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Unformatted text preview: OPIM 632 Final Exam Study Guide Eugene Belashchenko Inc. Using Historical A/F Rations to choose a normal distribution for demand forecast 1. Find the usually given initial forecast 2. Evaluate the A/F ratios of historical data ( A/F ratio = Actual Demand/Forecast) 3. Solve equation for Actual Demand , and set the mean of normal distribution to ( Expected actual demand = Expected A/F ratio * forecast) 4. Set the SD of normal distribution to: Standard Deviation of actual demand = SD of A/F ratios * Forecast. NEWSVENDOR MODEL – CRITICAL RATION (SESSION 1) C o = Overage Cost = Cost – Salvage Value = c – v- Occurs if you over-order - The consequence of ordering one more unit you would have if you knew actual demand. o So, this is the profit you have enjoyed if you didn’t order that extra unit that is sitting in the warehouse. C u = underage cost = Price – Cost = p – c - Occurs if you underorder- If there is a penalty for ordering after a time, then p = the penalty price and c = the previous cost of ordering - The concequence of ordering one fewer unit than the actual demand. The increase in profit you would have enjoyed have you ordered one more unit that would have been sold. CRITICAL RATIO – Profit Maximizing Order Quantity: Using Empirical Distribution Function 1. Find the inputs p (price), c (cost), v (salvage cost), C u , C o 2. Evaluate F(Q) = C u / (C o + C u ) 3. Look up the resulting F(Q) in the empirical distribution function table (if falls between two values, round up ) 4. Convert the chosen A/F ratio into order quantity Q = Forecast * A/F Using Normal Distribution Function 1. Find the inputs p (price), c (cost), v (salvage cost), C u , C o 2. Determine Critical Ratio F(Q) = C u / (C o + C u ) 3. NORMAL DIST: Find mean = μ and SD = σ (both usually given) 1. Look up the critical ratio in the Standard Normal Distribution Function (round up) 2. Convert z-statistic into order quantity: Q = u + z*σ i. If using options contracting C o = just like before C u = New Cost – total cost of options (2004-15) 4. POISSON: 1. Look up the F(Q) and mean Poisson in the Poisson Distribution Function Table to determine S 2. (If inventory is on hand, then subtract it from the total) NEWSVENDOR MODEL PERFORMANCE MEASURES: (SESSION 2) Expected Lost Sales: The average number of units demand exceeds order Q o Use this function when asked expected payment planning (HW1 Problem 4) 1. Normalize the order Q to find z-stat: z = (Q-u)/σ 2. Look up in the Std Normal Loss Function Table the expected lost sales for the z-stat: L(z) = X 3. Evaluate the lost sales for actual Normal distribution: Expected Lost Sales = σ*L(z) 4. If asked for dollar amount expected lost sales: multiply the Expected Lost Sales by cost/unit o Then you can solve for total expenditure by adding u + dollar amount for expected lost sales Expected Sales: (The average number of units sold) = u – Expected Lost Sales- Note: Expected Sales is always less than expected demand (u)...
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- Fall '11
- Normal Distribution, Eugene Belashchenko Inc