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Lecture

Lecture. 5. MGMT 650 Inventory Models – Chapter 11. Announcements. HW #3 solutions and grades posted in BB HW #3 average = 134.4 (out of 150) Final exam next week Open book, open notes…. Final preparation guide posted in BB Proposed class structure for next week Lecture – 6:00 – 7:50

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Lecture

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  1. Lecture 5 MGMT 650 Inventory Models – Chapter 11

  2. Announcements • HW #3 solutions and grades posted in BB • HW #3 average = 134.4 (out of 150) • Final exam next week • Open book, open notes…. • Final preparation guide posted in BB • Proposed class structure for next week • Lecture – 6:00 – 7:50 • Class evaluations – 7:50 – 8:00 • Break – 8:00 – 8:30 • Final – 8:30 – 9:45

  3. Inventory Management – In-class Example • Number 2 pencils at the campus book-store are sold at a fairly steady rate of 60 per week. It cost the bookstore $12 to initiate an order to its supplier and holding costs are $0.005 per pencil per year. • Determine • The optimal number of pencils for the bookstore to purchase to minimize total annual inventory cost, • Number of orders per year, • The length of each order cycle, • Annual holding cost, • Annual ordering cost, and • Total annual inventory cost. • If the order lead time is 4 months, determine the reorder point. • Illustrate the inventory profile graphically. • What additional cost would the book-store incur if it orders in batches of 1000?

  4. Management Scientist Solutions

  5. Management Scientist Solutions Chapter 11 Problem #4 EOQ (Time between placing 2 consecutive orders - in days)

  6. EOQ with Quantity Discounts • The EOQ with quantity discounts model is applicable where a supplier offers a lower purchase cost when an item is ordered in larger quantities. • This model's variable costs are • annual holding, • Ordering cost, and • purchase costs. • For the optimal order quantity, the annual holding and ordering costs are not necessarily equal.

  7. EOQ with Quantity Discounts • Assumptions • Demand occurs at a constant rate of D items/year. • Ordering Cost is $Co per order. • Holding Cost is $Ch = $CiI per item in inventory per year • note holding cost is based on the cost of the item, Ci • Purchase Cost (C) • $C1 per item if quantity ordered is between 0 and x • $C2 if order quantity is between x1 and x2 , etc. • Lead time is constant

  8. EOQ with Quantity Discounts • Formulae • Optimal order quantity: the procedure for determining Q * will be demonstrated • Number of orders per year: D/Q * • Time between orders (cycle time): Q */D years • Total annual cost: (formula 11.28 of book) (holding + ordering + purchase)

  9. Example – EOQ with Quantity Discount • Walgreens carries Fuji 400X instant print film • The film normally costs Walgreens $3.20 per roll • Walgreens sells each roll for $5.25 • Walgreens's average sales are 21 rolls per week • Walgreens’s annual inventory holding cost rate is 25% • It costs Walgreens $20 to place an order with Fujifilm, USA • Fujifilm offers the following discount scheme to Walgreens • 7% discount on orders of 400 rolls or more • 10% discount for 900 rolls or more, and • 15% discount for 2000 rolls or more • Determine Walgreen’s optimal order quantity

  10. Management Scientist Solutions

  11. Economic Production Quantity (EPQ) • The economic production quantity model is a variant of basic EOQ model • Production done in batches or lots • A replenishment order is not received in one lump sum unlike basic EOQ model • Inventory is replenished gradually as the order is produced • hence requires the production rate to be greater than the demand rate • This model's variable costs are • annual holding cost, and • annual set-up cost (equivalent to ordering cost). • For the optimal lot size, • annual holding and set-up costs are equal.

  12. EPQ = EOQ with Incremental Inventory Replenishment

  13. EPQ Model Assumptions • Demand occurs at a constant rate of D items per year. • Production rate is P items per year (and P > D ). • Set-up cost: $Co per run. • Holding cost: $Ch per item in inventory per year. • Purchase cost per unit is constant (no quantity discount). • Set-up time (lead time) is constant. • Planned shortages are not permitted.

  14. EPQ Model Formulae • Optimal production lot-size (formula 11.16 of book) Q * = 2DCo /[(1-D/P )Ch] • Number of production runs per year: D/Q * • Time between set-ups (cycle time): Q */D years • Total annual cost (formula 11.14 of book) • [(1/2)(1-D/P )Q *Ch] + [DCo/Q *] (holding + ordering)

  15. Example: Non-Slip Tile Co. • Non-Slip Tile Company (NST) has been using production runs of 100,000 tiles, 10 times per year to meet the demand of 1,000,000 tile annually. • The set-up cost is $5,000 per run • Holding cost is estimated at 10% of the manufacturing cost of $1 per tile. • The production capacity of the machine is 500,000 tiles per month. • The factor is open 365 days per year. • Determine • Optimal production lot size • Annual holding and setup costs • Number of setups per year • Loss/profit that NST is incurring annually by using their present production schedule

  16. Management Scientist Solutions • Optimal TC = $28,868 • Current TC = .04167(100,000) + 5,000,000,000/100,000 = $54,167 • LOSS = 54,167 - 28,868 = $25,299

  17. Lecture 5 Forecasting Chapter 16

  18. Forecasting - Topics • Quantitative Approaches to Forecasting • The Components of a Time Series • Measures of Forecast Accuracy • Using Smoothing Methods in Forecasting • Using Trend Projection in Forecasting

  19. Time Series Forecasts • Trend - long-term movement in data • Seasonality - short-term regular variations in data • Cycle – wavelike variations of more than one year’s duration • Irregular variations - caused by unusual circumstances • Random variations - caused by chance

  20. Forecast Variations Irregularvariation Trend Cycles 90 89 88 Seasonal variations

  21. Smoothing Methods • In cases in which the time series is fairly stable and has no significant trend, seasonal, or cyclical effects, one can use smoothing methods to average out the irregular components of the time series. • Four common smoothing methods are: • Moving averages • Weighted moving averages • Exponential smoothing

  22. Example of Moving Average • Sales of gasoline for the past 12 weeks at your local Chevron (in ‘000 gallons). If the dealer uses a 3-period moving average to forecast sales, what is the forecast for Week 13? • Past Sales WeekSalesWeekSales 1 17 7 20 2 21 8 18 3 19 9 22 4 23 10 20 5 18 11 15 6 16 12 22

  23. Management Scientist Solutions MA(3) for period 4 = (17+21+19)/3 = 19 Forecast error for period 3 = Actual – Forecast = 23 – 19 = 4

  24. MA(5) versus MA(3)

  25. Exponential Smoothing • Premise - The most recent observations might have the highest predictive value. • Therefore, we should give more weight to the more recent time periods when forecasting. Ft+1 = Ft + (At - Ft)

  26. Linear Trend Equation Suitable for time series data that exhibit a long term linear trend • Ft = Forecast for period t • t = Specified number of time periods • a = Value of Ft at t = 0 • b = Slope of the line Ft Ft = a + bt a 0 1 2 3 4 5 t

  27. Linear Trend Example Linear trend equation F11 = 20.4 + 1.1(11) = 32.5 Sale increases every time period @ 1.1 units

  28. Actual vs Forecast Linear Trend Example 35 30 25 20 Actual Actual/Forecasted sales 15 Forecast 10 5 0 1 2 3 4 5 6 7 8 9 10 Week F(t) = 20.4 + 1.1t

  29. Measure of Forecast Accuracy • MSE = Mean Squared Error

  30. Forecasting with Trends and Seasonal Components – An Example • Business at Terry's Tie Shop can be viewed as falling into three distinct seasons: (1) Christmas (November-December); (2) Father's Day (late May - mid-June); and (3) all other times. • Average weekly sales ($) during each of the three seasons during the past four years are known and given below. • Determine a forecast for the average weekly sales in year 5 for each of the three seasons. Year Season1234 1 1856 1995 2241 2280 2 2012 2168 2306 2408 3 985 1072 1105 1120

  31. Management Scientist Solutions

  32. Interpretation of Seasonal Indices • Seasonal index for season 2 (Father’s Day) = 1.236 • Means that the sale value of ties during season 2 is 23.6% higher than the average sale value over the year • Seasonal index for season 3 (all other times) = 0.586 • Means that the sale value of ties during season 3 is 41.4% lower than the average sale value over the year

  33. Lecture 5 Decision Analysis Chapter 14

  34. Decision Environments • Certainty - Environment in which relevant parameters have known values • Risk - Environment in which certain future events have probabilistic outcomes • Uncertainty - Environment in which it is impossible to assess the likelihood of various future events

  35. Decision Making under Uncertainty Maximin - Choose the alternative with the best of the worst possible payoffs Maximax - Choose the alternative with the best possible payoff

  36. Payoff Table: An Example Possible Future Demand Values represent payoffs (profits)

  37. Maximax Solution Note: choose the “minimize the payoff” option if the numbers in the previous slide represent costs

  38. Maximin Solution

  39. Minimax Regret Solution

  40. Payoff 1 State of nature 1 Payoff 2 Choose A’1 2 Choose A’ State of nature 2 Payoff 3 Choose A’2 B 1 Payoff 4 Choose A’3 State of nature 1 2 Choose A’2 Payoff 5 Choose A’4 Decision Point Payoff 6 State of nature 2 Chance Event Decision Making Under Risk - Decision Trees

  41. Decision Making with Probabilities • Expected Value Approach • Useful if probabilistic information regarding the states of nature is available • Expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring • Decision yielding the best expected return is chosen.

  42. Example: Burger Prince • Burger Prince Restaurant is considering opening a new restaurant on Main Street. • It has three different models, each with a different seating capacity. • Burger Prince estimates that the average number of customers per hour will be 80, 100, or 120 with a probability of 0.4, 0.2, and 0.4 respectively • The payoff (profit) table for the three models is as follows. s1 = 80 s2 = 100 s3 = 120 Model A $10,000 $15,000 $14,000 Model B $ 8,000 $18,000 $12,000 Model C $ 6,000 $16,000 $21,000 • Choose the alternative that maximizes expected payoff

  43. Decision Tree Payoffs .4 s1 10,000 s2 .2 2 15,000 s3 .4 d1 14,000 .4 s1 8,000 d2 1 .2 3 s2 18,000 s3 d3 .4 12,000 .4 s1 6,000 4 s2 .2 16,000 s3 .4 21,000

  44. Management Scientist Solutions

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