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1 Lecture 5 Decision Analysis Chapter 14. 2  Certainty - Environment in which relevant parameters have known values  Risk - Environment in which certain.

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Presentation on theme: "1 Lecture 5 Decision Analysis Chapter 14. 2  Certainty - Environment in which relevant parameters have known values  Risk - Environment in which certain."— Presentation transcript:

1 1 Lecture 5 Decision Analysis Chapter 14

2 2  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 Decision Environments

3 3 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 Decision Making under Uncertainty

4 4 Payoff Table: An Example LowModerateHigh Small facility $10 Medium facility 712 Large facility Possible Future Demand Values represent payoffs (profits)

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

6 6 Maximin Solution

7 7 Minimax Regret Solution

8 8 Decision Making Under Risk - Decision Trees State of nature 1 B Payoff 1 State of nature 2 Payoff 2 Payoff 3 2 Choose A’ 1 Choose A’ 2 Payoff 6 State of nature 2 2 Payoff 4 Payoff 5 Choose A’ 3 Choose A’ 4 State of nature 1 Choose A’ Choose A’ 2 1 Decision Point Chance Event

9 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 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. s 1 = 80 s 2 = 100 s 3 = 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 11 Decision Tree d1d1d1d1 d2d2d2d2 d3d3d3d3 s1s1s1s1 s1s1s1s1 s1s1s1s1 s2s2s2s2 s3s3s3s3 s2s2s2s2 s2s2s2s2 s3s3s3s3 s3s3s3s3 Payoffs 10,000 15,000 14,000 8,000 18,000 12,000 6,000 16,000 21,

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

13 13 Lecture 5 Inventory Management Chapter 11

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

15 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 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 17  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 Key Inventory Terms

18 18  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 Inventory Classification Systems ABC Analysis

19 19 Item Stock Number Percent of Number of Items Stocked Annual Volume (units)xUnit Cost= Annual Dollar Volume Percent of Annual Dollar VolumeClass # %1,000$ 90.00$ 90, %72%A # , %A #127601, $ 26, %B # % ,0016.4%23%B #105001, ,5005.4%B ABC Analysis Example # $ 14.17$ 8,5023.7%C #140752, ,200.5%C # % %5%C #013071, %C # %C $232,057

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

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

22 22 Total Cost Annual carrying cost Annual ordering cost Total cost =+ Q 2 ChCh D Q CoCo TC = + Formula (11-4)

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

24 24 Deriving the EOQ & Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Number of orders per year = D/Q 0 Length of order cycle = Q 0 /D Formula (11-5)

25 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 26 Management Scientist Solutions (a) (b) (c) (d) (e) (f) (g)

27 27  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 Assumptions of EOQ Model

28 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 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 of book) (holding + ordering + purchase)

30 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 31 Management Scientist Solutions


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