Statistical Inventory control models

1. Statistical Inventory control models Using Excel

2. Learning objective • After this class the students should be able to: • calculate the appropriate order quantity in the face of uncertain demand using Excel and Cumulative Probability for Newsboy Model simplified.

3. Time management • The expected time to deliver this module is 50 minutes. 30 minutes are reserved for team practices and exercises and 20 minutes for lecture.

4. Introduction • We will study situations in which inventory cannot be carried from period to period similar to Newsboys Model. • perishable products are fruits and vegetables in supermarkets. • products that rapidly become obsolete, such as fashion items, and • those that are bought for specific time periods, such as a promotional sale for a holiday.

5. The Strawberry Ordering Model • Cora, buyer for the Fresh Foods supermarket, is considering the computer specifications for the ordering of strawberries. • Baskets of strawberries are delivered daily: • If she orders too few, there will be many stockouts, sales will be lost, and profit will be low. • If she orders too many, there will be a surplus of strawberries in the evening that will have to be unloaded to canneries at a large discount. • What quantity should Cora order?.

6. Data • Each basket of strawberries sells for $6.00, • the cost is $4.00, and • the salvage value of any surplus sold to a cannery is $3.00. • So, each unit sold brings a profit of $2.00, and each unit salvaged leads to a loss of $1.00.

7. Data • basket of strawberries price: $6.00, • basket of strawberries cost: $4.00, and • the salvage value: $3.00. • Each unit sold brings a profit of $2.00, and each unit salvaged leads to a loss of $1.00.

8. Decision tree Cora knows from past computer records that most daily sales are between 11 and 20 baskets, so she has 10 alternatives for the order quantity: 11, 12, . . . , 20. This decision tree visually represents her choices and possible outcomes.

9. Dealing with uncertainty • Cora do not have enough information to derive a sophisticated probability distribution, then… • She assumes a uniform distribution and sets the probability of each of the ten values equal to 0.1.

10. The model Go to worksheet

11. General Profit function

12. Individual Profits

13. Probability

14. Expected Profits Optimum

16. A mathematical shortcut • The solution method used to help Beth just described enumerates all alternatives and selects the best one. • This "brute force" approach is not practical when there are too many alternatives. • Fortunately, there is a mathematical procedure for finding the optimal order quantity.

17. Notation • P=Unit sales price • C=Unit cost • S=Unit salvage value • CF=Critical factor The critical factor is calculated as • CF= (P- C)/(P- S)

18. Procedure to find Q* • Plot the cumulative probability distribution of demand. • Mark point A on the y-axis at the value of CF. • Move horizontally to point B on the curve. Drop vertically to point C on the x-axis. • The point immediately to the right is Q*.

19. The strawberry problem P= $6.00 C = $4.00 S = $3.00 CF= (6 ‑ 4)/(6 ‑ 3)=2/3 Q* = 17 baskets

20. Exercise • Robin Lowe, a buyer at the Newstorm Department Store, must decide how many high‑fashion hats to order. • The unit sales price P = $125; • The cost C = $60, and • there is no salvage value because Robin does not want any of the high‑fashion item sold by some discount house.

21. Exercise How many hats should she order? Use the method used in this class to solve this problem (20 minutes)

22. Reflections Each team is invited to analyze the following insights, based on the statistical model (10) minutes): • “Cycle stock increase as replenishment frequency decrease” • “Safety stock provide a buffer against stockout”

23. Reference • Operations Management Using Excel .Weida; Richardson and Vazsony, Duxbury, 2001, Chapter 6, p.136-143