Problem 4.1 The Traffic Court of King James County operates 9 am-1 pm. Each morning, roughly at 9 p. m., 200 defendants show up for trial involving traffic violations. On a Monday, a sample of 10 defendants were selected at random. For each defendant, the actual time spent in discussion with the judge and the time paying the fine ( not including waiting) were recorded. Also recorded were the times the defendant arrived and left the court. November 11, 2011 Ardavan Asef-Vaziri

Problem 4.1 a) Estimate the flow time. (9:30-8:45) + (9:45-8:45) + …… + (12:55-9:00) + (9:20-9:00) = 1200. Average Flow Time = 1200/10 = 120 min. b) Estimate the theoretical flow time. Average time with judge = (1+1.5+…..+ 1+1.5)/10 = 1.55 min. The average time to pay fine = (5+2+…..+ 2+3)/10 = 2.4 min. Theoretical flow time: 1.55 + 2.4 = 3.95 min. c) What is the flow- time efficiency? 3.95/120 = 3.3% November 11, 2011 Ardavan Asef-Vaziri

Problem 4.2 Wonder Shed Inc. ( Example 4.3) produces, in addition to the standard model, a deluxe version for the discriminating customer. The production process for the two models are identical and depicted in Figure 4.1. The activity times for deluxe models is listed below. All the times mentioned represent flow time at the various activities and include the effects of waiting. November 11, 2011 Ardavan Asef-Vaziri

Problem 4.2 a) Compute the process flow time for producing a deluxe shed. Path 1 (roof) : = 20+ 45 +45 +25+ 40 = 175 min. Path 2 (base): = 20+35+10 +30+ 25+ 40= 160 min. The critical path is path 1, and the flow time is 175 min. b) What is the impact on flow time of the process if the flow time of Activity 2 is increased to 40 minutes? Activity 2 is on path 2 ( not the critical path). Increasing the time of this activity by 5 minutes does not make path 2 critical. c) What is the impact on flow time of the process if the flow time of Activity 3 is reduced to 40 minutes? The flow time will be reduced to 170 minutes. (170 still >160) November 11, 2011 Ardavan Asef-Vaziri

Problem 4.3 When a guest calls room service, the room-service manager takes down the order. She submits an order ticket to the kitchen to begin preparing the food, and an order to the wine waiter to prepare alcoholic beverages . Finally, she assigns the order to a waiter. It takes 4 minutes to take down the order and to assign the work. It takes the kitchen 18 minutes to prepare the typical order, and the sommelier 6 minutes to prepare the drinks for the order. While the kitchen and the sommelier are doing their tasks, the waiter prepares the cart. This takes 10 minutes per order. Once the food, wine, and cart are ready, it takes the waiter 12 minutes to deliver the meal to the customer. It takes the waiter additional 4 minutes to return to the station and debit the guest’s account. All the times mentioned represent flow time at the various activities, and include the waiting times. November 11, 2011 Ardavan Asef-Vaziri

Activity 2 is not on the critical path c. The lead time will be reduced to 170 minutes. 4.3. a. Problem 4.3 a) Draw a process map from receipt of order to delivery of food Order Food Alcohol Bill Deliver Cart 4 18 10 12 6 b) What is the flow time of the process? The critical path time is 4+18 + 12 +4 = 34 min November 11, 2011 Ardavan Asef-Vaziri

Activity 2 is not on the critical path c. The lead time will be reduced to 170 minutes. 4.3. a. Problem 4.3 c) What is the effect on the process flow time if the waiter could prepare the cart in 8 minutes, instead of 10? Cart preparation is not on the critical path. d) What is the effect on the process flow time if the waiter could deliver the order in 10 minutes, instead of 12? The critical path (flow time) is reduced by 2 min. November 11, 2011 Ardavan Asef-Vaziri

Problem 4.4 A home insurance application consists of two forms: F1 and F2 . On receipt, each application is processed and separated into F1 and F2; 10 min. F1 requires Activity A for 15 min and then Activity B for 10 min. F2 requires Activity C for 20 min. F1 and F2 are then combined and further processed by a loan officer for 15 min. All the times mentioned represent flow time at the various activities, and include the effects of waiting. a) Draw a process flowchart for the processes. F1 F2 Process And Separate Activity C Loan Officer B A 10 15 20 November 11, 2011 Ardavan Asef-Vaziri

Problem 4.4 b) What is the flow time? The flow time is 50 minutes. The critical path is the one of F1. c) What is the effect on flow time if 50% of F1 forms must repeat Activity A one more time due to quality problems? Since 50% of F1 forms return to A, then 100% of F1 forms spend 15 minutes in A and the other 50% spend 15 more minutes at A. On average an F1 form spends 15+ 0.5(15) = 22.5. Therefore activity A takes 7.5 minutes more. Since activity A is on the critical path, the flow time will increase 7.5 minutes, to 57.5 minutes. November 11, 2011 Ardavan Asef-Vaziri

Problem 4.5 A single security line in Vancouver International Airport comprising an X- ray scanner for carry on items and a screening station for passengers. Passengers first prepare themselves for the inspection by removing belts, coats and shoes, emptying their pockets, etc. and deposit all the bags in the trays on the scanner. They then proceed and pass through the screening station . They then retrieve their belongings. The X- ray scanner takes 40 seconds per tray, and the average passenger utilizes 1.5 trays. The personal screening station requires 30 seconds per person. Finally, retrieving of belongings and getting reorganized takes 60 seconds. All the times mentioned represent activity time at the various activities and do not include the effects of waiting. November 11, 2011 Ardavan Asef-Vaziri

Problem 4.5 a) Draw a process map for the security check process. b) What is theoretical flow time of the security check process? The critical path is the one through the X-ray scanner. The flow time is 30 + 40*1.5 + 60 = 150 seconds. November 11, 2011 Ardavan Asef-Vaziri

Problem 4.5 c) A sample of 20 passengers were selected at random and the time required for each to clear the security check was recorded. The average of the individual times was 530 seconds. What is the process flow-time efficiency? The flow time efficiency is 150/530 = 28% d. What is the impact on theoretical flow time of the process if the personal screening activity is expedited to 20 seconds? The personal scanner is not on the critical path. November 11, 2011 Ardavan Asef-Vaziri

Critical Path Example of Flow Time A temp work service maintains an “inventory” of 200 computer specialists who are assigned to various customers on a short term basis. The typical tour of duty lasts for 7 weeks, and the period between assignments typically lasts for 3 weeks. Assume 50 weeks per year. a) On average, how many specialists start on a new assignment each week? November 11, 2011 Ardavan Asef-Vaziri

Critical Path Example of Flow Time Lets assume each job is composed of 7 weeks of activity A (working on a job) and activity B (doing nothing). Therefore we always have 200 of these jobs. Some specialist are working on The flow time of entire process is 3+7 = 10 weeks Inventory is 200 RT = I  R= I/T = 200/10 = 20 per week Alternatively, each job takes 10 weeks. Each specialist will be assigned 1/10 of a new job per week. There are 200 specialists, they will be assigned 200(1/10) = 20 new jobs per week. R = 20. November 11, 2011 Ardavan Asef-Vaziri

Critical Path Example of Flow Time b) On average, how many specialists are idle (between assignments)? The flow time of “idle” is 3 weeks  R=3 R = The throughput is 20 per week RT = I  20(3) = 60 Alternative way % of idle time 3/10= 30%. Thus 30% of staff will be idle on average, ( 30% of 200 = 60) November 11, 2011 Ardavan Asef-Vaziri

Practice: Draw the Network of Activities Task Pred. Dur. Task Pred. Dur. a -- 4 g c,d 1 b -- 3 h e 4 c a 3 i f 5 d a 2 j e,g 6 e b 6 k h,i 1 f b 4 For each task, compute ES, EF, LF, LS, slack November 11, 2011 Ardavan Asef-Vaziri

Practice: Compute the Theoretical Flow Time Start Finish a=4 slack= b=3 c=3 d=2 e=6 f=4 g=1 h=4 i=5 j=6 k=1 Task=dur slack=xxx LST LFT EFT EST November 11, 2011 Ardavan Asef-Vaziri

Practice: Compute the Theoretical Flow Time Start Finish a=4 slack= b=3 c=3 d=2 e=6 f=4 g=1 h=4 i=5 j=6 k=1 Task=dur slack=xxx LST LFT EFT EST November 11, 2011 Ardavan Asef-Vaziri

Practice: Compute the Theoretical Flow Time Start Finish a=4 slack= b=3 c=3 d=2 e=6 f=4 g=1 h=4 i=5 j=6 k=1 Task=dur slack=xxx LST LFT EFT EST November 11, 2011 Ardavan Asef-Vaziri

Practice: Compute the Theoretical Flow Time Start Finish a=4 slack= b=3 c=3 d=2 e=6 f=4 g=1 h=4 i=5 j=6 k=1 Task=dur slack=xxx LST LFT EFT EST November 11, 2011 Ardavan Asef-Vaziri

Practice: Compute the Theoretical Flow Time Start Finish a=4 slack= b=3 c=3 d=2 e=6 f=4 g=1 h=4 i=5 j=6 k=1 Task=dur slack=xxx LST LFT EFT EST November 11, 2011 Ardavan Asef-Vaziri

Critical Path Example of Flow Time EZS is a small fast food outlet serving mainly the corporate clientele. EZS’ main fare is a freshly prepared, customizable line of sandwiches. It is supplemented with an assortment of drinks, light salads, seasonal fruit and snacks. The restaurant is open 10:00AM to 10:00PM, but the peak demand is during lunch hours, 11:30 to 2:00PM. A customer joining the line makes a sandwich selection by consulting the billboard, marks her selection on a customized form, and hands the form to one of several assemblers who produce the sandwich. The customer does not wait for the sandwich to be assembled, but proceeds directly down the line to select additional items onto her tray. Next, the customer proceeds to pay at the cash register. Finally, (after the payment is completed) she collects her prepared sandwich at a designated location. Selecting the sandwich and marking the form takes 45 seconds. Assembling the sandwich requires 90 seconds. Selecting additional items takes 60 seconds. Paying at the cash register requires 40 seconds. Collecting the prepared sandwich requires 20 seconds. The restaurant employs 2 cash registers and 6 sandwich assemblers, and one person to disburse the prepared sandwiches. November 11, 2011 Ardavan Asef-Vaziri

Critical Path Example of Flow Time a) Draw a process map b) What is the theoretical flow time of the process? The critical path is the top one, = 45 +60 + 40 +20 = 165 sec November 11, 2011 Ardavan Asef-Vaziri

Capacity and Buttleneck c) What is the capacity of the process? Assembly Capacity = 6*60/90 = 4 per min. Cash register Capacity = 2*60/40 = 3 per min. Disburse capacity = 1*60/20= 3 per min (assuming time to collect = time to disburse). d) During rush hour, demand exceeds capacity and long lines form. Does it make sense to add a sandwich assembler No. Assembler is not a bottleneck November 11, 2011 Ardavan Asef-Vaziri

Problem 4. 4 from Second Edition Problem 4.4 from Second Edition. Four major subassemblies; Engine, Frame, Fenders, Seats. Honda's he "American Classic Edition" (ACE) motorcycle is assembled in the US from four major subassemblies. The first subassembly produces the engine: (i) The left and right part of the engine block come out of the automatic mold every 2 min. (ii) These parts are welded together, requiring 1 min of welding machine. (iii) It takes the engine assembler 3 min to insert the two pistons and four valves. The second subassembly produces the frame in two steps: (i) Heavy metal bars are bent in the 10K-pound press in 1 min. (ii) It takes 3 min to weld the multiple bars together with the welding machine to produce the frame. The third subassembly consists of the front and rear fenders, both of which are formed using the same 10K-pound press for 1 min each. The fourth subassembly makes the seat. It takes an assembler 7 min to cut the padding, pit it on a performed piece of sheet metal and wrap the two with synthetic leather. In final assembly, first the four subassemblies are put together. It takes 30 min to finish assembly of one motorcycle. Currently, Honda ACE staffing is as follows there is 1 molding machine operator, 1 welder 1 press operator, 1 engine assembler, 2 seats assemblers, and 10 final assemblers. a) Draw a process flowchart identifying resources, activity times, and any potential storage buffers

Problem 4. 4 from Second Edition Problem 4.4 from Second Edition. Four major subassemblies; Engine, Frame, Fenders, Seats. 2 min 1 min 3 min molding eng. ass. welding aut. molding machine 1 engine assembler 1 molding operator 1 min 3 min stamping welding 30 min start welding machine end FA 1 welder 2 min stamping 10K lbs press 10 final assemblers 1 press operator 7 min seat ass. 2 seat assemblers November 11, 2011 Ardavan Asef-Vaziri 26

Problem 4.4 from Second Edition. b) What is the theoretical flow time of the ACE production process? We have 4 paths, the critical path is the longest path = 37 minutes (going through seat assembly). Therefore, the theoretical flow time = 37 minutes. c) Knowing the benefits of flow-time reduction, Honda would like to decrease the theoretical flow time of the ACE process. Which specific action(s) do you recommend? November 11, 2011 Ardavan Asef-Vaziri 27

Problem 4.4 from Second Edition. We can decrease the theoretical flow time only by decreasing the length of the critical path. Thus we need to decrease the theoretical flow times of seat assembly and/or final assembly: try to change the design and process so that we can perform subtasks parallel. Easiest is to do final assembly of the first three subassemblies first and seat assembly at the end. November 11, 2011 Ardavan Asef-Vaziri 28

Cross-traning Cross training may not reduce flow time if the activities cannot be subdivided into smaller activities that could be done in parallel. 5 1 3 2 5 1 3 2 3 1 2 November 11, 2011 Ardavan Asef-Vaziri 29