Inventory Management

1. Inventory Management

2. Independent vs. dependent demand • Independent demand: • Influenced only by market conditions • Independent from operations • Example: finished goods • Dependent demand: • Related to the demand for another item with independent demand • Example: product components, raw materials, labour

3. Independent Demand Dependent Demand A C(2) B(4) D(2) E(1) D(3) F(2) Independent demand is uncertain. Dependent demand is certain.

4. Inventory management • A subsystem of logistics • Inventory: • a stock of materials or other goods to facilitate production or to satisfy customer demand • a stock or store of goods • Main decisions: • Which items should be carried in stock? • How much should be ordered? • When should an order be placed?

5. The need to hold stocks 1 • Buffer between Supply and Demand • To keep down production costs: • To achieve low unit costs, production have to run as long as possible (setting up machines is tend to be costly) • Todecoupleoperations • To take account of variable supply (lead) times: safety stock to cover delivery delays from suppliers • To minimize buying costs associated with raising an order • To accommodate variations (on the short run) in demand (to avoid stock-outs) • To account for seasonal fluctuations: • There are products popular only in peak times • There are goods produced only at a certain time of the year

6. Adaptation o the fluctuation of demand with building up stocks DEMAND Inventory reduction Inventory accumulation CAPACITY

7. The need to hold stocks 2 • To take advantage of quantity discounts (buying in bulk) • To allow for price fluctuations/speculation: to buy large quantities when a good is cheaper • To help production and distribution operations run smoothly: to increase the independence of these activities. • Work-in-progress: facilitating production process by providing semi-finished stocks between different processes • To provide immediate service for customers • To minimize production delays caused by lack of spare parts (for maintenance, breakdowns)

8. Types of Stock-holding/Inventory • raw material, component and packaging stock • in-process stocks (work-in-progress; WIP) • finished products (finished goods inventory; FGI) • pipeline stocks: held in the distribution chain • general stores: contains a mixture of products to support • spare partsforproduction: • Consumables (nuts, bolts, etc.) • Rotables and repairables

9. An alternativetypology of stocks • working stock: reflects the normaldemand • cycle stock: follows the production (or demand) cycles • seasonal stock: goods stockpiled before peaks • safety stock: to cover unexpected fluctuations in demand • speculative stock: built up on expectations

10. Inventory cost • Item cost: the cost of buying or producing inventory items • Ordering cost: does not depend on the number of items ordered. Form typing the order to transportation and receiving costs. • Holding (carrying) cost: • Capital cost: the opportunity cost of tying up capital • Storage cost: space, insurance, tax • Cost of obsolescence, deterioration and loss • Stock-out cost: economic consequences of running out of stock (lost profit and/or goodwill)

11. Evaluatingstocks: the ABC analysis

12. Data Capture • Techniques and error rates (Rushton et al. 2006) • Written entry – 25,000 in 3,000,000 • Keyboard entry – 10,000 in 3,000,000 • Optical character recognition (OCR) – 100 in 3,000,000 • labels that are both machine- and human-readable • for example: license plates • Bar code (code 39) – 1 in 3,000,000 • fast, accurate and fairly robust • reliable and cheap technique • Transponders (radio frequency tags) – 1 in 30,000,000 • a tag (microchip + antenna) affixed to the goods or container • receiver antenna • reader • host station that relays the data to the server • can be passive or active

13. Inventory models

14. Economic Order Quantity (EOQ) • Assumptions of the model: • Demand rate is constant, recurring and known • The lead time (from order placement and order delivery) is constant and known • No stockouts are allowed • Goods are ordered and produced in lots, and the lot is placed into inventory all at one time • Unit item cost is constant, carrying cost is linear function of average inventory level • Ordering cost is independent of the number of items in a lot • The item is a single product (no interaction with other products)

15. The ‘SAW-TOOTH’ Inventory level Order inteval Orderquantity(Q) Average inventory level = Q/2 Time

16. Total cost of inventory (trade-off between ordering frequency and inventory level) cost Total cost Holding cost (H ∙Q/2) Minimumcost Ordering cost (S ∙ D/Q) EOQ lot size

17. Calculating the total cost of inventory • Let… • S be the ordering cost (setup cost) per oder • D be demanded items per planning period • H be the stock holding cost per unit • H=i∙C, whereCis the unit cost of an item,and i is thecarryingrate • P be the market price of theitemdemanded • Q be the ordered quantity per order (= lot) • TC = S ∙ (D/Q) + H ∙ (Q/2) + P ∙ D • (D/Q) is the number of orders per period • (Q/2) is the average inventory level in this model

18. The minimum cost (EOQ) • TC = S ∙ (D/Q) + H ∙ (Q/2) + P ∙ D • бTC/бQ = 0 • 0 = – S ∙ (D/Q 2) + H/2 • H/2 = S ∙ (D/Q 2) • Q 2 = (2 ∙ S ∙ D)/H • EOQ = √ (2 ∙ S ∙ D)/H

19. D = 1000 units per year S = 100 euro per order H = 20 euro per unit per year Find the economic order quantity! (we assume a saw-tooth model) Example EOQ = √ (2 ∙ 1,000units ∙ 100euro)/20euro/unit EOQ = √ 10,000units2 = 100units

20. Reordering (or replenishment) point • Whento start theorderingprocess? • Itdependsonthe… • Stock position: stockon-hand (+ stockon-order) • in a simplesaw-toothmodelit is Q, • insomecases, therecan be an initialstock, that is differentfrom Q. • lead time (L): thetimeintervalfromsettingupordertothe start of usinguptheorderedstock • Averagedemand per day (d) • ROP = d ∙ L

21. Q = 200 tons d = 10 tons per day L = 8 days ROP = ? ROP = 10 ∙ 8 = 80 tons Examples ROP = 16 ∙ 20 = 320 tons • Q = 400 tons • d = 16 tons per day • L =20 days • ROP = ?

22. D = 2,000 tons S = 100 euros per order H = 25 euros per unit per year L = 12 days N = 250 days EOQ = √ (2 ∙ 2,000ts ∙ 100euro)/25euro/ts= 126,49tons d = 2,000ts/250ds = 8 ts/ds ROP = 8 ∙ 12 = 96 tons Example on both EOQ and R Calculatethefollowing: EOQ d ROP

23. The SAW-TOOTHwith safety stock Inventory level Continuous demand Orderquantity b Safety stock or buffer stock Time

24. Buffer (safety) stock b = z ∙ σ where z = safety factor from the (normal) distribution σ = sandard deviation of demand over lead time Let z be 1,65 (95%), and the standard deviation of demand is 200 units/lead time. b = 1,65 ∙ 200units = 330units

26. When to order, when there is a buffer stock? ROP = d * L + b IfQ = 60tons, L = 2 days, b = 10tons, D = 300tons, N = 100 days, thenROP = ? ROP = 2 * 3 + 10 = 16 tons

27. Example • Lead time = 10 days • Average demand over lead time: 300 tons • Standard deviation over lead time: 20 tons • Accepted risk level: 5% • Safety stock = ? Reorder quantity = ? • b = z * σ = 1,65 * 20 = 33 tons • ROP = 300 + 33 = 333 tons

28. Q0 = 600 tons Q = 200 tons d = 10 tons per day L = 8 days b = 33 tons ROP = 8 * 10 + 33 = 113 Examples ROP = 386 • Q0 = Q = 400 tons • d = 16 tons per day • L =20 days • b = 66 tons

29. L L L T T T Alternative models 1 Periodic review system: • Stock level is examined at regular intervals • Size of the order depends on the quantity on stock. it should bring the inventory to a predetermined level Stock on hand Q Q Q time

30. Stock on hand Q Q R L L L Alternative models 2 Fixed-order-quantity system: • A predetermined stock level (reorder point) is given, at which the replenishement order will be placed • The order quantity is constant

31. Some more examples CalculateROP, and EOQ, if… • L = 2 days, b = 12tons, D = 300tons, N = 100 days, S = 50 euro, H = 20 euro/tons/year • L = 12 days, b = 20tons, D = 1300tons, N = 80 days, S = 10 euro, H = 25 euro/ton/year • D = 1000 units, N = 500 days, S = 110 euro, H = 100 euro/unit/year, L = 20 days, b = 50tons