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Lecture

Lecture. 5. Decision Analysis Chapter 14. Decision Environments. Certainty - Environment in which relevant parameters have known values Risk - Environment in which certain future events have probabilistic outcomes

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Lecture

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  1. Lecture 5 Decision Analysis Chapter 14

  2. 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

  3. 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 Minimax Regret- Choose the alternative that has the least of the worst regrets

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

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

  6. Maximin Solution

  7. Minimax Regret Solution

  8. 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

  9. 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.

  10. 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

  11. 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

  12. EVPI = expected payoff under certainty – expected payoff under risk Management Scientist Solutions

  13. Lecture 5 Inventory Management Chapter 11

  14. Types of Inventories • Raw materials & purchased parts • Partially completed goods called work in progress • Finished-goods inventories • (manufacturingfirms) or merchandise (retail stores) • Replacement parts, tools, & supplies • Goods-in-transit to warehouses or customers

  15. Functions of Inventory • To meet anticipated demand • To smooth production requirements • To decouple operations • To protect against stock-outs • To take advantage of order cycles • To help hedge against price increases • To permit operations • To take advantage of quantity discounts

  16. Objective of Inventory Control • To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds • Level of customer service • Costs of ordering and carrying inventory

  17. Key Inventory Terms • Lead time: time interval between ordering and receiving the order • Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year • Ordering costs: costs of ordering and receiving inventory • Shortage costs: costs when demand exceeds supply

  18. Inventory Classification SystemsABC Analysis • Divides inventory into three classes based on annual dollar volume • Class A - high annual dollar volume • Class B - medium annual dollar volume • Class C - low annual dollar volume • Used to establish policies that focus on the few critical parts and not the many trivial ones • No “hard-and-fast” rule to classify into different categories

  19. ABC Analysis Example $232,057

  20. Economic Order Quantity Models • Economic order quantity (EOQ) model • Quantity discount model • Economic production model (EPQ)

  21. The Inventory Cycle Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point Time Place order Receive order Receive order Receive order Place order Lead time

  22. Annual carrying cost Annual ordering cost Total cost = + Q D Co Ch TC = + 2 Q Total Cost Formula (11-4)

  23. Cost Minimization Goal The Total-Cost Curve is U-Shaped Annual Cost Ordering Costs Order Quantity (Q) QO (optimal order quantity)

  24. Deriving the EOQ & Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Formula (11-5) Number of orders per year = D/Q0 Length of order cycle = Q0/D

  25. 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. • Holding costs are $0.005 per pencil per year. • Determine • (a) The optimal number of pencils for the bookstore to purchase to minimize total annual inventory cost, • (b) Number of orders per year, • (c) The length of each order cycle, • (d) Annual holding cost, • (e) Annual ordering cost, and • (f) Total annual inventory cost. • (g) 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?

  26. Management Scientist Solutions (a) (d) (e) (f) (g) (b) (c)

  27. Assumptions of EOQ Model • Only one product is involved • Annual demand requirements known/deterministic • Demand is even throughout the year • Lead time does not vary • Each order is received in a single delivery • There are no quantity discounts

  28. EOQ with Quantity Discounts • EOQ with quantity discounts model • 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

  29. 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)

  30. 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

  31. Management Scientist Solutions

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