Chapter 6. Manufacturing Processes home work

3. Problem 6-4 Safety regulations require that the time between airplane takeoffs (on the same runway) will be at least 2 minutes. When taking off, the run time of an airplane on the runway is 30 seconds. Planes are on average waiting 3 minutes and 18 seconds for take-off. On average there are 18 planes taking off per hour. How many planes are either on the runway or waiting to take off? (Round your answer to the nearest whole number.)

Number of airplanes 1 Explanation: TR = 18 planes per hour. TT = (0.50 + 3.30)/60 = 5/79 of an hour. WIP = TT × TR = 18.00 × 5/79 = 1 airplanes in line or taking off.

1. You are in a line at the bank drive-through and 5 cars are in front of you. You estimate that the clerk is taking about two minutes per car to serve. How long do you expect to wait in line?

Wait time 10 minutes Explanation: Wait time = 5 cars × 2 minutes per car = 10 minutes

6. Problem 6-12 A firm uses a serial assembly system and needs answers to the following: a. A desired output of 873 units per shift (9.7 hours) is desired for a new processing system. The system requires product to pass through four stations where the work content at each station is 38 seconds. What is the required cycle time for such a system? Cycle time seconds per unit b. How efficient is your system with the cycle time you calculated? (Round your answer to 2 decimal places.) Efficiency % c-1 Station 3 changes and now requires 42 seconds to complete. What will need to be done to meet demand (assume only 9.7 hours are available)? Station 3 needs to be duplicated. c-2 What is the efficiency of the new system? (Round your answer to 2 decimal places.) Efficiency %

a. 40 b. 95% c1.Station 3 needs to be duplicated. c2. 78% Explanation: a.C = Production time per day (seconds) = 9.7 × 60 × 60 /873= 40 seconds/unit Required output per day b. Efficiency=T/NaC =152/4(40) =0.9500 or 95.00% This balance is 95.00 percent efficient. c-1.&c-2. To make 873 units per shift, station 3 will need to be duplicated. Efficiency formula = 156/(5(40)) = 0.7800. This assumes that each of the other operators still take 40 seconds to complete. The system becomes less efficient due to the idle time at the parallel workstations 3.

5. Problem 6-11 The following tasks are to be performed on an assembly line: TASK SECONDS TASKS THAT MUST PRECEDE A 18 — B 10 A C 25 B D 15 B E 14 C F 17 D G 12 E, F H 20 G ________________________________________ The workday is six hours long. Demand for completed product is 625 per day.

a. Find the cycle time. (Round your answer to 2 decimal places.) Cycle time 34.56 seconds per unit b. What is the theoretical number of workstations? (Round up your answer to the next whole number.) Number of workstations 4 d. Balance the line using the longest-operating-time rule. (Round your answers to 2 decimal places.) Workstation Task Idle Time I A, B 6.56 II C 9.56 III D, F 2.56 IV E, G 8.56 V H 14.56 ________________________________________ e. What is the efficiency of the line balanced as in (d)? (Round your answer to 1 decimal place.) Efficiency 75.8 % f. Suppose that demand rose from 625 to 750 units per day. What would you do? (Input all amounts as positive values. Round your answer to the nearest whole number) Reduce cycle time to ~ 32 seconds and work ~2400 seconds of overtime. g. Suppose that demand rose from 625 to 950 units per day. What would you do? (Input all amounts as positive values. Round your answer to the nearest whole number.) Reduce cycle time to 32 seconds and work 8800 seconds of overtime. Explanation: a. C = Production Time Per day (seconds) = 6 × 60 × 60 = 34.56 seconds/unit Required Output per day 625 b. Ni = T = 131 = 3.79 → 4 workstations C 34.56 d. Workstation Task Task Time Idle Time I A, B 18, 10 6.56 II C 25 9.56 III D, F 15, 17 2.56 IV E, G 14, 12 8.56 V H 20 14.56 ________________________________________ Total task time T = 131 e. Efficiency = T = 131 = 0.758 or 75.8% NaC 5(34.56) f. Reduce cycle time to 32. New production level is (6 hours/day)(3600 seconds per hour)/(32 seconds per unit) = 675 units per day. Therefore, they are 750 - 675 = 75 units short. Work (75 units)(32 seconds per unit) = 2,400 seconds or 40.00 minutes overtime. g. 950 - 675 = 275 units short, work (275 units) (32 seconds per unit) = 8,800 seconds or 146.67 minutes or 2.44 hours of overtime. May want to consider rebalancing the line.

2. Problem 6-3 The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 36 minutes. a. How many Avis buses are traveling to and from the airport? (Round your answer to the nearest whole number.) b. The branch manager wants to improve the service and suggests dispatching buses every 1.5 minutes. She argues that this will reduce the average traveling time (a round trip) to 1.5 minutes. Is she correct? If your answer is negative, then what will the average traveling time be?

a. Number of Avis buses 12 b. No, average traveling time minutes. Explanation: a.The throughput rate is 20 buses per hour. The throughput time is 36/60 = 3/5 hours. Inventory = Throughput × Flow time = 20 × 3/5 = 12 buses are traveling to and from the airport at any one time. b. This reduces the average waiting time, but has no effect on the average traveling time. The average traveling time does not change and will remain 36 min. This would however result in 24 buses being in transit between the airport and the office at any given time.

4. Problem 6-7 Money Laundry has 21 washers and 38 dryers. All orders are first sent to wash and then to dry. It takes on average 43 minutes to wash one order and 50 minutes to dry.

a. What is the capacity of the washing stage? (Round your answer to 2 decimal places.) Capacity of washing stage 29.30 orders per hour b. What is the capacity of the drying stage? (Round your answer to 2 decimal places.) Capacity of drying stage 45.60 orders per hour c. Identify the bottleneck(s). Washer d. What is the capacity of Money laundry? (Round your answer to 2 decimal places.) Capacity of Money laundry 29.30 orders per hour e. If Money Laundry would like to increase the capacity by buying one more machine, should they buy a washer or a dryer? Washer The manager, Mr. Money, decided not to buy a machine. He still has 21 washers and 38 dryers. The manager estimates that on average Money Laundry receives eight orders every hour. The manager also finds that on average there are five orders in the washing stage and three orders in the drying stage. f. What is the utilization of washers, on average? (Round your answer to 2 decimal places.) Average utilization 27.30 % g. What is the utilization of dryers, on average? (Round your answer to 2 decimal places.) Average utilization 17.54 % h. On average, how long does it take an order to finish the washing process, from the time the order is received? (Round your answer to 2 decimal places.) Average time taken 0.62 hour i. On average, how long does it take an order to finish the drying process, from the time the order finishes the washing process? (Round your answer to 2 decimal places.) Average time taken 0.38 hour j. On average, how long does an order stay in Money Laundry? (Round your answer to 2 decimal places.) Average time taken 1.00 hour Explanation: a. Capacity of washing stage = 21 × 60/43 = 29.30 orders/hour b. Capacity of drying stage = 38 × 60/50 = 45.60 orders/hour f. Average utilization = 8 orders/hour / 29.30 orders/hour = 27.30% g. Average utilization = 8 orders/hour / 45.60 orders/hour = 17.54% h. WIP = 5, TR = 8 orders/hour. TT = WIP/TR = 5/8 = 0.625 hour or 37.50 minutes. i. WIP = 3, TR = 8 order/hour. TT = WIP/TR = 3/8 = 0.375 hour or 22.50 minutes. j. WIP = 0.625 + 0.375 = 1.00 hour or 60.00 minutes.

7. Problem 6-13 Francis Johnson's plant needs to design an efficient assembly line to make a new product. The assembly line needs to produce 10 units per hour and there is room for only four workstations. The tasks and the order in which they must be performed are shown in the following table. Tasks cannot be split, and it would be too expensive to duplicate any task. TASK TASK TIME IMMEDIATE (MINUTES) PREDECESSOR A 4 — B 3 — C 5 — D 2 A, B, C E 2 C F 2 E G 3 E ________________________________________ b. What is the workstation cycle time? c. Balance the line using the largest number of following tasks, so that only four workstations are required. Use the longest task time as a secondary criterion. (Leave no cells blank - be certain to enter "0" wherever required.) d. What is the efficiency of your line balance? (Round your answer to 2 decimal places.)

b. 6 c . Work Station Task Idle Time I C 1 II E A 0 III B G 0 IV D F 2 ________________________________________ d. 87.50% Explanation: b. C = Production time per day (seconds) = 60 = 6 minutes/unit Required output per day 10 c. Work station Task Task time Idle time I C 5 1 II E A 2, 4 0 III B G 3 , 3 0 IV D F 2 , 2 2 ________________________________________ Total task time T = 21 d. Efficiency=T/NaC=21/4(6)= 0.8750 or 87.50%