Inventory management in operation research

inventory

1. Course Code: BAC506A Course Title: Operations Management Course Leader: Dr. Chandra Sen Mazumdar Email: [email protected]

2. Inventory Management

3. Learning Objectives You should be able to: Define the term inventory , list the major reasons for holding inventories, and list the main requirements for effective inventory management Discuss the nature and importance of service inventories Explain periodic and perpetual review systems Explain the objectives of inventory management Describe the A-B-C approach and explain how it is useful Describe the basic EOQ model and its assumptions and solve typical problems Describe reorder point models

4. Inventory A stock or store of goods Independent demand items Items that are ready to be sold or used Inventory Inventories are a vital part of business: (1) necessary for operations and (2) contribute to customer satisfaction A “typical” firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory

5. Inventory Management Management has two basic functions concerning inventory: Establish a system for tracking items in inventory Make decisions about When to order How much to order

6. Periodic System Physical count of items in inventory made at periodic intervals Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item An order is placed when inventory drops to a predetermined minimum level Two-bin system Two containers of inventory; reorder when the first is empty Inventory Counting Systems

7. Purchase cost The amount paid to buy the inventory 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 Setup costs The costs involved in preparing equipment for a job Analogous to ordering costs Shortage costs Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit Inventory Costs

8. An inventory classification system based on some measure of importance, usually the annual dollar (monetary) value Typically three classes of items are used: A (very important): 10 to 20% of inventory items but 60 to 70% of annual dollar value B (moderately important) C (least important): 50 to 60% of inventory items but only about 10 to 15% of annual dollar value Actual number of categories may vary from organization to organization A-B-C Approach

9. Basic Economic Order Quantity (EOQ) Model Assumptions Only one product is involved. Annual demand requirements are known. Demand is spread evenly throughout the year so that the demand rate is reasonably constant. Lead time is known and constant. Each order is received in a single delivery. There are no quantity discounts.

10. Derivation of EOQ Model Fig 1: Carrying costs are linearly related to order size Fig 2: Ordering costs are inversely and nonlinearly related to order size Fig 3: Total cost curve is U-shaped

11. Derivation of EOQ Model contd. Annual carrying cost = Where, Q = Order quantity in Units H = Holding (carrying) cost per unit per year Annual ordering cost = Where, D = Demand in units per year S = Ordering cost per order Total cost = Annual carrying cost + Annual ordering cost = + Optimal order quantity occurs when, Annual carrying cost = Annual ordering cost Or, =  

12. Example A local distributor for a national tire company expects to sell approximately 9,600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year. a. What is the EOQ? b. How many times per year does the store reorder? c. What is the length of an order cycle? d. What is the total annual cost if the EOQ quantity is ordered? Solution: D = 9600 units H = $16 per unit per year S = $75 = tires No. of orders per year = D/Q = 9600/300 = 32 Length of order cycle = Q /D = (1/32)*288 = 9 days Total Cost (TC) = + = (300/2)*16 + (9600/300)*75 = $4800  

13. When to Reorder Reorder point When the quantity on hand of an item drops to this amount, the item is reordered. Determinants of the reorder point The rate of demand The lead time The extent of demand and/or lead time variability The degree of stockout risk acceptable to management

14. Reorder Point: Under Certainty

15. Demand or lead time uncertainty creates the possibility that demand will be greater than available supply To reduce the likelihood of a stockout, it becomes necessary to carry safety stock Safety stock Stock that is held in excess of expected demand due to variable demand and/or lead time Reorder Point: Under Uncertainty

16. The amount of safety stock that is appropriate for a given situation depends upon: The average demand rate and average lead time Demand and lead time variability The desired service level How Much Safety Stock?

17. Reorder Point: Demand Uncertainty Note: If only demand is variable, then

18. Fixed-order-interval (FOI) model Orders are placed at fixed time intervals Reasons for using the FOI model Supplier’s policy may encourage its use Grouping orders from the same supplier can produce savings in shipping costs Some circumstances do not lend themselves to continuously monitoring inventory position How Much to Order: FOI

19. FOI Model

20. Technology in Inventory Management Real-time data capture RFID tags GPS navigation ERP system https://www.youtube.com/watch?v=BnQG4NGyyAU

21. Behind the Scenes – Amazon Warehouse

22. Operations Strategy Improving inventory processes can offer significant cost reduction and customer satisfaction benefits Areas that may lead to improvement: Record keeping Records and data must be accurate and up-to-date Variation reduction Lead variation Forecast errors Lean operations Supply chain management

23. Summary Discussed need for inventory management and inventory costs The EOQ model and numerical problems related to that Discussed the terms reorder point, safety stock – under demand certainty and uncertainty

24. References Essential Reading Stevenson, William J. (2015) Operations Management, 11th Edition, Mc Graw Hill Education Recommended Reading Kumar, S. A., & Suresh, N. (2008) Operations Management, 2nd edition. New Age International Publishers Magazines and Journals Operations Research/Management Science Today International Journal of Operational Research, Inderscience Publishers Websites https://harvardmagazine.com/tags/quantitative-methods https://sloanreview.mit.edu/

25. Disclaimer All data and content provided in this presentation are taken from the reference books, internet – websites and links, for informational purposes only.