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Quantitative Review II Taguchi Loss Function (p.199) • Design the product or service so that it will not be sensitive to variations during the manufacturing or delivery process • For example, design a manufactured good with a smaller design tolerance = better quality Taguchi Loss Function L( x) k ( x T ) 2 where L(x) = k = x T = = the monetary value of the loss associated with deviating from the target limit “T” the constant that translates the deviation into dollars the actual value of the dimension target limits A quality characteristic has a specification (in inches) of 0.200 0.020. If the value of the quality characteristic exceeds 0.200 by the tolerance of 0.020 on either side, the product will require a repair of $150. Develop the appropriate Taguchi loss function (k). L( x) k ( x T ) 2 150 k (0.200 0.220or0.180) 2 k (0.020) 2 150 k /(0.020) k 375,000 2 A quality engineer has a manufacturing specification (in cm) of 0.200 plus or minus 0.050. Historical data indicates that if the quality characteristic takes on values larger than .250 cm or smaller than .150 cm, the product fails and a cost of $75 is incurred. Determine the Taguchi Loss Function and estimate the loss for a dimension of 0.135 cm. L( x) $75 ( x T ) (0.200 0.250or0.150) 0.050 k (75) /(0.050) k 30,000 2 L( x) 30,000( x T )2 L(0.135) 30,000(0.200 0.135)2 $126.75 Reliability Management (pp.651-654) • Series product components Rs ( p 1 )( p2 )( p3 ).......(pn ) • Parallel product components R p 1 (1 p1 )(1 p 2 )(1 p3 )........( 1 pn ) The manufacturing of compact disks requires four sequential steps. The reliability of each of the steps is 0.96, 0.87, 0.92, and 0.88 respectively. What is the reliability of the process? Rs ( p 1 )( p2 )( p3 ).......(pn ) Rs (0.96)(0.87)(0.92)(0 .88) 0.6762 The system reliability for a two-component parallel system is 0.99968. If the reliability of the first component is 0.99, determine the reliability of the second component. R p 1 (1 p1 )(1 p 2 )(1 p3 )........( 1 pn ) 0.99968 0.99968 0.99968–1 p2 = = = = 1 – (1 – 0.99)(1 – p2) 1 – (0.01 – 0.01p2) -0.01 + 0.01p2 0.968 Redundancy B .91 A C .98 .97 B .91 RB 1 (1 0.91)(1 0.91) 0.9919 RS (0.98)(0.9919)(0.97) 0.9429or94.29% Given the diagram below, determine the system reliability if the individual component reliabilities are: A = 0.94, B = 0.92, C = 0.97, and D = 0.93. A C B D RaRb = 1 - (1 - 0.94)(1 - 0.92) = 0.9952 RcRd = 1 - (1 - 0.97)(1 - 0.93) = 0.9979 RabRcd = (0.9952)(0.9979) = 0.9931 Kanban (pp.632-634) d ( p w)(1 ) K C where: K = the number of Kanban cards d = the average production rate OR demand of product p = the processing time w = the waiting time of Kanban cards α = safety stock as a %, usually ranging from 0 to 1 C = the capacity of a standard container Computing the number of kanbans: An aspirin manufacturer has converted to JIT manufacturing using Kanban containers. They wish to determine the number of containers at the bottle filling operation which fills at a rate of 400 per hour. Each container holds 35 bottles, it takes 30 minutes to receive more bottles (processing plus delivery time) and safety stock is set at 10%. d = 400 bottles per hour p+w = 30 minutes or 0.5 hour C = 35 bottles per container α = 0.10 d ( p w)(1 ) 400 (0.5)(1 .1) 220 K 6.29 kanbans C 35 35 Location Analysis Methods (Chapter 8) Factor Rating Method (pp.319-320): Σ (Factor Weighti * Factor Scorei) 5*10= 4*20= 2*30= 5*10= 3*30= 2*10= 2*20= 5*30= 3*10= 5*30= Location Analysis Methods Center-of-Gravity Method (pp.322-323): where dix = x-coordinate of location i diy = y-coordinate of location i Qi = Quantity of goods moved to or from location i Center-of-Gravity Method X Y coordinate coordinate Number of Containers Shipped per Week Chicago 30 120 2,000 Pittsburgh 90 110 1,000 New York 130 130 1,000 Atlanta 60 40 2,000 Location Where would be the best place to put the warehouse? Location Analysis Methods Load Distance Model: Find load distance score by: Calculate the rectilinear distance and multiply by the number of loads Load Distance Model Calculate Rectilinear Distance DAB X A X B YA YB DAB 30 10 40 15 DAB 20 25 DAB 45m iles Identify Loads, i.e., 4 loads from A to B Load Distance Score for AB = 45*4 = 180 TT Logistics Co. has just signed a contract to deliver products to three locations, and they are trying to decide where to put their new warehouse. The three delivery locations are A, B, and C. The two potential sites for the warehouse are D and E. The total quantity to be delivered to each destination is: 200 to A, 100 to B, and 300 to C. The x, y coordinates for the delivery locations and warehouses are as follows: Where to locate warehouse, D or E? X Y coordinate coordinate Location A 92 42 Location B 80 40 Location C 90 35 Warehouse D 90 45 Warehouse E 90 40 Location Location Load Distance Score Warehouse D Location A Location B Location C X coordinate Y coordinate Location A 92 42 Location B 80 40 Location C 90 35 Warehouse D 90 45 Warehouse E 90 40 Distance 2+3=5 10+5=15 0+10=10 Loads 200 100 300 Score 1000 1500 3000 5500 Distance 2+2=4 10+0=10 0+5=5 Loads 200 100 300 Score 800 1000 1500 3300 Warehouse E Location A Location B Location C Designing Process Layouts (Chapter 9) Step 1: Gather information Space needed, space available, importance of proximity between various units Step 2: Develop alternative block plans Using trial-and-error or decision support tools Step 3: Develop a detailed layout Consider exact sizes and shapes of departments and work centers including aisles and stairways Tools like drawing, 3-D models, and CAD software are available to facilitate this process. Process Layout (Step 1: Gather information) Recovery First Sports Medicine Clinic Layout (total space 3750 sq.ft.) A 400 sq.ft. D 800 sq.ft. B 300 sq.ft. E 900 sq.ft. C 300 sq.ft. F 1050 sq.ft. Process Layout (Step 2: Develop a block layout) Current Proposed A 400 sq.ft. B 300 sq.ft. C 300 sq.ft. A 400 sq.ft. D 800 sq.ft. C 300 sq.ft. D 800 sq.ft. E 900 sq.ft. F 1050 sq.ft. E 900 sq.ft. B 300 sq.ft. F 1050 sq.ft. Proposed layout would require less walking. Load Distance Problem What is the load distance for this layout? B A D C E F Trips between departments Dept. A B C E A B 10 C 30 D 10 30 20 E 0 15 15 F 10 15 5 25 Load Distance Problem B A D Dept. C E F A Depts. Trips Distance Score B C D E F 10 30 10 0 10 B 30 15 15 20 15 5 AB 10 1 10 C AC 30 2 60 E AD 10 1 10 AF 10 2 20 BD 30 2 60 BE 15 2 30 BF 15 3 45 CD 20 3 60 CE 15 1 15 CF 5 2 10 EF 25 1 25 345 A 25 Assembly Line Balancing (Chapter 9) Step 1: Identify task & immediate predecessors Step 2: Calculate the cycle time Step 3: Determine the output rate Step 4: Compute the theoretical minimum number of workstations Step 5: Assign tasks to workstations (balance the line) Step 6: Compute efficiency, idle time & balance delay Assembly Line Balancing (Step 1: Identify tasks & immediate predecessors) Example 10.4 Vicki's Pizzeria and the Precedence Diagram Immediate Task Time Work Element Task Description Predecessor (seconds A B C D E F G H I Roll dough Place on cardboard backing Sprinkle cheese Spread Sauce Add pepperoni Add sausage Add mushrooms Shrinkwrap pizza Pack in box None A B C D D D E,F,G H Total task time 50 5 25 15 12 10 15 18 15 165 Layout Calculation Step 2: Determine cycle time (The amount of time each workstation is allowed to complete its tasks.) Cycle time = Station A (50 seconds) -- the bottleneck Step 3: Determine output rate AvailableT ime 3600 sec/ hour MaximumOut put 72 Pizzas / hour Bottleneck 50 sec/ unit Step 4: Compute the theoretical minimum number of workstations (number of station needed to achieve 100% efficiency) TotalTaskTim es 165sec TM 3.30Stations CycleTim e 50sec Assembly Line Balancing (Step 5: Balance the line) 3 Work Stations (A,B), (C,D,G), (E,F,H,I) 55 sec 55 sec 55 sec Assembly Line Balancing (Step 6: Compute efficiency, idle time & balance delay) Efficiency TotalTaskTim es Efficiency(%) (100%) ( Num berOfStations)(NewCycleTim e) 165 sec 165 Efficiency (%) 100 % 3 * 55 165 Balance Delay Balance Delay = 1 – Assembly Line Efficiency BalanceDelay 1 1 0IdleTime Line Balancing Problem What is the bottleneck? What is the maximum production per hour? What is efficiency and balance delay? How to minimize work stations? How should they be groups? New efficiency? 3.4 mins B E 2.3 mins A C 2.7 mins 4.1 mins D F G 1.6 mins 3.3 mins 2.6 mins Line Balancing Problem What is the bottleneck? 4.1 minutes What is the maximum production per hour? 60/4.1 = 14.63 units/hour What is efficiency and balance delay? Efficiency = 20/(7*4.1) = 69.69% Balance Delay = 1-.6969 = 30.31% How to minimize work stations? TotalTaskTim es 20 TM 4.88WorkStations CycleTim e 4.1 Should we use 4 or 5 work stations? 4 Work Stations Efficiency = 20/(4*6) = 20/24 = 83.3% Balance delay = 1-.833 = 16.7% Maximum production/hour = 60/6 = 10 units/hour 5.7 mins 3.4 mins B 6 mins E 2.3 mins A C 2.7 mins 4.1 mins 5.7 mins D F G 1.6 mins 3.3 mins 2.6 mins 2.6 mins 5 Work Stations Efficiency = 20/(5*5.7) = 20/28.5 = 70.18% Balance delay = 1-.7018 = 29.82% Maximum production/hour = 60/5.7 = 10.52 units/hour 5.7 mins 3.4 mins B E 2.3 mins A C 4.1 mins 4.9 mins 2.7 mins 2.7 mins 4.1 mins D F G 1.6 mins 3.3 mins 2.6 mins 2.6 mins Should we use 4 or 5 or 7 work stations? 4 Work Stations Efficiency = 83.3% Balance delay = 16.7% Maximum production/hour = 10 units/hour 5 Work Stations Efficiency = 70.18% Balance delay = 29.82% Maximum production/hour = 10.52 units/hour 7 Work Stations Efficiency = 69.69% Balance delay = 30.31% Maximum production/hour = 14.63 units/hour Supply Chain Efficiency Measuring Cash to Conversion Cycle Inventory Turnover (IT) Inventory Days’ Supply (IDS) Accounts Receivable Turnover (ART) Accounts Receivable Days’ Supply (ARDS) Accounts Payable Turnover (APT) Accounts Payable Days’ Supply (APDS) Cash-to-Cash Conversion Cycle = IDS + ARDS - APDS Inventory Ratios Inventory Turnover (IT): # of times you turn your inventory annually Inventory Days’ Supply (IDS): how many days inventory you keep Accounts Receivable Ratios Accounts Receivable Turnover (ART): # of times you turn your accts. rec. annually Accounts Receivable Days’ Supply (ARDS): how long it takes to get $ owed paid to you Accounts Payable Ratios Accounts Payable Turnover (APT): # of times you turn your accts. payable annually Accounts Payable Days’ Supply (APDS): how long you take to pay your bills Dell’s Financial data Revenue Cost of goods sold Average Inventory Value Average Accounts Receivable Average Accounts Payable $35.40 billions $29.10 billions $0.306 billions $2.586 billions $5.989 billions Dell’s Example Dell’s Inventory Turnover Dell’s Inventory Days’ Supply Dell’s Example Dell’s Accounts Receivable Turnover Dell’s Accounts Receivable Days’ Supply Dell’s Example Dell’s Accounts Payable Turnover Dell’s Accounts Payable Days’ Supply Dell’s Example Dell’s Cash-to-Cash Conversion Cycle = IDS + ARDS – APDS = 3.84 days + 26.66 days – 61.76 days = -31.26 days The negative value means that Dell receives customers’ payments (accounts receivable) 31.26 days, on average, before Dell has to pay its suppliers (accounts payable). This means that Dell’s value chain is a selffunding cash model. Dell’s Negative Cash-to-Cash Conversion Cycle Breakeven Analysis (Make/Buy Decision) Total Cost of Outsourcing: Total Cost of Insourcing: Indifference Point: The Bagel Shop Problem Jim & John plan to open a small bagel shop. The local baker has offered to sell them bagels at 50 cents each. However, they will need to invest $2,000 in bread racks to transport the bagels back and forth from the bakery to their store. Alternatively, they can bake the bagels at their store for 20 cents each if they invest $20,000 in kitchen equipment. They expect to sell 80,000 bagels each year. What should they do? The Bagel Shop Problem Indifference Point Calculation: The Bagel Shop Problem Make vs Buy Decision at 80,000 bagels Outsource (Buy) $2,000+($.5*80,000) = $42,000 In House (Make) $20,000+($.2*80,000) = $36,000 Make vs Buy Decision at 50,000 bagels Outsource (Buy) $2,000+($.5*50,000) = $27,000 In House (Make) $20,000+($.2*50,000) = $30,000 If the demand is lower than the indifference point, outsourcing is a cheaper alternative, and vice versa. That’s all, folks! Good Luck!