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Quantitative Review II

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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

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where L(x) =the monetary value of the loss associated with deviating from the target limit “T” k =the constant that translates the deviation into dollars x =the actual value of the dimension T =target limits Taguchi Loss Function

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A quality characteristic has a specification (in inches) of If the value of the quality characteristic exceeds by the tolerance of on either side, the product will require a repair of $150. Develop the appropriate Taguchi loss function (k).

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A quality engineer has a manufacturing specification (in cm) of plus or minus 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 cm.

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Reliability Management (pp ) Series product components Parallel product components

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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?

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The system reliability for a two-component parallel system is If the reliability of the first component is 0.99, determine the reliability of the second component =1 – (1 – 0.99)(1 – p2) =1 – (0.01 – 0.01p2) –1= p2 p2=0.968

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Redundancy A B C B

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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 = A D C B RaRb = 1 - ( )( ) = RcRd = 1 - ( )( ) = RabRcd = (0.9952)(0.9979) =

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Kanban (pp ) 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

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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

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Location Analysis Methods (Chapter 8) Factor Rating Method (pp ): Σ (Factor Weight i * Factor Score i ) 5*10= 4*20= 2*30= 5*10= 3*30= 2*10= 2*20= 5*30= 3*10= 5*30=

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Location Analysis Methods Center-of-Gravity Method (pp ): where d ix = x-coordinate of location i d iy = y-coordinate of location i Q i = Quantity of goods moved to or from location i

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Where would be the best place to put the warehouse? Location X coordinate Y coordinate Number of Containers Shipped per Week Chicago301202,000 Pittsburgh901101,000 New York130 1,000 Atlanta60402,000 Center-of-Gravity Method

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Location Analysis Methods Load Distance Model: Find load distance score by: Calculate the rectilinear distance and multiply by the number of loads

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Load Distance Model Calculate Rectilinear Distance Identify Loads, i.e., 4 loads from A to B Load Distance Score for AB = 45*4 = 180

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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? Location X coordinate Y coordinate Location A9242 Location B8040 Location C9035 Warehouse D9045 Warehouse E9040

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Load Distance Score Warehouse D DistanceLoadsScore Location A 2+3= Location B10+5= Location C0+10= Warehouse E DistanceLoadsScore Location A 2+2= Location B10+0= Location C 0+5= LocationX coordinate Y coordinate Location A9242 Location B8040 Location C9035 Warehouse D9045 Warehouse E9040

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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.

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Process Layout (Step 1: Gather information) Recovery First Sports Medicine Clinic Layout (total space 3750 sq.ft.) A 400 sq.ft. B 300 sq.ft. C 300 sq.ft. D 800 sq.ft. E 900 sq.ft. F 1050 sq.ft.

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Process Layout (Step 2: Develop a block layout) Current Proposed A 400 sq.ft. B 300 sq.ft. C 300 sq.ft. D 800 sq.ft. E 900 sq.ft. F 1050 sq.ft. A 400 sq.ft. D 800 sq.ft. C 300 sq.ft. E 900 sq.ft. B 300 sq.ft. F 1050 sq.ft. Proposed layout would require less walking.

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What is the load distance for this layout? Trips between departments BAD CEF Dept. ABCDEF A B3015 C20155 E25 Load Distance Problem

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Depts.TripsDistanceScore AB101 AC30260 AD101 AF10220 BD30260 BE15230 BF15345 CD20360 CE151 CF5210 EF BAD CEF Dept. ABCDEF A B3015 C20155 E25

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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

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Assembly Line Balancing (Step 1: Identify tasks & immediate predecessors)

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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 Step 4: Compute the theoretical minimum number of workstations (number of station needed to achieve 100% efficiency)

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Assembly Line Balancing (Step 5: Balance the line) 3 Work Stations (A,B), (C,D,G), (E,F,H,I) 55 sec

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Assembly Line Balancing (Step 6: Compute efficiency, idle time & balance delay) Efficiency Balance Delay Balance Delay = 1 – Assembly Line Efficiency

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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? A B C 4.1 mins D 1.6 mins E 2.7 mins F 3.3 mins G 2.6 mins 2.3 mins 3.4 mins Line Balancing Problem

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What is the bottleneck? 4.1 minutes What is the maximum production per hour? 60/4.1 = units/hour What is efficiency and balance delay? Efficiency = 20/(7*4.1) = 69.69% Balance Delay = = 30.31% How to minimize work stations? Should we use 4 or 5 work stations?

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4 Work Stations A B C 4.1 mins D 1.6 mins E 2.7 mins F 3.3 mins G 2.6 mins 2.3 mins 3.4 mins 5.7 mins 6 mins 2.6 mins Efficiency = 20/(4*6) = 20/24 = 83.3% Balance delay = = 16.7% Maximum production/hour = 60/6 = 10 units/hour

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5 Work Stations A B C 4.1 mins D 1.6 mins E 2.7 mins F 3.3 mins G 2.6 mins 2.3 mins 3.4 mins 5.7 mins 4.9 mins 2.7 mins 2.6 mins Efficiency = 20/(5*5.7) = 20/28.5 = 70.18% Balance delay = = 29.82% Maximum production/hour = 60/5.7 = units/hour 4.1 mins

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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 = units/hour 7 Work Stations Efficiency = 69.69% Balance delay = 30.31% Maximum production/hour = units/hour

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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

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Inventory Ratios Inventory Turnover (IT): # of times you turn your inventory annually Inventory Days’ Supply (IDS): how many days inventory you keep

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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

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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

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Dell’s Financial data Revenue$35.40 billions Cost of goods sold$29.10 billions Average Inventory Value$0.306 billions Average Accounts Receivable$2.586 billions Average Accounts Payable$5.989 billions

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Dell’s Example Dell’s Inventory Turnover Dell’s Inventory Days’ Supply

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Dell’s Example Dell’s Accounts Receivable Turnover Dell’s Accounts Receivable Days’ Supply

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Dell’s Example Dell’s Accounts Payable Turnover Dell’s Accounts Payable Days’ Supply

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Dell’s Example Dell’s Cash-to-Cash Conversion Cycle = IDS + ARDS – APDS = 3.84 days days – days = days The negative value means that Dell receives customers’ payments (accounts receivable) days, on average, before Dell has to pay its suppliers (accounts payable). This means that Dell’s value chain is a self- funding cash model.

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Dell’s Negative Cash-to-Cash Conversion Cycle

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Breakeven Analysis (Make/Buy Decision) Total Cost of Outsourcing: Total Cost of Insourcing: Indifference Point:

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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?

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The Bagel Shop Problem Indifference Point Calculation:

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The Bagel Shop Problem Make vs Buy Decision at 80,000 bagels Outsource (Buy) In House (Make) $2,000+($.5*80,000) $20,000+($.2*80,000) = $42,000 = $36,000 Make vs Buy Decision at 50,000 bagels Outsource (Buy) In House (Make) $2,000+($.5*50,000) $20,000+($.2*50,000) = $27,000 = $30,000 If the demand is lower than the indifference point, outsourcing is a cheaper alternative, and vice versa.

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That’s all, folks! Good Luck!

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