2 1. (15 marks) A large electrical parts retailer estimates that the demand for a certain type of circuit breaker is 2500 units per year. The costs associated with placing an order for these circuit breakers are estimated to be $8 per order. The annual holding cost as a fraction of the unit price is estimated to be 20%. The supplier of these circuit breakers offers the following price discounts for larger order sizes: Order Size less than 90 90 or more 400 or more Price per Unit $26 $20 $19 Determine the optimal order quantity based on this information. 2. (10 marks) An large retailer uses a fixed order size with safety stock system to control inventory of a fast-moving item. The inventory position of the item is tracked continually. The following is relevant information about the item. Expected annual demand Average weekly demand Ordering cost Annual holding cost as a fraction of unit value Unit purchase price Lead time Standard deviation of weekly demand 1560 units per year 1560/52 = 30 units per week $60 per order 12 percent $25 per unit 5 weeks 10 units The manager specifies the probability of no stockout in an inventory cycle to be 96 percent. a. Determine EOQ. b. What is the safety stock for this item? Assume that demand in any given week is normally distributed and is independent of demand in other weeks. MGSC 368v9 Assignment 2 December 8, 2016 c. Determine R, the reorder point. 3. (20 marks) Product A is made of one unit of C, one unit of D, and two units of E. Product B is made of one unit of E and one unit of F. Component F is made of one unit of D and two units of G. The shipping (i.e., gross) requirements for A and B are given below: Week Product A Product B 1 2 20 3 25 4 40 5 10 25 6 10 7 30 50 8 10 a. Draw product structure trees for A and B. b. Develop the MRP schedule for all items given the following information: Item Present on hand Lead time Lot-size rule A B C D E F G 0 0 30 100 100 30 0 1 week 1 week 2 weeks 1 week 1 week 2 weeks 1 week L4L L4L *FOQ of 50 units L4L L4L *FOQ of 60 units L4L *Note: FOQ stands for fixed order quantity. For example, FOQ = 30 indicates that any order quantity must be 30 units or some integer multiple of 30 units. FOQ is usually because our supplier is only willing to sell the item by the box (and in this example, each box contains 30 units). In your tables, show on hand at the beginning of a given period before receiving the planned order receipt for the period. Also, assume that all receipts and releases are at the beginning of each period. MGSC 368v9 Assignment 2 December 8, 2016 Week A 1 2 Gross Req'ts On Hand Net Req'ts P.O. Receipts P.O. Releases B Gross Req'ts On Hand Net Req'ts P.O. Receipts P.O. Releases C Gross Req'ts On Hand Net Req'ts P.O. Receipts P.O. Releases D Gross Req'ts On Hand Net Req'ts P.O. Receipts P.O. Releases MGSC 368v9 Assignment 2 December 8, 2016 3 4 5 6 7 8 E Gross Req'ts On Hand Net Req'ts P.O. Receipts P.O. Releases F Gross Req'ts On Hand Net Req'ts P.O. Receipts P.O. Releases G Gross Req'ts On Hand Net Req'ts P.O. Receipts P.O. Releases 4. (20 marks) The following are the operation times and due dates for six jobs (each job undergoes a single operation): Job A B C D E F MGSC 368v9 Assignment 2 Processing Time (days) 5 6 10 3 7 4 December 8, 2016 Due Date (days hence) 17 25 24 9 16 21 The firm operates seven days per week. Assign the jobs according to each of the following priority rules: a. shortest operation time (SOT) b. earliest due date (EDD) c. slack time remaining (STR) d. critical ratio (CR) If a priority rule results in a tie between two or more jobs, break the tie by scheduling the tied jobs in alphabetical order. Evaluate each of the above priority rules with the objective of minimizing the mean tardiness. The term tardiness is used here, rather than lateness, to indicate that there is no credit for a job completed early. A job completed early simply has a tardiness value of 0. In other words, lateness and tardiness are the same if the job is completed after the due date, but different if the job is completed before the due date. For minimizing mean tardiness, no rule is best under all circumstances. Which one of the priority rules did you determine to be best in this particular case? 5. (15 marks) While the process was operating in control, 30 samples of size n = 5 were taken from a process that fills boxes of cereal and checked for weight. The average of the sample means was 370.0 grams, and the average of the sample ranges was 10.2 grams. a. Calculate 3 control limits for mean and range charts to monitor this process. MGSC 368v9 Assignment 2 December 8, 2016 b. Recently six additional samples of size 5 have been taken from the cereal box filling line; the individual weights in grams are recorded in the following table: Sample No. 1 2 3 4 5 6 Sampl e Mean 361.2 372.3 364.2 363.2 369.8 364.2 364.7 375.8 373.6 379.1 373.5 371.5 378.5 367.7 365.4 371.8 369.5 372.3 367.7 374.6 363.0 372.4 374.6 368.7 371.4 366.1 370.3 376.5 376.1 373.8 ? ? ? ? ? ? Sampl e Range ? ? ? ? ? ? Calculate the mean and range for each sample. c. Draw the mean and range charts for this process. Plot the results of the six samples on the chart. d. Does the process appear to be in control? 6. (5 marks) The Prudent Insurance Company has found that when their process for completing application forms is operating in control, the proportion of forms containing errors is 0.05 (i.e. 5%). To monitor the process, the company plans to take a sample of 100 forms each day and evaluate the proportion of forms in the sample with errors. Calculate 3 control limits for a p-chart to monitor this process. 7. (15 marks) The following diagram shows a simple project network with probabilistic activity durations: A B C D Start Finish E MGSC 368v9 Assignment 2 December 8, 2016 F This table gives the three PERT time estimates (in days) for each activity in the project: Activity A B C D E F a 10 2 4 4 13 8 m 11 4 8 10 15 12 b 12 6 14 16 17 20 a. Calculate the expected time for each activity and the variance of each activity time b. Which of the three possible paths from start to finish of the project is the critical path? What is the expected completion time for the project? c. What is the probability that project will be completed in 30.0 days? MGSC 368v9 Assignment 2 December 8, 2016