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problem set 2

problem set 2 - COMM 399 Logistics and Operations...

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Unformatted text preview: COMM 399: Logistics and Operations Management Problem Set 2 (Due Wednesday, June 16th, 2010) Note: The full mark of this problem set is 90. You must show your work to fully justify your answers. 1. Scheduling (13 points) a. (2 points) Assume there are five jobs (i.e., A, B, C, D, and E) that need to be sequenced in a production schedule. The remaining operating time necessary for completion of job A is 4 days (i.e., job A will take 4 more days to complete), B will take 7 days, C will take 8 days, D will take 2 days, and E will take 5 days, which job should be scheduled first if you use the shortest processing time (SPT) priority rule for job sequencing? b. (8 points) A work center has five jobs assigned to it. They are labeled, in the order of their arrival in the shop, as jobs A, B, C, D and E. The work center may work on only one job at a time and must complete any job it starts before starting another job. Job A has a processing time of 6 days and is due to the customer in 9 days. Job B has a processing time of 2 days and is due in 16 days. Job C has a processing time of 4 days and is due in 10 days. Job D has a processing time of 3 days and is due in 7 days. Job E has a processing time of 5 days and is due in 12 days. Using the SPT priority rule, what will be the average lateness of these orders? How is your answer changed if you use the earliest due date (EDD) rule or critical ratio (CR) rule? (Show your work under all three priority rules.) c. (3 points) Johnson’s rule: A machine shop has two machines, A and B. Four jobs need to be processed through machine A first and B second. Job 1 will take one hour on machine A and three hours on machine B. Job 2 will take three hours on A and two hours on B. Job 3, seven on A and three on B. Job 4, five hours on A and one hour on B. Using Johnson's rule, in what order should these jobs be done? 1 2. Project Management (13 points) A company must perform a maintenance project consisting of seven activities. The activities, their predecessors, and their respective time estimates are shown below: Activity Break down both machines Clean machine 1 Clean machine 2 Reset machine 1 Reset machine 2 Recalibrate both machines Final test Designation Immediate Predecessor Time in Days A None 7 B C D E A A B C 8 5 8 9 F D and E 10 G F 5 a. (3 points) What is the total time required to complete the project? Now we are adding cost information into the above table (time in days): Designation A B C D E F G Immediate Predecessor None A A B C D and E F Normal Time 7 8 5 8 9 10 5 Normal Cost $100 $200 $150 $300 $400 $500 $200 Crash Time 6 8 4 5 8 9 4 Crash Cost $220 $200 $200 $450 $480 $620 $350 b. (1 point) What is the total normal cost? c. (3 points) If you crash this project to reduce the total time by one day with minimum cost what is the total cost of the project? (Show your calculation and reasoning steps.) d. (6 points) If you crash this project to reduce the total time by four days with minimum cost what is the total cost of the project? What is the order in which you crash the activities? (Show your calculation and reasoning steps.) 2 3. Inventory Management Warm‐up Questions (7 points) a. (3 points) A company is planning for its financing needs and uses the basic fixed‐order quantity inventory model. What is the total cost (T) of the inventory given an annual demand of 24,500, order setup cost of $432, a carrying cost rate per unit 12%, an order quantity 500 units, and a cost per unit of inventory of $100? b. (2 points) (EOQ Model) Assuming no safety stock, what is the re‐order point (ROP) given an average daily demand of 72 units, a lead time of 3 days and 907 units on hand? c. (2 points) Which of the following is NOT necessary to compute the order quantity using the fixed‐time period model with uncertain demand? A. Forecast average daily demand; B. Safety stock; C. Inventory currently on hand; D. Ordering cost; E. Lead time in days. 4. Revenue Management (12 points) a. (6 points) Suppose that you manage a hotel with 200 rooms in Richmond near the airport. There are generally two types of guests: (1) early guests who book rooms in advance; and (2) random guests who don’t book the room until the last minute. Accordingly, you charge a bargain rate of $80 per night for the advance booking and a premium rate of $150 per night for the late booking. Based on previous observations, you are confident to fill all the 200 rooms with early guests as there are plenty of them. On the other hand, however, you are also interested in collecting the premiums from last‐minute guests whose reservations follow a normal distribution with mean 75 and standard deviation 25. In order to maximize the hotel revenue per night, how many rooms are you going to reserve for the late booking? b. (6 points) On a given Vancouver‐Toronto flight there are 200 seats. Suppose the ticket price is $475 on average and the number of passengers who reserve a seat but do not show up for departure is normally distributed with mean 6 and standard deviation 3. You decide to overbook the flight and estimate that the average loss from a passenger who will have to be “bumped” (if the number of passengers exceeds the number of seats) is $800. What is the maximum number of reservations that should be accepted? 3 5. EOQ‐Model (12 points) a. (8 points) An exporting company sells 3,000 pounds of coffee beans in oversea market per year on average. These beans are purchased from a coffee farm at a price of $3/pound. The cost of paperwork and labor for setting up an order is $45. For any investment in inventory, there is a 10% opportunity rate, 0.5% damage/ deterioration rate and 2% tax and insurances. Suppose there is zero lead time, determine how often the company should order and what size each order should be. What is the difference in total cost if the company orders 10% more than the optimal quantity each time? b. (4 points) Two duopoly air conditioner retailers in Vancouver order from the same manufacturer M. The order setup cost with M is $200 and the annual inventory holding cost is $400. There is no demand uncertainty. As the inventory manager of one of the retailers, you happen to know that the other retailer is ordering 20 air conditioners every time and it uses EOQ model in making order decision. Can you use this information to deduce the demand facing the competing retailer? 6. Safety Stock (9 points) a. (4 points) Using the fixed‐time period inventory model, and given an normally distributed daily demand of mean 120 units and standard deviation 10 units, 1 week between inventory reviews, 3 days for lead time, 113 units of inventory on hand, a target service level of 98%, what is the optimal order quantity? b. (5 points) A company wants to determine its reorder point (ROP) for maintaining a 96% product availability rate. The market demand during lead time shows a discrete distribution pattern as follows: Demand Quantity 80 90 100 110 120 130 Probability 0.15 0.15 0.35 0.17 0.15 0.03 What is the safety stock that the company should hold? (Hint: different from ROP) If the company reduces the target to an 80% availability rate, what will be the safety stock? 4 7. Newsvendor Model (4 points) During summer season June‐August, the total demand facing an apparel retailer for T‐shirts is normally distributed with mean 1000 and standard deviation 200. Suppose that it costs the retailer $15 to purchase a t‐shirt from its supplier, and the selling price is $30 on average. At the end of the season, any unsold unit is salvaged at a price of $10 (sold in outlet store). What is the over‐stocking cost? What is the retailer’s optimal order quantity? 8. Risk Pooling (20 points) A mail‐order firm has four regional warehouses. Weekly demand at each warehouse is normally distributed with a mean of 10,000 units and a standard deviation of 2,000 units. The company purchases each unit of product at $10. Annual holding cost of one unit of product is 25% of its value. Each order incurs an ordering cost of $1,000 (primarily from fixed transportation costs), and lead time is 1 week. The company wants the probability of stocking out during the lead time at each warehouse to be no more than 5%. Assume 50 working weeks in a year. a. (2 points) What is the optimal order quantity for one single warehouse? b. (2 points) Assuming that each warehouse operates independently, how much safety stock does each warehouse hold? c. (2 points) How much average inventory is held at each warehouse? d. (2 points) What are the combined annual holding costs and ordering costs for all four warehouses? 10 e. (2 points) On average, how long ‐ in weeks ‐ does a unit of product spend in the warehouse before being sold (Hint: Little's Law)? f. (2 points) Assume that the firm has centralized all inventories in a single warehouse and that the probability of stocking out during the lead time is still no more than 5%. What is this optimal order quantity for the central warehouse? g. (2 points) How much safety stock does the central warehouse hold? h. (2 points) Ideally, how much average inventory can the company now expect to hold? i. (2 points) What are the annual holding cost and ordering cost for this central warehouse? 10 j. (2 points) On average, how long ‐ in weeks ‐ does a unit of product spend in the central warehouse before being sold (Hint: Little's Law)? 5 ...
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