7 Costs associated with operations are as follows: Wages = $2,000 per worker per month Hiring cost = $1,000 per worker Layoff cost = $1,500 per worker The current workforce level is 10 workers. Use the spreadsheet approach and the preceding data to answer the following questions: a. What is the total cost of a staffing plan, including the cost of regular wages, hiring, and layoffs using a chase strategy with hiring and layoffs, but no overtime? b. What is the total cost of the staffing plan, using a level strategy in which no overtime is allowed and the undertime paid for? c. Suppose that overtime is allowed up to 25% of the regular-time capacity, and that overtime wages are 150% of the regular-time rate. What is the total cost of the level strategy with overtime and undertime that also minimizes undertime?

Q: Happiness, Inc. uses a Kanban system. The daily demand for the most critical part, the Smylie, is 400 units over an eight-hour production period. The average waiting time for a container of Smylies is 30 minutes. The processing time for a container filled with Smylies is 6 minutes, and a container holds 5 units. If the company wishes to use a 5% policy variable, how many containers are needed?

Q: The single milling machine at Fred's Manufacturing was severely overloaded last year. The plant operates 8 hours per day, 5 days per week, and 50 weeks per year. Management prefers a capacity cushion of 20 percent. Two major types of products are routed through the milling machine. The annual demand for product A is 4,000 units and 3,000 units for product B. The batch size for A is 20 units and 30 units for B. The standard processing time for A is 0.5 hours/unit and 0.8 for B. The standard setup time for product A is 2 hours and 8 hours for product B. How many new milling machines are required if Fred's does not resort to any short-term capacity options?

Q: A manufacturer enjoys both a Cpk and a CP = 2.0. How high does the process mean have to drift (in number of standard deviations) away from target in order to result in a 1% chance of making a product out of specification? Illustrate this situation (both before shift and after shift) with a diagram.

Q: A bank randomly looks at loan applications and checks them for errors. Ten applications and the number of errors identified on the applications are found in the following table. When the process is working correctly, the average number of errors found is 2. Construct a c-chart to determine if the process is in control. Application number Number of errors 1 3 2 0 3 1 4 0 5 3 6 2 7 4 8 4 9 1 10 1

Q: Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Is the process under control? Unit # Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 73.5 70.8 72.2 73.6 71.0 2 71.3 71.0 73.1 72.7 72.2 3 70.0 72.6 71.9 72.4 73.3 4 71.1 70.6 70.3 74.2 73.6 5 70.8 70.7 70.7 73.5 71.1

Q: Develop a process chart for one of the following: 1) Researching and writing a paper for your Operations Management class 2) Managing, developing and completing a team project for a Finance (or other) class 3) Planning for your job interview process as you approach graduation (including resume preparation, developing interview skills, researching company backgrounds, etc.) 4) Studying and developing a process improvement plan for a business or other process you are familiar with (e.g., fast food restaurant, obtaining tickets to a university-sponsored event, dry cleaners, book purchases for next term, and the like)

Q: Develop a process chart for a manual car wash.

Q: Because a telephone customer service center has experienced several problems, it has begun to analyze the data from customer complaints. The first step was to construct the following table. Use this data to build a Pareto chart to help identify the "vital few" problems. Process Failure Total Failures Person not available 5 Incorrect information given 12 Phone line busy 7 Long delay 39 Phone tree confusing 20 People unfriendly 17

Q: The estimated time to produce the first unit is 100 hours. If a 90 percent learning rate is applicable, what is the estimated time of producing the first ten units? Refer to the copy of Table I.1 appended to this exam.

Q: Refer to the bank process model. The bank's process improvement group has developed a number of process and technology changes that will improve the Teller's process rate per customer from a mean of 3.0 minutes to 2.5 minutes (standard deviation remains at 0.5 minutes). The Bank Manager wants to determine if the improved process rate, along with the special promotion for new customers, will allow the "arrive and immediately leave" rate and average customer wait time in line achieved to still be met (12% balk rate, 9.95 minutes in line). If so, the manager will implement the process and technology changes and allow the special promotion to proceed. Using SimQuick, estimate the new arrive and immediately leave rate and average time in line. What decision should the manager make?

Q: Walter White must satisfy an annual demand of 50,000 pounds per year. The setup cost for each batch is $6,500 and once the setup is complete, the product may be produced at the rate of 1800 pounds per day. There is a holding cost of $15 per unit per year and the plant operates on a 350-day production year. How big should the production batch be and how long (in days) will it take to produce the batch?

Q: SimQuick is to be used to simulate the following bank process: Customers arrive at the Entrance Door of the bank with an average time between arrivals of 2.5 minutes. The Line Buffer holds 6 customers. If a customer arrives and the buffer line is filled, the customer leaves. The Work Station Teller's processing time per customer is normally distributed, with a mean of 3.0 minutes and a standard deviation of 0.5 minutes. The Served Customer Buffer in the flowchart is used to count the number of customers processed during the simulation period. A 2-hour period is to be simulated and the simulation should be repeated 30 times. Determine: a) The number of customers served during the 2-hour period; b) The percentage of customers who arrived at the bank and left because the buffer line was full; c) The utilization of the teller (% of time working) during the 2-hour period;

Q: What is degeneracy in the context of linear programming? Why is degeneracy a concern?

Q: Construct a 3-sigma and R-chart for the length in centimeters of a part from the following table. Sample # Observation 1 Observation 2 Observation 3 Observation 4 1 0.486 0.499 0.493 0.511 2 0.499 0.506 0.516 0.494 3 0.496 0.5 0.515 0.488 4 0.495 0.506 0.483 0.487 5 0.472 0.502 0.526 0.469 6 0.473 0.495 0.507 0.493 7 0.495 0.512 0.49 0.471 8 0.525 0.501 0.498 0.474 9 0.497 0.501 0.517 0.506 10 0.495 0.505 0.516 0.511

Q: The three-person crew worked their way through the neighborhood, testing doorknobs and windows and slipping past security systems like a team of ninjas. Of course, they weren't ninjas, but a crew of brazen burglars, hoping to grab cash and other valuables to fence at the next level of their supply chain. Fortune smiles on them on this day in the prestigious Edmond Oaks neighborhood. A lawn maintenance crew is creating a tremendous racket mowing and edging lawns, which completely drowns out the sounds of breaking glass. Details of the day's haul appear in Table C. a. What is the multifactor productivity? b. What is the labor productivity? Table C: The Haul ITEM SALES PRICE LABOR MATERIAL Krugerrand $1,500 1 hr $2 Flat screen TV $250 .25 $1 $200 cash $200 .05 $45 Lava lamp $5 .15 $25 Rolex watch $180 .10 $1 Workers are paid at a flat rate of 20% of the sales price of the merchandise. Materials cost represents the cost of gasoline and surgical gloves, and overhead is 20% of the sales price of the merchandise.

Q: Consider this list of jobs that have just arrived and are ready for processing. They all require processing first on machine 1 and then on machine 2. Both machines are now idle. Develop a schedule that minimizes makespan and calculate this makespan time. Now assume that each job can be split into two jobs, each having half the duration on both machine 1 and machine 2. Using the original sequence that minimized average flow time, calculate the flow times for all split jobs What is the effect of this new schedule on the average flow time for these split jobs? Job Machine 1 Machine 2 1 14 6 2 11 12 3 16 14 4 12 8 5 22 9 6 13 15 7 10 12 8 8 13

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