MOSS 3300 Operations Management Professor Burjaw Fall/Winter

Learning Objectives: 1.Purposes of inventory 2.Inventory control systems 3.Inventory costs 4.EOQ models 5.Safety stock MOS 3330Inventory Management2 Formula Sheet Formula Sheet

Inventory: A stock of items or materials held to satisfy eventual demandInventory: A stock of items or materials held to satisfy eventual demand –Raw materials, purchased parts and supplies –Work-in-process (partially completed) products –Finished goods –Rework items –Tools, machinery, and equipment –Labour MOS 3330Inventory Management3

Types of inventory based on different purposesTypes of inventory based on different purposes –Anticipation inventory  to meet demand forecast (e.g., seasonality) –Safety stock  buffer to protect against uncertainties –Lot-size inventory  result of batch ordering –Pipeline inventory  in transit –Hedge inventory  to protect against future events (e.g., price increase of raw materials) –Maintenance, Repair and Operating (MRO) inventory  to support general operations and maintenance –Decoupling  work-in-process items waiting for the next step MOS 3330Inventory Management4

Why keep inventory? Why keep inventory? Buffer against expected & unexpected changes Faster customer service Economies of scale (production, purchasing) Not to be dependent on suppliers Why is too much inventory bad? Why is too much inventory bad? Cost (ties up working capital, may deteriorate or get stolen) Need for storage space Need for labour (material handling, transfer) Complacency  General objective: To keep enough inventory to meet customer demand and be cost efficient  Main operational concerns: When to order and how many to order MOS 3330Inventory Management5

Different ways of determining when & how many to orderDifferent ways of determining when & how many to order –Q system  fixed quantity –P system  fixed time period –ABC system MOS 3330Inventory Management6

Q System Reorder a fixed quantity (Q) whenever the inventory falls to or below a reorder point (R) Continuous review system: reviews the inventory each time a withdrawal occurs Time between orders varies P System Reorder after a fixed time period (P) Periodic review system: reviews the inventory periodically Order quantity (Q) varies Q = (Target inventory level) – (Current inventory level) MOS 3330Inventory Management7 Compare in terms of record keeping system, administration cost, responsiveness to demand variability, average inventory level, and ease to combine orders to the same supplier

An inventory classification system in which a small percentage of items (A-level) account for most of the inventory value Level% of units% of dollar value (e.g., annual volume x unit cost) A B3015 C Step 1: Classify products into ABC categories Step 2: Apply a different inventory policy to each category MOS 3330Inventory Management8

A items High priority Tight control with regular review Carefully determined Q, frequent deliveries, continuous review Very accurate and detailed inventory records, update monthly B items Moderate priority Moderate control with regular attention Order quantities or order points reviewed quarterly Batch updating of inventory records MOS 3330Inventory Management9 C items Low priority Simple control Large inventories, visual review Simplified counting, annual review

Ordering (set-up) cost: Fixed cost incurred whenever a replenishment order is placed, regardless of the quantity –Requisition and purchase ordering, transportation and shipping, receiving and storage, inspection, accounting and auditing costs Holding (carrying) cost: Cost to keep one item in inventory for a period of time (usually one year) –$ per unit per period or % of a unit cost/price –Rent, heating, cooling, lighting, security, record keeping costs –Interest on loans, depreciation, obsolescence, spoilage Shortage (stockout) cost: Cost of not being able to meet customer demand –Loss of sales, loss of future sales, loss of production, penalties –Backorder: the order is filled from the next shipment MOS 3330Inventory Management10

Polaris automaker unable to meet customer demands, lowering revenue and profit, after cutting inventory to cope with recession  html html In 2009, automakers offered “cash for clunkers” program, allowing consumers to trade in old vehicles for new more fuel efficient ones, as an incentive to lower inventory  Inventory Management11MOS 3330

For managing anticipatory inventory Mathematical model for determining order quantity and when to reorderAssumptions: Demand is independent, known, and constant Supply is certain and received all at once in a batch Replenishment lead time is known and constant –Lead time: Time between order placed and order received Cost information is fixed and constant No shortages and no back orders MOS 3330Inventory Management12

EOQ Inventory Model: MOS 3330 Inventory Management 13 Average daily demand (d) 0Time Leadtime(L) OrderPlacedOrderPlacedOrderReceivedOrderReceived InventoryLevel Reorder point (R) Order qty (Q) Leadtime(L) Annual demand (D) R = d L Order cycle time = (No. of days in a year) / (No. of orders) Order cycle time = (No. of days in a year) / (No. of orders) FormulaSheet

Total annual inventory management cost (TC) = (Annual ordering cost) + (Annual holding cost) = (Ordering cost)  (No. of orders) + (Holding cost)  (Average inventory)  TC = C O (D/Q) + C H (Q/2) EOQ objective: to minimize TC  EOQ = (2DC O / C H ) ½ MOS 3330 Inventory Management 14 EOQ Total Cost Ordering Cost = C o D/Q Order Quantity (Q) Annual cost ($) Minimum total cost Holding Cost = C H Q/2 Formula Sheet Formula Sheet

Example 1 Example 1: Western Jeans Company (WJC) purchases denim from Huron Textile Mills. WJC uses 36,000 yards of denim per year. The cost of ordering denim from Huron is $500 per order. It costs Western $0.40 per yard annually to hold a yard of denim in inventory. a) What is the total inventory cost if each order is for 6000 yards? b) What is the total inventory cost if denim is ordered every month? c) Calculate the optimal order quantity and the total annual inventory cost. MOS 3330Inventory Management15

Quantity discount:Quantity discount: A price discount on an item if a predetermined number of units is ordered Total annual inventory management cost (TC) = (Ordering cost) + (Holding cost) + (Purchase cost)  TC = C O (D/Q) + C H (Q/2) + P·D P = per unit purchase price D = annual demand MOS 3330Inventory Management16 Formula Sheet

1.Calculate the basic EOQ. 2.If EOQ qualifies for the lowest purchase price, then EOQ is the optimal order quantity. 3.If EOQ does not qualify for the lowest price, then calculate TC for EOQ and for the lowest quantity of each price category –Why only consider the lowest quantity from each category? –Can you ignore any of the price categories? 4.Choose the order quantity with the lowest total inventory cost. –Does the lowest purchase price always lead to the lowest TC? MOS 3330Inventory Management17 ATTENTION

Example 2 Example 2: Based on Example 1 scenario, the textile company has offered the Western Jeans Company the following volume discount. The price without discount is $2.50 per yard. What is the optimal order quantity? Order SizeDiscount Less than 50000% % % and up10% MOS 3330Inventory Management18

An order is received gradually, not all at once Common when inventory user is also the producer Inventory is depleted while it is being replenished MOS 3330Inventory Management19 Q-(Q/p)d Inventory level (1-d/p) Q2Q2 Time Begin order receipt End order receipt Maximum inventory level Average inventory level Demand rate (d) Replenishment rate (p-d) Production & usage Usage only

Total annual inventory cost (TC)Total annual inventory cost (TC) = (Annual set-up cost) + (Annual holding cost) = (Set-up cost)  (No. of production runs) + (Holding cost)  (Avg.inventory)  TC = C O (D/Q) + C H (Q/2)(1 – d/p) d = daily demand rate p = daily production rate, where p > d Optimal production quantity: EPQ = [2DC O / C H (1 – d/p)] ½ Length of production run = Q/p Max. inventory level = Q(1 – d/p) MOS 3330Inventory Management20 Formula Sheet Formula Sheet Formula Sheet Formula Sheet

Example 3: Example 3: Western Jeans Company (WJC) produces and sells its own jeans. The cost of setting up the production process to make jeans is $150. The annual holding cost is $0.75 per pair, and the annual demand is 10,000 pairs. The manufacturing facility operates 311 days a year and produces 150 pairs of jeans per day. a) What is the length of production run? b) What is the maximum inventory level? MOS 3330Inventory Management21

Safety stockSafety stock: Buffer added to on-hand inventory to protect from demand/supply variability during the lead time EOQ model considers only anticipatory inventory and says nothing about safety stock General objective: to minimize shortage costs –Method 1: % of annual demand as safety stock  Simplistic but common –Method 2: Satisfy a specified service level –Service level: The probability that the inventory available during lead time will meet demand –Service level method includes demand behaviour and probability of stockout in consideration MOS 3330Inventory Management22

MOS 3330 Inventory Management 23 Reorder point (R) Q 0 Lead time (L) Lead Time SafetyStock SafetyStock Averagedemand during LT Reorder point (R) Between receipt & order (P)

Daily demand during the lead time is independent, uncertain, and can be described by a normal distribution Lead time is constant Reorder point = (Average demand during lead time) + (Safety stock) R = d L + z  d (L) ½  R = d L + z  d (L) ½ d = average daily demand L = lead time z = number of standard deviations corresponding to the service level  d = standard deviation of daily demand MOS 3330Inventory Management24 Standard deviation of daily demand during lead time Service level z % % % % % % Formula Sheet Formula Sheet

Example 4: Example 4: A large hospital believes that demand for acetaminophen is normally distributed with a mean of 2000 tablets/day and a standard deviation of 250 tablets/day. The hospital wishes no more than a 5% chance of stockout during an inventory cycle. Assuming that the lead time is 4 days, how much safety stock should be held? What is the reorder point? MOS 3330Inventory Management25

Time between receipt and order is fixed (P) Daily demand: independent, uncertain, and normally distributed during the lead time Lead time is constant (L) Order quantity, Q = (Target inventory level) – (Current inventory position) = [(Avg. demand during P&L) + (Safety stock)] – (Inv. in stock)  Q = d (P + L) + z  d (P + L) ½ – I MOS 3330Inventory Management26 Formula Sheet