Statical Control
PROBLEM 1 (30 points) Proctor & Gamble (P&G), the manufacturer of Crest toothpaste, is considering subcontracting with a new vendor, Guangzhou Packaging, to provide the caps for their travel-size toothpaste containers. Their first step is to determine if Guangzhou Packaging’s cap manufacturing process is able to consistently produce caps of the same dimensions or if their manufacturing process has a lot of variation in it. Therefore, P&G went to the Guangzhou Packaging manufacturing facility and, over the course of 3 days, took 10 samples of 7 caps each. They measured each cap (in millimeters) and put the measurements in a table as shown below. Use the data collected to answer the following questions. Carry calculations out to at least 2 decimal places. Show your calculations. a) What is type of control chart(s) should be constructed to completely assess the variation in this process based on the data provided in the table below (i.e., c, p, X-bar, and/or R)? Explain your answer. (4) b) Calculate the control limits (show your calculations) and construct the control chart(s) making sure all control chart elements are present. The spacing between the control limits should be wide enough to easily read all data points plotted. (10) Note: The control chart(s) may be created in Excel; however, clear, easy to read copies must be embedded as a picture in your test document. c) Is the process in control? Explain your answer. (5) Sample Cap1 Cap2 Cap3 Cap4 Cap5 Cap6 Cap7 1 7.5 8.1 8.0 7.7 7.6 7.2 5.4 2 6.3 6.2 6.8 7.7 7.6 6.0 7.7 3 7.0 7.0 6.2 7.5 6.8 5.1 8.2 4 5.4 5.7 6.9 6.9 5.7 6.8 8.3 5 5.3 7.6 5.8 7.6 6.1 7.4 8.0 6 5.4 6.4 5.5 5.1 6.4 7.1 6.3 7 5.4 6.5 6.0 6.6 8.3 7.9 6.8 8 6.7 6.9 7.5 5.4 7.6 5.0 7.5 9 7.1 7.8 6.5 6.0 6.9 8.3 7.3 10 7.2 5.3 7.0 7.4 5.2 5.8 5.9 The second step in the evaluation is to determine if the process is capable of meeting P&G’s cap specification. d) Given that P&G’s specification for the caps is 6.5mm ± 1.0mm, calculate the appropriate capability metrics. Show your calculations. Round calculations to 3 decimal places. (6) e) Comment on the process’ capability of meeting P&G’s specification. Provide a thorough interpretation of your response. (5) PROBLEM 2 (20 points) Above the Top, LLC is a sports apparel company. One of their top selling products is a baseball cap for the local university. Last year, the university’s football, basketball, and baseball teams all made it to their respective conference and the football and basketball teams won their division’s title. Above the Top expects demand for the baseball caps to increase in the upcoming year. They create an annual production plan and update it quarterly, but demand varies considerably from quarter to quarter. The forecasted demand and available capacities for the next four quarters are shown in the table below. Quarter Demand 1 2 3 4 300 1300 2400 3300 Regular Capacity 1200 1200 1200 1200 Overtime Capacity 300 300 300 300 Beginning inventory Inventory holding cost per unit per period Regular production cost per unit Overtime production cost per unit Subcontracting cost per unit Subcontracting Capacity 500 500 500 500 150 $1 $5 $8 $10 a) Use the transportation method to design a minimum cost production plan that will satisfy demand for the upcoming year. (Note: Include the completed transportation method table on the next page as a means of showing your work). (10) b) Use a table following the format below to specify how many units will be produced using the 3 types of capacity for each quarter. (5) Period Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Regular Overtime Subcontracting c) Calculate the total production plan cost for the year. Show your calculations. (5) Transportation Method Table PERIOD OF PRODUCTION Beginning Inventory Regular 1 Overtime Subcontract 2 Regular Overtime Subcontract 3 Regular Overtime Subcontract 4 Regular Overtime Subcontract Demand Unmet Demand PERIOD OF USE 1 2 3 4 Unused Capacity Capacity PROBLEM 3 (20 points) Luggage Guru manufactures high-end suitcases. Instead of mass producing their products, each case is produced by master craftsmen who focus on quality manufacturing and attention to detail, which results in an exceedingly labor-intensive production process. There are 6 primary steps in the process. The current production process consists of a separate workstation for each of the 6 steps in the process, as shown in the diagram below. The average time it takes to complete each step is shown in the diagram as well. While some processes can occur simultaneously with other steps in the process, each unit of product must go through each step. Use the information in the diagram below to answer the following questions. a) Which step in this process is the bottleneck? (2) b) How many suitcases are processed at the bottleneck workstation per hour? Show your calculations. (2) c) What is the throughput time of the overall process? Show your calculations. (2) d) If the manufacturing facility operates 2 shifts per day, 8 hours per shift, 250 days a year, what is the annual capacity of this manufacturing process? Show your calculations. (2) e) Assume the company decides to hire additional workers to duplicate the bottleneck step identified in part (a) so that there are 2 of these workstations instead of 1. Redraw the diagram showing the flow of the revised process. (4) f) Answer parts (a) through (d) again based on the new process created in part (e)? (8) PROBLEM 4 (15 points) Infinity International is a US-based company that manufactures semiconductors that are sold to companies worldwide. The company’s CEO wants to build a new warehouse and distribution center in Europe to more quickly distribute its products. The company has identified potential sites in the port cities of Barcelona, Le Havre, Amsterdam, Hamburg, and Rotterdam. Each site was graded from 0 = worst to 100 = best based upon 8 location factors. The following table shows the grade each location received for the factors associated with the location decision. The weights depicting the importance of each location factor are not provided. a) Determine what you believe each of these weights should be. Thoroughly explain/justify your weight assignments. (3) b) Based on your weights and the data provided, calculate the score for each location. Show your work. (10) c) Based on the scores calculated in part (b), which location would you recommend for the new distribution center and why? Thoroughly explain your answer. (2) Location Factors Infrastructure Transportation Facility cost Labor availability Container availability Labor rates Duties, tariffs, and fees Trade regulations (a) Weight Barcelona 65 65 55 65 70 70 80 80 Port Scores (0 to 100) Le Havre Amsterdam Hamburg 95 70 85 90 75 75 75 65 80 70 80 85 65 75 85 60 95 85 70 90 80 75 80 65 Rotterdam 80 75 90 70 80 75 75 75 PROBLEM 5 (15 points) Rise and Shine has been buying cereal directly from the manufacturer for $32 per case. The company’s annual demand for cereal is 275,000 cases and the company believes that the demand is constant for each of the 250 days per year that it is open for business. Average lead time from the supplier for new orders is a constant 5 working days. The purchasing agent at Rise and Shine estimates the annual inventory carrying cost is $3 per case and it costs approximately $55 to prepare, send, and receive an order. You are expected to show your calculations to each part of this question in the test document, not in an Excel file. Round calculations to at least 2 decimal places. a) Based on the economic order quantity, how many cases of cereal should Rise and Shine order each time it places an order? (3) b) What would the average annual inventory be based on the answer to (a)? (2) c) What is the reorder point based on the answer to (a)? (2) d) Rise and Shine discovered if it orders certain quantities each time it places an order, they can obtain a specific price break per case from the supplier (see table below). Identify the optimal order quantity within each price point quantity range and calculate the total annual cost associated with each price point. Show your calculations. Transfer your final answers into a table like the one below. (6) Quantity Price 0–1,999 cases $32.00 2,000-3,999 cases $30.00 4,000+ cases $28.00 Optimal Q Total Cost e) What order quantity should Rise and Shine place based on this information? Explain your answer. (2)
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