On the real final exam on Dec. 13, 2006, you will receive a printed copy of the questions with a cover page showing your last name and campus

Transcription

1 On the real final exam on Dec. 13, 2006, you will receive a printed copy of the questions with a cover page showing your last name and campus computing ID. You will also be able to access the questions through the course web, both as a PDF file and in the Excel file for the exam. Notes: This practice exam is based on a final exam in this course from December The exam given in December 2002 included a section on project management, a topic that we did not cover this term. This problem has been deleted, and for that reason the practice exam is a bit shorter than you should expect the real exam to be. You can find additional old final exams for MGTSC 352 in the Student Union s exam registry see We will not be posting solutions for these exams but you are welcome to ask questions about them.

2 Aggregate Planning (24 points) 1. (1 point) One of the ways in which a firm can vary its capacity over time is through pricing, that is, charging its customers higher prices during periods of high demand. a. True b. False 2. (1 point) When solver complains, set cell values do not converge, this means that it is not possible to satisfy all the constraints in the model at the same time. a. True b. False 3. (2 points) In an aggregate planning model such as the one for the Mountain Wear case, one needs to include a constraint that ensures that forecast demand is satisfied in every time period. What is the appropriate constraint to ensure this? a. Production Forecast demand, for every time period b. Ending inventory 0, for every time period c. Beginning inventory 0, for every time period d. Ending inventory 0 for the last time period e. Not necessary to include any constraint, this will happen automatically The WhipSnip Company The AP worksheet shows all the data required for this problem. This paragraph and the next describe the meaning of the data. The WhipSnip Company manufactures two types of lawn trimmers: an electric model and a gas model. The company has contracted to supply a national discount retail chain with amounts shown in the worksheet during the next month. WhipSnip s resources are limited in three departments: Engine, Assembly, and Packaging. The worksheet shows how many hours of processing time will be available in the next month in each department. It also shows the processing time needed in each department to manufacture one trimmer and the variable production cost ("cost to make"), for both trimmer models. WhipSnip also has the option of purchasing finished electric and gas trimmers from an affiliate at the prices shown in the worksheet ( cost to buy ). 4. (2 points) Suppose all of the hours available in the Engine department are used for electric trimmers. How many trimmers can then be processed in that department? 5. (2 points) The hourly labor cost is the same in all three departments. Which trimmer model has the higher total labour cost? a. Electric b. Gas c. Labor costs are the same d. Cannot answer without knowing the actual labor cost in $/hour 6. (2 points) The upcoming month has 25 working days. All workers in the three departments work eight hours every working day. How many workers does the Assembly department have? 7. (3 points) Suppose WhipSnip decides to manufacture enough trimmers to fill one third of the contracted amount for each trimmer and buy the remaining two thirds of the contracted amount from its affiliate. What will this cost WhipSnip? Is this plan feasible? 8. (5 points) How many electric and gas trimmers should WhipSnip make, and how many should they buy from their affiliate in order to fulfill the contract in the least costly manner? What is the total cost?

3 9. (3 points) Suppose the contract stipulates that WhipSnip manufacture at least 60% of each product. How much incremental cost does this stipulation impose? (In other words, what is the difference between the optimal costs with and without this stipulation?) 10. (3 points) Ignore the stipulation from the last question. Suppose WhipSnip has a well-trained workforce that can be shifted between departments without any loss in productivity. What are the savings over the plan found in question 10? In other words, what is a perfectly-flexible workforce worth to WhipSnip? Distribution Planning (15 points) The R n R Company The R n R company manufactures rocking chairs. The rocking chairs are made in three separate plants and transported from the plants to four separate warehouses. The warehouses then supply retailers with rocking chairs. The DP worksheet shows the transport cost per shipment from each plant to each warehouse, the supply at each plant, and the demand at each warehouse. Both supplies and demands are measured in shipments. The worksheet also shows distances in kilometers and net margins, but don t worry about those yet. All formulas entered in the DP worksheet are correct. 1. (2 points) What is the cost of transporting 3 shipments of rocking chairs from plant 1 to warehouse 3? How many shipments of rocking chairs are available in total, at all of R n R s plants? 2. (4 points) Find the least costly way to transport rocking chairs from plants to warehouses so as to satisfy demand at each warehouse without exceeding the supply at any plant. Report the number of shipments to send from each plant to each warehouse and the total transport cost. 3. (2 points) Near the bottom of the DP worksheet, you can see the distances in kilometers from each plant to each warehouse. The shipping company that transports rocking chairs for R n R charges R n R on the following basis: cost per shipment = (fixed cost) + (variable cost) (distance in kilometers). What is the fixed cost and the variable cost that the shipping company uses? 4. (2 points) Instead of minimizing cost, one could minimize total transport distance, measured in shipment-kilometers. Could this lead to a different optimal shipment plan? (Answer yes or no, and keep in mind how the cost depends on distance, as explained in the previous question.) 5. (2 points) The rocking chairs are distributed to retailers from the warehouses. The net margin per shipment varies between warehouses, as shown at the bottom of the DP worksheet. The net margin for a shipment equals the revenue obtained for the shipment minus all applicable variable costs, except the transport cost from the plants to the warehouses is not included. What is the total net margin that R n R will receive, given that it uses the plan you found in question 2? 6. (3 points) Suppose R n R can choose to satisfy as much or as little of the demand at each warehouse and use as much or as little of the supply at each plant, without any negative consequences. Find the plan that maximizes total net margin minus total transport cost. Report the number of shipments to send from each plant to each warehouse, the total net margin, and the total transport cost.

4 Inventory Management (16 points) 1. (2 points) Demand for a product is 25 per week on average. The holding cost is $40 per unit per year and the order cost is $20 per order. The company is open 365 days per year. Then the optimal order quantity, according to the EOQ model, is a. 5 b c d e. Can't tell without knowing the lead-time 2. (2 points) Assume that demand for a product is constant and equal to 25 per week. The current inventory policy is Q = 100 units and ROP = 40. The lead-time is one week. Then the average inventory will be a. 15 b. 40 c. 50 d. 65 e. Can't tell without knowing the holding cost Inventory Simulation The Bug Hunt! The IP worksheet contains the inventory simulation model we developed for the A&E Noise example. This model is based on exactly the same data as in the lecture notes, except that the lead-time has been changed from 5 to 4 days and the model only includes the first 18 days of the year. 3. (12 points) Unfortunately, this model contains several mistakes. Some cells have incorrect or missing formulas. Your job is to find as many mistakes as you can. An incorrect formula that is propagated across a row or down a column counts as one mistake. For example, if an incorrect formula in cell A1 is propagated to cells A2:A10, then just report A1. If you report two cells in the range A1:A10 (For example A1 and A3), you will get credit for having found one mistake. The total number of mistakes in the model is more than one and less than twelve. The Answers sheet provides cells where you can enter references for cells that you think contain mistakes. You will get X points for each mistake that you find and you will lose X points for each cell that you indicate has an error but is actually correct. The quantity X equals 12/(total number of mistakes in the model). Therefore, if you find all of the mistakes, you will get 12 points. Your total mark for this part will not be negative. Forecasting (21 points) Newspaper sales are influenced by many cyclical factors, such as the season of the year, the day of the week, inserts that appear once a week (such as a TV guide or real estate classifieds), as well as by non -cyclical factors, such as special events (Grey Cup preview) or breaking news (September 11, 2001). The general state of the economy has an effect on sales as well. The FC worksheet shows monthly sales for a newspaper over a 24-month period. 1. (3 points) What are the average, minimum, and maximum monthly sales? 2. (2 points) Which month seems to have the highest sales, on average? 3. (2 points) Use a 3-month moving average to forecast sales for November (2 points) Use exponential smoothing with LS = 0.4 to forecast sales for November 2002 and December The SLR w SI worksheet has a partially completed implementation of the SLR w SI forecasting method.

5 5. (3 points) Set the intercept to 2,000,000 and the slope to 10,000. Keep all seasonality indices at 1.0. What then is the SLR w SI forecast for May 2003? Calculate MSE for the SLR w SI forecast. 6. (6 points) Minimize MSE by changing the seasonality indices, the intercept, and the slope. Use the following starting values: intercept = 2,000,000, slope = 10,000, all seasonality indices = 1. Include a constraint that the average seasonality index equals 1.0. Report the seasonality indices, intercept, slope, and minimum MSE. Also report forecasts for September to December (3 points) December 2002 has 31 days. Suppose newspaper sales are forecast to be 3,000,000 in December An analysis of daily newspaper sales (this data is not available to you) yielded the following daily seasonality indices: Monday 0.65 Tuesday 0.75 Wednesday 0.75 Thursday 1.20 Friday 1.25 Saturday 1.35 Sunday 1.05 Forecast sales for Tuesday, December 17, Assume that there are no important variations in sales from week to week during December. Congestion Management (20 points) The waiting line analysis template worksheets are in the exam workbook. You will need them for some of the questions in this part. 1. (1 point) If the average service time in an M/M/1 queue is cut in half, then the average time a customer spends waiting in line is cut in half. 2. (2 points) A small town is served by a single ambulance, located at the town s health clinic. When someone calls for an ambulance, the following steps are taken: The ambulance travels to the location of the patient. Average time 5 minutes. The paramedics attend to the patient and prepare him or her for transport. Average time 10 minutes. The patient is transported to the health clinic and the paramedics fill out the necessary paperwork. Average time 15 minutes. What is the service rate for the ambulance? a. 12 per hour b. 4 per hour c. 2 per hour d. Depends on how many calls for service come in per hour North Country Trucking North Country Trucking transports goods by truck throughout northern Alberta. The company is opening a new depot in Grande Prairie and is considering three possible configurations for the depot. Assume that trucks arrive to the depot at a rate of 6 per hour and that truck inter-arrival times and service times are exponentially distributed. The three configurations are as follows. Configuration 1: One service bay with one employee that would take an average of 7.5 minutes to unload a truck. Configuration 2: One service bay with two employees. The two employees would work together to unload each truck and would take 5 minutes on average to do so.

6 Configuration 3: Two service bays, each with one employee that would take an average of 7.5 minutes to unload a truck. Arriving trucks would enter a queue and then be unloaded in the first available service bay. The capital and operating cost of building and maintaining a service bay is $25 per hour. Employees are paid $20 per hour, including benefits. The company loses $30 per hour per truck, due to lost productivity, whenever a truck is waiting to be unloaded or being unloaded. You are asked to determine the cost per hour of each configuration. Answer questions 3) to 8) for each configuration separately. 3. (3 points) Which model is appropriate to analyze this configuration? What is the service rate per server per hour? How many servers are there? 4. (1.5 points) What is the total labor cost per hour? 5. (1.5 points) What is the total capital and operating cost per hour? 6. (3 points) What is the expected number of trucks waiting to be unloaded or being unloaded? 7. (3 points) What is the average time each truck spends waiting to be unloaded or being unloaded? 8. (3 points) What is the cost of lost productivity per hour? 9. (2 points) Which is the minimum cost configuration? a. Configuration 1 b. Configuration 2 c. Configuration 3