上海交通大学试卷(B卷) (2011至2012学年第2学期) 班级号 学号 姓名 课程名称Production and Operations Analysis(生产计划与控制)成绩 1.(15%)Willian Beebe has contracted to complete eight computer programming jobs.Some jobs must be completed in a certain sequence because they involve program modules that will be linked. Job 2 3 5 6 7 8 Processing 10 2 1 6 time(days) Due Date June 8 June 15 June 10 June 12 July 1 July 6 June 25 June 29 Precedence restrictions: 1+2+5+6 4◆7·8 Assume that the current date is Monday,June 1,and that Willian Beebe does not work on weekends.Let us assume that a project due on any day must be ready in the morning of that day so that,for example,he would have only 5 working days available for a project due on June 8. Using Lawler's algorithm,find the sequence in which he should be performing the jobs in order to minimize maximum lateness subject to the precedence constraints. 2.(10%)Over a one-year period,the Topper Company sold the following numbers of lawn mowers: Week 1 23456789101112 Sales23822019524534538027022028012011085 B卷总6页第1页姓名
B 卷 总 6 页 第 1 页 姓名 上 海 交 通 大 学 试 卷（ B 卷） （ 2011 至 2012 学年 第 2 学期 ） 班级号____________ 学号 ______________________ 姓名 课程名称 Production and Operations Analysis (生产计划与控制) 成绩 1. (15%) Willian Beebe has contracted to complete eight computer programming jobs. Some jobs must be completed in a certain sequence because they involve program modules that will be linked.Job 1 2 3 4 5 6 7 8 Processing time (days) 4 10 2 1 8 3 2 6 Due Date June 8 June 15 June 10 June 12 July 1 July 6 June 25 June 29 Precedence restrictions: Assume that the current date is Monday, June 1, and that Willian Beebe does not work on weekends. Let us assume that a project due on any day must be ready in the morning of that day so that, for example, he would have only 5 working days available for a project due on June 8. Using Lawler’s algorithm, find the sequence in which he should be performing the jobs in order to minimize maximum lateness subject to the precedence constraints. 2. (10%)Over a one-year period, the Topper Company sold the following numbers of lawn mowers: Week 1 2 3 4 5 6 7 8 9 10 11 12 Sales 238 220 195 245 345 380 270 220 280 120 110 85 1 2 5 6 4 7 8
a.Compute the six-month moving-average forecast. b.Determine the forecast errors for these periods. c.Compute the MAD,the MSE,and the MAPE based on the forecast errors computed in part(b). 3.(10%)A project consists of seven activities.The precedence relationships are given in the table. Activity Time Immediate (days) Predecessors A 32 B 21 C 30 D 45 A E 26 A,B F 28 C G 20 E,F a.Construct a network for this project(Activity on Are). b.Compute the earliest and the latest starting and finishing times for each activity and identify the critical path. B卷总6页第2页姓名
B 卷 总 6 页 第 2 页 姓名 a. Compute the six-month moving-average forecast. b. Determine the forecast errors for these periods. c. Compute the MAD, the MSE, and the MAPE based on the forecast errors computed in part (b). 3. (10%) A project consists of seven activities. The precedence relationships are given in the table. Activity Time (days) Immediate Predecessors A B C D E F G 32 21 30 45 26 28 20 _ _ _A A, B C E, F a. Construct a network for this project (Activity on Arc). b. Compute the earliest and the latest starting and finishing times for each activity and identify the critical path
4.(15%)A local supermarket sells a popular brand of shampoo at a fairly steady rate of 380 bottles per month.The cost of each bottle to the supermarket is 45 cents,and the cost of placing an order has been estimated at $8.50.Assume the holding costs are based on a 25 percent annual interest rate.Stock-outs of the shampoo are not allowed. a.Determine the optimal lot size the supermarket should order and the time between placements of orders for this product. b.If the procurement lead time is three months,find the reorder point based on hand inventory. 5.(15%)The Pairs Paint Company is in the process of planning labor force requirements and production level for the next four quarter.The marketing department has provided production with the following forecast of demand for Pairs Paint over the next year: Assume that there are currently 280 employees with the company.Employees are hired for at least one full quarter.Hiring costs amount to $1,200 per employee and firing costs are $2,500 per employee.Inventory costs are $1 per gallon per quarter.It is estimated that one worker produces 1,000 gallons of paint each quarter. Assume that Pairs currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of at least 20,000 gallons. B卷总6页第3页姓名
B 卷 总 6 页 第 3 页 姓名 4. (15%) A local supermarket sells a popular brand of shampoo at a fairly steady rate of 380 bottles per month. The cost of each bottle to the supermarket is 45 cents, and the cost of placing an order has been estimated at $8.50. Assume the holding costs are based on a 25 percent annual interest rate. Stock-outs of the shampoo are not allowed. a. Determine the optimal lot size the supermarket should order and the time between placements of orders for this product. b. If the procurement lead time is three months, find the reorder point based on hand inventory. 5. (15%) The Pairs Paint Company is in the process of planning labor force requirements and production level for the next four quarter. The marketing department has provided production with the following forecast of demand for Pairs Paint over the next year: Assume that there are currently 280 employees with the company. Employees are hired for at least one full quarter. Hiring costs amount to $1,200 per employee and firing costs are $2,500 per employee. Inventory costs are $1 per gallon per quarter. It is estimated that one worker produces 1,000 gallons of paint each quarter. Assume that Pairs currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of at least 20,000 gallons
Quarter Demand Forecast(in thousands of gallons) 1 380 2 630 3 220 160 a.Determine the minimum constant workforce plan for Pairs Paint and the cost of the plan. Assume that stock-outs are not allowed. b.Determine the zero inventory plan that hires and fires workers each quarter to match demand as closely as possible and the cost of that plan. 6.(20%)The home appliance department of a large department store is using lot size-reorder point system to control the replenishment of a particular model of FM table radio.The store sells an average of 10 radios each week.Weekly demand follows a normal distribution with variance 26.You may assume that there are 52 weeks in a year. The store pays $20 for each radio,which it sells for $75.Fixed costs of replenishment amount to $28.The accounting department recommends a 20 percent interest rate for the cost of capital. Storage costs amount to 3 percent and breakage to 2 percent of the value of each item. B卷总6页第4页姓名
B 卷 总 6 页 第 4 页 姓名 Quarter Demand Forecast (in thousands of gallons) 1 2 3 4 380 630 220 160 a. Determine the minimum constant workforce plan for Pairs Paint and the cost of the plan. Assume that stock-outs are not allowed. b. Determine the zero inventory plan that hires and fires workers each quarter to match demand as closely as possible and the cost of that plan. 6. (20%) The home appliance department of a large department store is using lot size-reorder point system to control the replenishment of a particular model of FM table radio. The store sells an average of 10 radios each week. Weekly demand follows a normal distribution with variance 26. You may assume that there are 52 weeks in a year. The store pays $20 for each radio, which it sells for $75. Fixed costs of replenishment amount to $28. The accounting department recommends a 20 percent interest rate for the cost of capital. Storage costs amount to 3 percent and breakage to 2 percent of the value of each item
If a customer demands the radio when it is out of stock,the customer will generally go elsewhere.Loss-of goodwill costs are estimated to be about $25 per radio. Replenishment lead time is three months. a.If lot sizes are based on the EOQ formula,what reorder level should be used for the radios? b.Using Equation:1-F(R)=Oh/(Oh+p),find the optimal values of (O,R). c.Compare the average annual costs of holding,ordering,and stock-out for policies that you found in parts (a)and (b). B卷总6页第5页姓名
B 卷 总 6 页 第 5 页 姓名 If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of goodwill costs are estimated to be about $25 per radio. Replenishment lead time is three months. a. If lot sizes are based on the EOQ formula, what reorder level should be used for the radios? b. Using Equation: 1-F(R)=Qh/(Qh+p), find the optimal values of (Q,R). c. Compare the average annual costs of holding, ordering, and stock-out for policies that you found in parts (a) and (b)
7.(15%)A component used in a manufacturing facility is ordered from an outside supplier. Because the component is used in a variety of end products,the demand is high.Estimated demand over the next 10 weeks is Week 1 2 34 56 7 10 Demand 2200034000320001200080004400054000160007600030000 The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week.The fixed order cost is estimated to be $200. a.What ordering policy is recommended by the least unit cost heuristic? b.What ordering policy is recommended by the part period balancing heuristic? 我承诺，我将严 题号 1 2 格遵守考试纪律。 得分 承诺人： 批阅人（流水阅） 卷教师签名处) B卷总6页第6页姓名
B 卷 总 6 页 第 6 页 姓名 7. (15%) A component used in a manufacturing facility is ordered from an outside supplier. Because the component is used in a variety of end products, the demand is high. Estimated demand over the next 10 weeks is Week 1 2 3 4 5 6 7 8 9 10 Demand 22000 34000 32000 12000 8000 44000 54000 16000 76000 30000 The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. a. What ordering policy is recommended by the least unit cost heuristic? b. What ordering policy is recommended by the part period balancing heuristic? 题号 1 2 3 4 5 6 7 得分 批阅人(流水阅) 卷教师签名处) 我承诺，我将严 格遵守考试纪律。 承诺人：