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Show all formulas and work! You can either use word or excel for this assignment

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Show all formulas and work! You can either use word or excel for this assignment. Please choose only one. Do not submit PDF files. PDF files will NOT be graded. 1. Given the following diagram, determine the total system reliability (10 points). A = 0.85 B = 0.92 C = 0.85 D = 0.92 2. Suppose that a design specification for a new metal rode producing machine is 16 cm ± 2.5 cm. Actual process value at either boundary: $18.5 (rode adjustment cost) a. Find the k value (5 points) b. State the Taguchi loss function (5 points) 3. Suppose a tire manufacturer has presented you with the following information: Taguchi loss function: L(x) = 988 (x – T)2 Design specifications for a tire press machine: 6 ± 0.05 a. Calculate the estimated loss if the tire quality characteristic is 6.06 and 50 tires were produced (5 points) b. The tire manufacturer hires an engineer to readjust the tire press machine after which the manufacturer discovers an x-bar of 5.06. What would this tell us regarding the readjustment change? (5 points) 4. Answer the following two short-answer questions: a. What are the implications of the Taguchi loss function? (5 points) b. Why is the ‘voice of the customer’ used within The House of Quality? (5 points) 5. Identify and briefly explain three variables that organizations need to consider when designing their supply chain (10 points). 6. A large shoe manufacturer is trying to decide whether to manufacture or outsource a new type of leather shoe of which they plan on selling 25,000 units. To manufacture the shoe, they estimate their fixed cost will be $200,000 while their variable cost of in-house manufacturing per shoe is estimated to be $3.85. A supplier is willing to supply each shoe for $5.95. a. Using the above information, should the shoe manufacturer manufacture the shoe in-house or outsource? (5 points) b. Calculate the break-even point. What does this calculation tell us? (5 points) 7. Company XYZ has identified 5 different market segments in Montreal for which they can rent out bicycles. They plan on opening one center in the city and are trying to decide on the optimum location. They have identified the coordinates and number of customers for each segment as follows: Segment 1: (4, 12), 1200 customers Segment 2: (16, 19), 500 customers Segment 3: (6, 21), 900 customers Segment 4: (10, 2), 3000 customers Segment 5: (21, 3), 400 customers What will be the optimum or best location for their new center using the center-of-gravity method? (10 points) 8. A rollercoaster at Treasure Island Amusement Park consists of 16 cars, each of which can carry up to three passengers. According to a time study, each run takes 2.5 minutes, and the time to unload and load riders is 3.5 minutes. What is the maximum effective capacity of the system in number of passengers per hour? (10 points) FORMULAS 3308 Value = Perceived Benefits Price (cost) to the customer Productivity = Output Input Productivity Growth = Quantity of Output Quantity of Input = current period productivity-previous period productivity previous period productivity Value of a Loyal Customer VLC = (P)(RF)(CM)(BLC) Where: P = the revenue per unit CM = contribution margin to profit and overhead expressed as a fraction (eg .45; .50, etc) RF = repurchase frequency = number of purchases per year (eg if they buy one every 4 years it is represented as .25) BLC = buyer’s life cycle, computed as 1 divided by the defection rate, expressed as a fraction Moving Average = ∑ Demand in selected time series n where: n = number of periods (data points) in the moving average Single Exponential Smoothing: • Mean Square Error: Σ(At - Ft)² Ft = αAt + (1 – α) Ft or Ft + α(At – Ft) T Mean Absolute Deviation: Σ IAt – FtI T Mean Absolute Percentage Error: Σ[(At – Ft) / At] x 100 T Tracking Signal: Σ(At – Ft) MAD Linear Trend Equation Line Coefficients of the line a, and b can be computed from historical data using the following two equations: Template to use: Time Period(x) Demand (y) x² xy Then calculate: b = n∑xy - ∑x∑y n∑x² - (∑x)² a = ∑y - b∑x where: n = total number of periods n Then apply formula to a and b: Yt = a + bt y = value of the time series FORMULA SHEET Outsourcing Total cost of production: (VC1)Q + FC Total cost of outsourcing: (VC2) Q Break-even Formula for Outsourcing Q = FC VC2 – VC1 Where: VC1 = variable cost per unit if produced in house VC2 = variable cost per unit if outsourced Q = quantity FC = fixed cost Centre of Gravity C = ΣX W /ΣW x i i i Earliest Start Time Rule Earliest Finish Rule ES = Max (EF of all immediate predecessors) Latest Finish Time Rule Latest Start Time Rule LF = Min (LS of all immediate following activities) Slack = LS – ES; or Slack = LF – EF Expected Activity Time Variance of Activity completion time t = (a + 4m + b)/6 a=optimistic m = most likely b = pessimistic Project variance (σ²p) = add up the variances of all the critical path activities Project Standard Deviation Probability of completing project on or before deadline Computing probability for any completion date (σp) = square root of the project variance Little’s Law = depending upon what you are trying to calculate, there are 3 ways to solve for the solution: 1) WIP = R x T 2) R = WIP/T 3) T = WIP/R EF = ES + Activity Time = LS = LF – Activity Time Variance = (b-a) ² /36 where b = pessimistic time and a = optimistic time Z = (due date – expected date of completion)/σp. From this calculation, find the probability in the normal distribution chart. Find the percentage you want to test on the normal distribution chart (Z). Then apply the formula: Due date = Expected date of completion + (Z x σp) 1 Two ways to compute resource utilization (you have to know which one to use!). Also use these formulas for capacity calculations such as numbers required (eg equipment, servers, etc) and target utilization. For target utilization you need to set up your formula as a quadratic equation and solve for “X” based on what you are being asked to solve in the problem. Utilization (U) = Demand Rate / [(Service Rate x Number of Servers)] Utilization (U) = Resources Used / Resources Available Crash cost per unit of time = crash cost – normal cost normal time – crash time System Reliability of an n-component series system System Reliability of an n-component parallel system Taguchi Loss Function = Rs = (p?)(p2)(p3) ...(pn) = Rp = 1 – (1- p?) (1- p2) (1- p3) ... (1-pn) L(x) = k(x – T )2 Where L(x) - Monetary value of the loss associated with deviating from the target T – the target x - Actual value of the dimension k - Constant that translates the deviation into dollars (x-T) – loss associated with deviation 2