PROCESS ANALYSIS PROFESSOR DAVID GILLEN (UNIVERSITY OF BRITISH COLUMBIA) & PROFESSOR BENNY MANTIN (UNIVERSITY OF WATERLOO)

Transcription

1 PROCESS ANALYSIS PROFESSOR DAVID GILLEN (UNIVERSITY OF BRITISH COLUMBIA) & PROFESSOR BENNY MANTIN (UNIVERSITY OF WATERLOO) Istanbul Technical University Air Transportation Management M.Sc. Program Logistic Management in Air Transport Module December 2014

2 UNDERSTANDING PROCESSES 2

3 Ramp (Outside) Inside WITH A BANKED SCHEDULE, MINIMUM CONNECT TIMES DRIVE TURNAROUND TIMES NOT GROUND OPERATIONS Ground Operations Required Time for a Turnaround ( Carriers ) min Extend jetway and open door (1 min) Deplane (10 min) Cater (15 min) Clean cabin (10-15 min) Boarding (13 min) Weight and Balance (2 min) Close door and jetway (1 min) Prearrival Equipment Set Up (2 Min) min Arrival (2 min) Ground power A/C bin door (3 min) Fuel (10-15 min) Unload/load bags and cargo (20-30 min) Close cargo door (1 min) Departure Dispatch (4 min) Opportunities To Compress Ground Operations Turnaround Times 3

4 Ramp (Outside) Inside BUT, WITH A CONTINUOUS SCHEDULE, GROUND OPERATIONS DRIVES TURNAROUND TIME, AND THUS AIRPLANE/CREW UTILIZATION Ground Operations Required Time for a Turnaround ( Southwest ) min Extend jetway and open door (<1 min) Deplane Cleaning (6 min) (2-5 min) Cater (13-16 min) Boarding (9-13 min) Weight and Balance (1-2 min) Close door and jetway (<1 min) Prearrival Equipment Set Up (1-2 Min) min Arrival (2-7 min) Ground power A/C bin door (<2 min) Unload/load bags and cargo (18-21 min) Fuel (6-11 min) Close cargo door (<1 min) Departure The LCCs Have Engineered Rapid Turnaround Processes emulated on short haul routes by network carriers 4

5 AIRCRAFT TURNAROUND AT AIRPORTS: Activities: Passengers disembark Unload luggage and freight Load data Clean Fuel Southwest says that if its boarding time increased by 10 minutes per flight, it would need 40 more planes at a cost of $40 million each to run the same number of flights it does currently!!! 5

6 AIRCRAFT TURNAROUND AT AIRPORTS: Passengers boarding is the longest activity. In the mid-60s it took 20/minute, today 9/minute Have you ever wondered whether there is a better way for boarding? Air Canada: back to front United Airlines: window first America West: reverse pyramid WestJet: random 6

7 MATHEMATICIAN DEVISES WAY TO BOARD AIRPLANES FASTER A Chinese mathematician is touting a new way to get people onto commercial airline flights faster. Dr Tie-Qiao Tang, along with a small team of researchers, has suggested that airlines should assign seating after evaluating each passenger on several variables. "Each passenger has their own individual properties. For example, each passenger's luggage has a different attribution and thus has different influences on boarding behavior; the time that the passenger's ticket is checked at the gate is different; the time that the passenger deals with his or her carried luggage is different; seat conflicts have different effects on the passenger. Each passenger has a different optimal speed, maximum speed and safe distance." Basically, passengers are evaluated by how fast they can board the plane, and then are assigned a seat. The researchers compared their method to two others; the free-for-all, where passengers board in any order they like, and assigned seating. According to Tang, "overtaking, queue-jumping, seat conflict congestions and jams may occur under the first two boarding strategies," but doesn't happen with Tang's proposed method. And to boot, the third method is the fastest, according to the study. The only problem with the method is that it would require airlines to keep detailed profile information on their customers, like average boarding speed. Last year, Jason Steffen, from the Fermilab Center for Particle Astrophysics, designed a system where passengers line up in a "very specific" order and then board. His method also proved faster than getting on a plane in groups or in a back-to-front order. CBC November 13, 2012 You can find the paper at : 7

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9 THE FLYING CARPET BY ROB WALLACE 9

10 LEARNING OBJECTIVES Understand the following concepts: Flow Time Capacity Rate Bottleneck Tool: Process Analysis Process mapping Capacity analysis (also called bottleneck analysis) Applications McDonald s make-to-order system Kristen s Cookie Company 10

11 PROCESSES What occurs during a transformation process? Processing Waiting Storage Inputs Raw material, people, information, capital etc. Transformation Process Outputs Goods Services 11

12 EXAMPLES OF PROCESSES wood metal Factory guitars students University alumni bulk items Distribution center small parcels Electronic Components Dell Computers Processes can involve both goods and services. Processes can have multiple inputs and/or multiple outputs. 12

13 PROCESS ENTITIES Flow units: The items that flow through the process May be homogenous or heterogeneous Activities: The transformation steps in the process Each activity takes some time to complete Resources: They perform the activities Have capacities Buffers: Storage units for flow units May have finite size 13

14 PROCESS FLOW DIAGRAM ELEMENTS Example: Bread making Activities, tasks or operations Buffers: Queues or inventories Decision points Flow of materials Raw Material Bread Making Finished Bread Packing Packed Bread Note: If different types of breads, the bread-making and packing activities may differ for each 14

15 AN EXAMPLE OF A RESERVATION PROCESSES Uninformed customers Online agency (Opodo) Informed customers Buy? No Leave Yes Order information Uninformed Airline Opodo s Information system Informed Airline 15

16 LEVEL OF DETAIL IN PROCESS ANALYSIS A process can be defined at an aggregate level: Food ingredients Transportation to catering facility Food ingredients Tray assembly Trays A/c catering Transportation and assembly can contain many sub-processes: Catered galley The purpose of the process analysis determines the level of detail in modeling the processes. 16

17 PROCESS MEASURES Cost Quality measures Time (Flow measures) Flexibility measures Capacity This course focuses on capacity and flow measures. 17

18 PROCESS MEASURES IN PRODUCTION AND SERVICE Production process Service process Flow unit Materials Customers Input rate Raw material releasing rate Customers arrival rate Output rate Flow time Finished goods output rate Time required to turn materials into a product Customers departure rate (service completion rate) Time that a customer is being served Inventory Amount of work-in-process Number of customers being served Capacity Maximum output rate Maximum service completion rate 18

19 KEY STEPS IN PROCESS ANALYSIS Step 1: Determine the Purpose of the analysis Step 2: Process mapping (Define the process) Determine the flow units Determine the tasks (sub-processes), and the sequence of the tasks Determine the time for each task Determine which resources are used in each task Determine where inventory is kept in the process Record this through a process flow diagram (Linear flow chart, Swim-lane (deployment) flow chart, Gantt chart) Step 3: Capacity Analysis (also called Bottleneck Analysis) Determine the capacity of each resource, and of the process Further analysis will be covered later during the course 19

20 EXAMPLE: MCDONALD S KITCHEN Purpose of the analysis: To determine the capacity rate of a McDonald s restaurant Link to video Given this purpose, we draw the process boundary around the kitchen We do not consider customers queue We do not consider meat cooking processes (we assume cooked meat is always available when needed during the make-to-order process) 20

21 LINEAR FLOW CHART Flow unit: An order (each order = one burger) Tasks and sequences Flow time of each task Place an order Toast buns Add dressings Add meat patties Package Deliver 8s 10s 8s 6s 2s 2s Determine which resources are used in each task Could indicate resources along each task Swim-lane diagram or Gantt chart may be better 21

22 SWIM-LANE (DEPLOYMENT) FLOWCHART RESOURC ES ACTIVITIES Cashier Place an order Worker1 Toaster Toast buns Worker 2 Add dressings Worker 3 Add meat patties Worker 4 Package Worker 5 Deliver 22

23 SWIM-LANE FLOWCHART: MODIFIED RESOURC ES ACTIVITIES Cashier Place an order Worker1 Toaster Toast buns Worker 2 Add dressings Add meat patties Package Worker 3 Worker 4 Worker 5 Deliver 23

24 GANTT CHART RESOURCES ACTIVITIES Time Span Cashier Place an order 8 s Worker1 Toaster Toast buns 10s Worker 2 Add dressings 8 s Worker 3 Add meat patties 6s Worker 4 Package 2s Worker 5 Deliver 2s Time 24

25 CHOICE OF CHARTS Flow chart (linear): how things flow Swim-lane flowchart: how things flow how resources are shared Gantt chart: when and where things flow when and which resources are used Typically, we start with flow-charting a process. If shared resources can be clearly indicated on flow charts, we can further analyze bottlenecks, etc. Otherwise, we need to rearrange the flow chart in swim-lanes to understand how resources are shared. Gantt chart is most useful in analyzing bottlenecks of complicated systems. Choice of charts is an art. 25

26 PROCESS MAPPING: SOME NOTES There is no one way to draw a process map Get feedback from all the people involved in the process to validate the process map Do not map the process as you think it works Map it as it actually works Process maps are surprisingly informative Common response: I never knew we did it that way! Starting point for process analysis, and a great tool for brainstorming process improvements

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28 BASIC PROCESS ANALYSIS SINGLE STAGE PROCESS Toast buns Toaster Worker 1 Flow Time (Time that buns spend in the toaster) 10 sec Capacity Rate??? 28

29 Basic Process Analysis Multiple Stage Process Place an order Toast buns Add dressings Add meat patties Package Deliver Cashier Worker 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr Theoretical Flow Time of the whole process: 36 Flow Time of the sec whole process:??? Capacity Capacity rate of rate the of whole the whole process: process: 360 orders/hr??? Note: The theoretical flow time ignores the possibility of waiting; so it is the lowest possible flow time 29

30 RESOURC ES GANTT CHART: MULTIPLE STAGE PROCESS ACTIVITIE S Time Span Cashier Place an order 8 s 8 s Worker1 Toaster Toast buns 10s 10s Worker 2 Add dressings 8 s 8 s Worker 3 Add meat patties 6s 6s Worker 4 Package 2s 2s Worker 5 Deliver 2s 2s 30 Time

31 THE BOTTLENECK The resource with the lowest capacity rate The slowest resource (or the resource with the highest unit load ) Unit load: Total amount of time the resource works to process each flow unit Determines the capacity rate of the entire process Increasing the capacity of non-bottleneck resources does not increase the capacity rate of the process 31

32 INCREASING THE CAPACITY RATE OF A PROCESS - WHAT IF WE ADD A CASHIER? Place an order Place an order Cashiers Toast buns Worker 1 Toaster Add dressings Add meat patties Package Deliver Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 900/hr (2 * 450/hr) 360/hr 450/hr 600/hr 1800/hr 1800/hr Theoretical Flow Time of the whole process: 36 Theoretical Flow Time sec of the whole process:??? Capacity Capacity rate of rate the of whole the whole process: process: 360 orders/hr??? 32

33 INCREASING THE CAPACITY RATE OF A PROCESS - WHAT IF WE ADD A TOASTER? Place an order Toast buns Toast buns Add dressings Add meat patties Package Deliver Cashier Worker 1 Toasters Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 720/hr (2 * 360/hr) 450/hr 600/hr 1800/hr 1800/hr Theoretical Flow Time of the whole process: 36 sec Theoretical Flow Time of the whole process:??? Which task is the bottleneck? Capacity rate of the whole process: 450 orders/hr Capacity rate of the whole process:??? 33

34 ADDING A TOASTER: GANTT CHART RESOURCES ACTIVITIES Time Span Cashier Place an order 8 s 8 s Worker1 Toaster 1 Worker1 Toaster 2 Toast buns Toast buns 10s 10s Worker 1 is not busy all the time, and can take care of 2 toasters Worker 2 Add dressings 8 s 8 s Worker 3 Add meat patties 6s 6s Worker 4 Package 2s 2s Worker 5 Deliver 2s 2s Time 34

35 THINKING IN TERMS OF UNIT LOADS Resource Unit Load (sec/unit) Capacity Rate (units/min) Capacity rate (units/hr) Cashier Toaster Worker Worker Worker Unit Load: Total amount of time the resource works to process each flow unit 35

36 INCREASING CAPACITY (1) INCREASE THE SIZE OF THE RESOURCE POOL One Toaster Capacity rate: 360/hr Two Toasters Working in Parallel Capacity rate: 720/hr 10 sec Toast buns 10 sec Toast buns Toast buns 10 sec 36

37 INCREASING CAPACITY (2) DECREASING THE UNIT LOAD This Toaster Capacity rate: 360/hr Faster Toaster Works twice as fast Capacity rate: 720/hr Toast buns 10 sec Toast buns 5 sec 37

38 INCREASING THE CAPACITY RATE OF A PROCESS Increase the capacity rate of the bottleneck Some other resources may become a bottleneck when capacity is added Important when we justify additional capacity 38

39 INCREASING THE CAPACITY RATE OF A PROCESS EXPAND THE RESOURCE POOL AT THE BOTTLENECK Place an order Toast buns Toast buns Add dressings Add meat patties Package Deliver Cashier Worker 1 Toasters Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 720/hr (2 * 360/hr) 450/hr 600/hr 1800/hr 1800/hr Theoretical Flow Time of the whole process: 36 sec Capacity rate of the whole process: 450 orders/hr 39

40 Increasing the capacity rate of a process - Reduce Unit Load at the Bottleneck Place an order Toast buns Add dressings Add meat patties Package Deliver Old Flow Time Old Capacity Rate New Flow Time New Capacity Rate Cashier Worker 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr 8 sec 5 sec 8 sec 6 sec 2 sec 2 sec 450/hr 720/hr 450/hr 600/hr 1800/hr 1800/hr Theoretical Flow Time :??? Capacity rate of the process: 40???

41 ANY OPERATIONAL BENEFIT OF REDUCING UNIT LOAD AT NON-BOTTLENECKS? Place an order Toast buns Add dressings Add meat patties Package Deliver Old Flow Time Old Capacity Rate New Flow Time New Capacity Rate Cashier Worker 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr 4 sec 10 sec 6 sec 4 sec 1 sec 1 sec 900/hr 360/hr 600/hr 900/hr 3600/hr 3600/hr Theoretical Flow Time :??? Capacity rate of the process: 41???

42 PROCESSES MAY BE UNBALANCED Place an Order Toast buns Flow Time 8 sec 10 sec Capacity Rate 450/hour 360/hour Process is Blocked When the next stage is busy, the order cannot be sent to the next stage after finishing the current stage, unless an inventory buffer is introduced 42

43 ANOTHER EXAMPLE Add dressings Add meat patties Flow Time 8 sec 6 sec Capacity Rate 450/hour 600/hour Process is starved 43

44 BOTTLENECK CHARACTERISTICS The bottleneck is fully utilized while other resources are not utilized If a buffer is provided at some upstream stage to the bottleneck, inventory may build up at the buffer Inventory will not build up at the (immediately) downstream stages to the bottleneck even if buffers are provided Shortening non-bottleneck tasks decreases flow time but does not affect capacity rate Reducing flow time improves response time 44

45 PROCESS ANALYSIS: MULTIPLE FLOW UNITS Resource Unit Load (minutes/unit) Product A Product B Product C If you produce only Product A, what is capacity rate of the process (per hour)? Which resource is the bottleneck? If your product mix is 1 unit of A, 2 units of B and 2 units of C, what is your capacity rate? Bottleneck? 45

46 PROCESS ANALYSIS: MULTIPLE FLOW UNITS Resource Unit Load (minutes/unit)1 Product A Product B Product C 1A + 1B + 1C 1A+2B+2C c When multiple flow units go through a process, the product mix needs to be considered while determining the unit load and the capacity The bottleneck depends on the product mix 46

47 PROCESS ANALYSIS: MULTIPLE FLOW UNITS Flow diagrams are not easy to draw How to identify bottleneck? Count the total amount of work per resource (also known as the unit load ) When multiple flow units go through a process, a product mix needs to be considered while determining capacity The bottleneck depends on the product mix The bottlenecks can move as the product mix changes 47

48 THEORETICAL VERSUS EFFECTIVE CAPACITY Some capacity is lost due to machine maintenance, machine set-ups, etc. Example. Changing over from one product type to another may require adjustments to the machine, tools, etc ( set-ups ) Railways/London Underground shut down lines to inspect and maintain track 48

49 WHAT INFORMATION DO UNIT LOADS GIVE US? Process with four tasks (A, B, C, D) each taking 5 minutes to complete One worker does all four tasks 4 workers working in parallel (The resource pool has four resources) A +B+C+D (20 min) A +B+C+D (20 min) A +B+C+D (20 min) A +B+C+D (20 min) Worker 1 Worker 2 Worker 3 Worker 4 Unit Load (for each worker) = 20 min Capacity rate for each worker = 3 units/hour Capacity rate for the resource pool = 12 units/hour 49

50 WHAT INFORMATION DO UNIT LOADS GIVE US? Now, suppose the work is redistributed among the four workers as follows: Task A (5 min) Task B (5 min) Task C (5 min) Task D (5 min) Worker 1 Worker 2 Worker 3 Worker 4 Unit Load (for each worker) = 5 min Capacity rate for each worker = 12 units/hour Capacity rate for the resource pool = 48 units/hour 50

51 WHAT INFORMATION DO UNIT LOADS GIVE US? Unit Load tells you something about how work is organized Small Unit Load for Each Resource High Unit Load for Each Resource Labor Skills Low High Equipment Specialization High Low Process Type Flow Shop Job Shop 51

52 An Experiment in humanistic production at its Kalmar and Uddevalla plants (late 1980s) Teams jointly assemble cars at a fixed location, no moving assembly line Plants shut down in Recommended reading THE VOLVO EXPERIMENT Edges Fray on Volvo s Brave New Humanistic World New York Times, July 7,

53 UTILIZATION Throughput Rate Actual output rate Utilization 100% Capacity Rate maximum output rate Utilization gives us information about excess capacity The utilization of each resource in a process can be presented with a utilization profile Resource Capacity Rate (units/hour) Input Rate (units/hour) What is the optimal utilization of a resource? Utilization % % % % % 53

54 OPERATIONAL CHALLENGE MISMATCH BETWEEN DEMAND AND SUPPLY In any process, the input and output rates will vary over time A key operational challenge is matching supply and demand i.e., matching the input and output rates For a variety of reasons, a perfect match is not possible What are some of these reasons? 54

55 AN EXAMPLE: SECURITY SCREENING AT YVR Time Input rate (passengers/15 min slot) Capacity rate (passengers/15 min slot) Excess Demand Excess Capacity 6: : : : : : : : : : : : : : : : TOTAL Data for a 4-hour shift in 15-min time slows: 7 arrive between 6:00 and 6:30 etc. Do we have enough capacity? but not at all times Enough capacity for the shift 55

56 SHORT-RUN VS. LONG-RUN AVERAGES Since the input and output rates may vary over time, both the short-run average and the long-run average rates provide useful information. Long-run average input rate must be less than the long-run average capacity rate Long-run average throughput rate = Long-run average input rate Short-run average input rate can be greater than the short-run average capacity rate Why? Why? But what would this lead to? 56

57 IMPLIED UTILIZATION To capture the idea that there may be excess demand in the short-run, another measure of utilization is often useful Throughput Input Rate Rate Implied Utilizatio Utilization n Capacity Capacity Rate Rate Implied utilization also allows us to capture the idea of overtime Organizations often budget for a fixed amount of capacity, and work overtime to meet excess demand 57

58 SECURITY SCREENING EXAMPLE REVISITED What is the capacity rate? Note: In this example, the capacity rate is given. In practice, it may not be obvious. Finding the capacity rate will involve drawing a process flow map, identifying activities, times, resources, etc, and finding the bottleneck What is the (average) size of the line? How long do passengers wait (flow time)? 58

59 Time INVENTORY BUILD-UP DIAGRAM Input rate (passengers/15 min slot) Capacity rate (passengers/15 min slot) Excess Demand Excess Capacity INVENTOR YBUILD-UP 6: : : : : : : : : : : : : : : : TOTAL

60 14 INVENTORY BUILD-UP DIAGRAM Inventory Build-Up :15 06:3006:45 07:00 07:15 07:30 07:45 08:0008:15 08:30 08:45 09:00 09:15 09:3009:45 10:00 What is the average inventory in the buffer? 60

61 Time CALCULATING AVERAGE INVENTORY Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity INVENTORY BUILD-UP 6: : : : : : Empty Buffer (No Queue) 7: : : : : : : : : : Buffer NOT empty Average Inventory =

62 CONSIDER ANOTHER EXAMPLE Time Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity INVENTORY BUILD-UP 14 Inventory Build-Up 6: : : : : : : : Average Inventory :00 08:00 09:00 10:00 08:30 09:00 09:30 10:00 62

63 AND ANOTHER Time Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity INVENTORY BUILD-UP 7: : : : Average Inventory Inventory Build-Up 07:00 08:00 09:00 10:00 63

64 AND ANOTHER Time Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity INVENTORY BUILD-UP 8: : Average 0.2 Inventory Inventory Build-Up 07:00 08:00 64

65 ESTIMATING PROCESS MEASURES Process measures changes over time Depending on the mismatch between input rate and the capacity rate the inevitably occurs over time We are interested in averages of these quantities Average values of process measures can be misleading It is often convenient to assume continuous input and output processes 65

66 DEFINITIONS Instantaneous Flow Rates R i (t) R o (t) R(t) = R i (t) R o (t) The input rate to the process at time t The output rate of the process at time t Instantaneous inventory accumulation at time t Inventory Level I(t) Flow Time T(t) The number of units within the process boundaries at time t The time that a unit which enters (leaves) the process at time t spends (has spent) within the process This can be defined in many ways 66

67 INVENTORY AND FLOW DYNAMICS Let (t 1,t 2 ) denote an interval of time starting at t 1 and ending at t 2 Suppose R(t) is constant over (t 1,t 2 ) and equals R. Then, I( t2) I( t1) R ( t2 t1) Ending Inventory Starting Inventory Change in Inventory I(t 2 ) I(t 1 ) I(t) t 1 t 2 R *(t 2 -t 1 ) t Average Inventory Starting Inventory 2 Ending Inventory 67

68 INVENTORY BUILD-UP DIAGRAM Input Rate Capacity rate = 100/hr AM Inventory (or Backlog) PM 2PM 6PM Assumes inventory level changes in discrete amounts Assumes inventory level changes in continuous amounts 10AM 12PM 2PM 6PM 68

69 ANOTHER INVENTORY BUILD-UP EXAMPLE I(t) Inventory in week t Week Input Rate Throughput Rate Inventory Week 69

70 AVERAGE INVENTORY Average inventory depends on whether inventory is assumed to change in discrete steps, or continuously I(t) Under the discrete assumption: The average inventory over weeks 0 to 3 is Under the continuous assumption: The average inventory? Area under?????? the curve Week 70

71 LITTLE S LAW Establishes a relationship between average inventory, average throughput rate, and average flow time Average Inventory I [units] Average throughput rate R [units/hr] Average Flow Time T [hrs] 71

72 LITTLE S LAW Throughput rate: 1 car/min 900 cars in the system Flow time? Flow Time (900 cars)(1 min/car ) 900 cars 1car/min inventory throughput rate (Average) Inventory = (Average) Throughput Rate * (Average) Flow Time I = R * T 72

73 LITTLE S LAW: EXAMPLE 1 Patients waiting for an organ transplant are placed on a list until a suitable organ is available. We can think of this as a process. Why? INPUT Patients in need of a transplant Patients matched to donated organs OUTPUTS Patients leaving the list hopefully with a successful transplant 73

74 LITTLE S LAW: EXAMPLE 1 Question (a) On average, there are 300 people waiting for an organ transplant On average, patients wait on the list for 3 years Assume that no patients die during the wait How many transplants are performed per year? 300 patients?? / year 3 years in system I = R * T Inventory I = 300 patients Flow Time T = 3 years Throughput Rate R = I/T = 100 patients / year 74

75 LITTLE S LAW: EXAMPLE patients 100/year??? years in system I = R * T Inventory I = 300 patients Throughput R= 100 patients/year Flow Time T = I/R = 3 years Question (b) On average, there are 300 people waiting for an organ transplant On average, 100 transplants are performed per year Assume that no patients die during the wait How long do patients stay on the list? 75

76 LITTLE S LAW: EXAMPLE 2 You are managing the construction of a new container terminal at the Port of Vancouver. You expect to process 1000 contains/day, and you have promised customers that containers will spend no more than 1 day waiting to be shipped. INPUT Containers to be shipped OUTPUT Containers shipped 76

77 Question (a) LITTLE S LAW: EXAMPLE 2 On average, your container storage yard can hold 500 containers. Is your yard big enough? 77

78 Question (b) LITTLE S LAW: EXAMPLE 2 Suppose the yard is expanded to hold 2000 containers Since container traffic is growing rapidly, you are soon processing 2000 containers/day You are asked to make improvement to the terminal to handle 4000 containers/day But there is no more room to expand the yard What changes can you make in order to process 4000 containers/day? 78

79 INSIGHTS FROM LITTLE S LAW Throughput rate, flow time, and inventory are related Depending on the situation, a manager can influence any one of these measures by controlling the other two You cannot independently choose flow time, throughput and inventory levels! Once two are chosen, the third is determined For example, if the flow time is fixed, the only way to reduce inventory is to increase throughput 79

80 INSIGHTS FROM LITTLE S LAW How would you reduce wait time for patients on the transplant waiting list? Increase throughput rate Decrease number of people on the list (inventory) How would you increase throughput rate of containers at the port Decrease flow time Increase inventory 80

81 LITTLE S LAW: EXAMPLE 3 Wal-mart imports Product X from an overseas factory. Each order from Wal-mart goes through several stages before it gets through several stages before it gets to the store, and it takes time to flow each stage Factory Port Ship Warehouse 2 days 1 day 5 days 3 days How much inventory is tied up at the warehouse? [Hint: What information is missing?] How much inventory is tied up in the supply chain? Little s Law can be applied to any process, or any part of a process 81

82 LESSONS Capacity rate versus throughput rate (Utilization) Short-run versus long-run averages Input and output rates vary over time resulting in Excess capacity Inventory build-ups Inventory build-up diagrams are useful tools, but Average can be misleading; need to be carefully calculated Little s Law helps make the connection between average flow measures 3 key performance measures-inventory, flow rate, flow time 82

83 LINE BALANCING: BATCHING DECISIONS Milling Machine Assembly Process 83

84 LINE BALANCING: BATCHING DECISIONS Milling Machine Assembly Process Set up times: 1 min to switch over. What is optimal batch size? Steer support parts: 1 min; 1 per unit Two ribs: 0.5 min; 2 per unit 84

85 THE IMPACT OF SET-UP TIMES ON CAPACITY Batch of 12 Batch of 60 Production cycle Production cycle 60 min (set up) + 12 min (steering) + 60 min (set up) +12 min (ribs) = 144 min Capacity = 12/144= Batch of 120 Batch of Time [minutes] 60 min (set up) + 300min (steering) + 60 min (set up) +300 min (ribs) = 720min Capacity = 300/720= Produce steer supports (1 box corresponds to 12 units = 12 scooters) Set-up from Ribs to Steer support 0.4 Produce ribs (1 box corresponds to 24 units = 12 scooters) 0.35 Set-up from steer support to ribs Capacity as a function of the batch size 85 1/p

86 BATCHING AND INVENTORY Production with large batches Production with small batches Cycle Inventory Cycle Inventory Produce Sedan Produce Station wagon Beginning of Month End of Month Beginning of Month End of Month 86

87 THE IMPACT OF SET-UP TIMES ON CAPACITY Milling Assembly: 3 min 133 Inventory [in units of xootrs] Rib inventory Consider B=200 Steer support inventory 60 min (set up) min (steering) + 60 min (set up) +200 min (ribs) = 520 min Time [minutes] Production cycle Produce ribs Set-up from Ribs to Steer support Produce steer supports Set-up from steer support to ribs Idle time Produce ribs at 1 per min Assembly requires 1 per 3 min So inventory accumulates at 2 per 3 min 200*2/3=133.3 This amount of is sufficient for 133.3*3 = 400 min. That is, until = 600 min Hence, 80 min idle time 87

88 ELIMINATE IDLE TIMES Milling Machine Assembly Process Set-up time, S 120 minutes - Per unit time, p 2 minutes/unit 3 minutes/unit Capacity (B=12) units/minute 0.33 units/minute Capacity (B=300) units/minute 0.33 units/minute If B=12: Batch size Capacity B = Setup time + Batch Size Processing time 0.5 = = unit/min 0.45 To balance the line, solve: B=120 B = 12 S+B p B B 2 = 1 3 unit/min Batch size is too small, Capacity of slowest step other than the one requiring set-up Batch size is too large 88

89 PROCESS MEASURES: FLOW MEASURES Identify flow units What is my product? Flow Rates (Input Rate and Output Rate) What is the demand on my system, and what is my capacity? Flow Times (Time spent in process) How long does it take me to produce one product? Inventory How much inventory (of flow units) is building up? Where do I need to hold inventory? 89