Inventory Management

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

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

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

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

Adaptation to the fluctuation of demand with building up stocks DEMAND CAPACITY Inventory accumulation Inventory reduction

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

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

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

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

Evaluating stocks: the ABC analysis

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

Inventory models

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

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

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

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

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

Example 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) EOQ = √ (2 ∙ 1,000 units ∙ 100 euro )/20 euro/unit EOQ = √ 10,000 units 2 = 100 units

Reordering (or replenishment) point When to start the ordering process? When to start the ordering process? It depends on the… It depends on the… Stock position: stock on-hand (+ stock on-order) Stock position: stock on-hand (+ stock on-order) in a simple saw-tooth model it is Q, in a simple saw-tooth model it is Q, in some cases, there can be an initial stock, that is different from Q. in some cases, there can be an initial stock, that is different from Q. lead time (L): the time interval from setting up order to the start of using up the ordered stock lead time (L): the time interval from setting up order to the start of using up the ordered stock Average demand per day (d) Average demand per day (d) ROP = d ∙ L ROP = d ∙ L

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

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

The SAW-TOOTH with safety stock Inventory level Time Order quantity Continuous demand Safety stock or buffer stock b

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 ∙ 200 units = 330 units

When to order, when there is a buffer stock? ROP = d * L + b If Q = 60tons, L = 2 days, b = 10tons, D = 300tons, N = 100 days, then ROP = ? ROP = 2 * = 16 tons

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

Examples Q 0 = 600 tons Q 0 = 600 tons Q = 200 tons Q = 200 tons d = 10 tons per day d = 10 tons per day L = 8 days L = 8 days b = 33 tons b = 33 tons ROP = 8 * = 113 Q 0 = Q = 400 tons Q 0 = Q = 400 tons d = 16 tons per day d = 16 tons per day L =20 days L =20 days b = 66 tons b = 66 tons ROP = 386

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

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

Some more examples Calculate ROP, and EOQ, if… 1. L = 2 days, b = 12tons, D = 300tons, N = 100 days, S = 50 euro, H = 20 euro/tons/year 2. L = 12 days, b = 20tons, D = 1300tons, N = 80 days, S = 10 euro, H = 25 euro/ton/year 3. D = 1000 units, N = 500 days, S = 110 euro, H = 100 euro/unit/year, L = 20 days, b = 50tons