Presentation on theme: "Quantitative Review II"— Presentation transcript:
1Quantitative Review II ISQS Introduction to Production and Operations Management Spring 2012Quantitative Review II
2Taguchi Loss Function (p.199) Design the product or service so that it will not be sensitive to variations during the manufacturing or delivery processFor example, design a manufactured good with a smaller design tolerance = better quality
3Taguchi Loss Function where L(x) = the monetary value of the loss associated with deviating from thetarget limit “T”k = the constant that translates thedeviation into dollarsx = the actual value of the dimensionT = target limits
4A quality characteristic has a specification (in inches) of 0. 200 0 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).
5A quality engineer has a manufacturing specification (in cm) of 0 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.
6Reliability Management (pp.651-654) Series product componentsParallel product components
7The manufacturing of compact disks requires four sequential steps 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?
8The system reliability for a two-component parallel system is 0. 99968 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 = p2p2 = 0.968
10Given 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.ADCBRaRb = 1 - ( )( ) =RcRd = 1 - ( )( ) =RabRcd = (0.9952)(0.9979) =
11Kanban (pp.632-634) where: K = the number of Kanban cards d = the average production rate OR demand of productp = the processing timew = the waiting time of Kanban cardsα = safety stock as a %, usually ranging from 0 to 1C = the capacity of a standard container
12Computing 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
14Location Analysis Methods Center-of-Gravity Method (pp ):where dix = x-coordinate of location idiy = y-coordinate of location iQi = Quantity of goods moved to or from location i
15Center-of-Gravity Method Where would be the best place to put the warehouse?LocationXcoordinateYNumber of Containers Shipped per WeekChicago301202,000Pittsburgh901101,000New York130Atlanta6040
16Location Analysis Methods Load Distance Model:Find load distance score by: Calculate the rectilinear distance and multiply by the number of loads
17Load Distance Score for AB = 45*4 = 180 Load Distance ModelCalculate Rectilinear DistanceIdentify Loads, i.e., 4 loads from A to BLoad Distance Score for AB = 45*4 = 180
18TT 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?LocationXcoordinateYLocation A9242Location B8040Location C9035Warehouse D45Warehouse E
19Load Distance Score Warehouse D Distance Loads Score LocationXcoordinateYLocation A9242Location B8040Location C9035Warehouse D45Warehouse ELoad Distance ScoreWarehouse DDistance Loads ScoreLocation A =Location B 10+5=Location C 0+10=5500Warehouse ELocation A =Location B 10+0=Location C 0+5=3300
20Designing Process Layouts (Chapter 9) Step 1: Gather informationSpace needed, space available, importance of proximity between various unitsStep 2: Develop alternative block plansUsing trial-and-error or decision support toolsStep 3: Develop a detailed layoutConsider exact sizes and shapes of departments and work centers including aisles and stairwaysTools like drawing, 3-D models, and CAD software are available to facilitate this process.
21Process Layout (Step 1: Gather information) Recovery First Sports Medicine Clinic Layout(total space 3750 sq.ft.)A400 sq.ft.B300 sq.ft.CD800 sq.ft.E900 sq.ft.F1050 sq.ft.
22Process Layout (Step 2: Develop a block layout) Current ProposedA400 sq.ft.B300 sq.ft.CD800 sq.ft.E900 sq.ft.F1050 sq.ft.A400 sq.ft.D800 sq.ft.C300 sq.ft.E900 sq.ft.BF1050 sq.ft.Proposed layout would require less walking.
23Load Distance Problem A B C D E F 10 30 15 20 5 25 What is the load distance for this layout?Trips between departmentsBADCEFDept.ABCDEF10301520525
24Load Distance Problem A B C D E F 10 30 15 20 5 25 Depts. Trips 1520525Depts.TripsDistanceScoreAB101AC30260ADAF20BDBE15BF345CDCECF5EF25345
25Assembly Line Balancing (Chapter 9) Step 1: Identify task & immediate predecessorsStep 2: Calculate the cycle timeStep 3: Determine the output rateStep 4: Compute the theoretical minimum number of workstationsStep 5: Assign tasks to workstations (balance the line)Step 6: Compute efficiency, idle time & balance delay
26Assembly Line Balancing (Step 1: Identify tasks & immediate predecessors)
27Layout CalculationStep 2: Determine cycle time (The amount of time each workstation is allowed to complete its tasks.)Cycle time = Station A (50 seconds) -- the bottleneckStep 3: Determine output rateStep 4: Compute the theoretical minimum number of workstations (number of station needed to achieve 100% efficiency)
28Assembly Line Balancing (Step 5: Balance the line) 3 Work Stations (A,B), (C,D,G), (E,F,H,I)55 sec55 sec55 sec
29Assembly Line Balancing (Step 6: Compute efficiency, idle time & balance delay) Balance Delay = 1 – Assembly Line Efficiency
30Line 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?ABC4.1 minsD1.6 minsE2.7 minsF3.3 minsG2.6 mins2.3 mins3.4 mins
31Line Balancing Problem What is the bottleneck?4.1 minutesWhat is the maximum production per hour?60/4.1 = units/hourWhat 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?
43Dell’s Example Dell’s Cash-to-Cash Conversion Cycle = IDS + ARDS – APDS= 3.84 days days – days= daysThe 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.
45Breakeven Analysis (Make/Buy Decision) Total Cost of Outsourcing:Total Cost of Insourcing:Indifference Point:
46The 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?
47The Bagel Shop ProblemIndifference Point Calculation:
48The 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, = $36,000Make vs Buy Decision at 50,000 bagels$2,000+($.5*50,000) $20,000+($.2*50,000)= $27, = $30,000If the demand is lower than the indifference point, outsourcing is a cheaper alternative, and vice versa.