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1 INVENTORY MANAGEMENT Chapter 13 MIS 373: Basic Operations Management Additional content from L. Beril Toktay

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LEARNING OBJECTIVES After this lecture, students will be able to 1.Define the term inventory 2.List the different types of inventory 3.Describe the main functions of inventory 4.Discuss the main requirements for effective inventory management 5.Describe the A-B-C approach and explain how it is useful 6.Describe the basic EOQ model and its assumptions and solve typical problems. 7.Describe reorder point models and solve typical problems. 8.Describe situations in which the fixed-order interval model is appropriate, and solve typical problems. 9.Describe service level and risk of stockout and use Z table to identify the z value for a service level or a risk of stockout MIS 373: Basic Operations Management2

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INVENTORY MANAGEMENT AT COX HARDWARE From the video, what are the elements relevant to inventory management?

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INVENTORY An inventory is a stock or store of goods. Inventories are a vital part of business: necessary for operations 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 But Costly May have limited shelf-life Carrier may have limited space MIS 373: Basic Operations Management4

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TYPES OF INVENTORY Raw materials and purchased parts Work-in-process (WIP) Finished goods inventories or merchandise Tools and supplies Maintenance and repairs (MRO) inventory Goods-in-transit to warehouses or customers (pipeline inventory) MIS 373: Basic Operations Management5

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COSTS OF INVENTORY Physical holding costs: out of pocket expenses for storing inventory (insurance, security, warehouse rental, cooling) All costs that may be entailed before you sell it (obsolescence, spoilage, rework...) Opportunity cost of inventory: foregone return on the funds invested. MIS 373: Basic Operations Management6

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With all these costs, why most companies still like to hold inventories?

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INVENTORY FUNCTIONS Inventories serve a number of functions such as: 1.To meet anticipated customer demand 2.To smooth production requirements Firms that experience seasonal patterns in demand often build up inventories during preseason periods to meet overly high requirements during seasonal periods. 3.To decouple operations Buffers between operations 4.To protect against stockouts Delayed deliveries and unexpected increases in demand increase the risk of shortages. MIS 373: Basic Operations Management8

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INVENTORY FUNCTIONS Inventories serve a number of functions such as: 5.To take advantage of order cycles It is usually economical to produce in large rather than small quantities. The excess output must be stored for later use. 6.To hedge against price increases Occasionally a firm will suspect that a substantial price increase is about to occur and purchase larger-than-normal amounts to beat the increase 7.To permit operations The fact that production operations take a certain amount of time (i.e., they are not instantaneous) means that there will generally be some work-in-process inventory. 8.To take advantage of quantity discounts Suppliers may give discounts on large orders. MIS 373: Basic Operations Management9

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OBJECTIVES OF INVENTORY CONTROL Inventory management has two main concerns: 1.Level of customer service Having the right goods available in the right quantity in the right place at the right time 2.Costs of ordering and carrying inventories The overall objective of inventory management is to achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds MIS 373: Basic Operations Management10

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MEASURES OF PERFORMANCE Measures of performance: Customer satisfaction Number and quantity of backorders Customer complaints Inventory turnover = a ratio of during a period MIS 373: Basic Operations Management (average) cost of goods sold (average) inventory investment 11

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INVENTORY MANAGEMENT Management has two basic functions concerning inventory: 1.Establish a system for tracking items in inventory 2.Make decisions about When to order How much to order MIS 373: Basic Operations Management12

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EFFECTIVE INVENTORY MANAGEMENT Requires: 1.A system keep track of inventory 2.A reliable forecast of demand 3.Knowledge of lead time and lead time variability 4.Reasonable estimates of holding costs ordering costs shortage costs 5.A classification system for inventory items MIS 373: Basic Operations Management13

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INVENTORY COUNTING SYSTEMS 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 Point-of-sale (POS) systems A system that electronically records actual sales Radio Frequency Identification (RFID) MIS 373: Basic Operations Management14

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ONE-BIND & TWO-BIN SYSTEMS One-Bin SystemTwo-Bin System MIS 373: Basic Operations Management15 Bin A Bin B

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INVENTORY COSTS 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 Interest, insurance, taxes (in some states), depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, workers, equipment, security). Ordering costs Costs of ordering and receiving inventory determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage. Shortage costs Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit MIS 373: Basic Operations Management16

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ABC CLASSIFICATION SYSTEM A-B-C approach Classifying inventory according to some measure of importance, and allocating control efforts accordingly A items (very important) 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value B items (moderately important) C items (least important) 50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value MIS 373: Basic Operations Management17

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ABC CLASSIFICATION How to classify? 1.For each item, multiply annual volume by unit price to get the annual dollar value. 2.Arrange annual values in descending order. 3.A items: the few with the highest annual dollar value C items: the most with the lowest dollar value. B items: those in between MIS 373: Basic Operations Management #Annual demand Unit price Annual value Class% of items % of value 81,0004,0004,000,000A 5.352.7 32,4005001,200,000B 31.440.8 61,000 1,000,000B 12,500360900,000B 41,500100150,000C 63.36.5 10500200100,000C 98,0001080,000C 21,0007070,000C 57007049,000C 720021042,000C 18,8007,591,000100 18

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ABC CLASSIFICATION: CYCLE COUNTING Cycle counting A physical count of items in inventory Cycle counting management How much accuracy is needed? A items: ± 0.2 percent B items: ± 1 percent C items: ± 5 percent When should cycle counting be performed? Who should do it? MIS 373: Basic Operations Management19

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HOW MUCH TO ORDER? ECONOMIC ORDER QUANTITY MODELS Economic Order Quantity (EOQ) models: identify the optimal order quantity by minimizing total annual costs that vary with order size and frequency 1.The basic Economic Order Quantity model (EOQ) 2.The Quantity Discount model 3.The Economic Production Quantity model (EPQ) 4.Reorder Point Ordering (uncertainty, when to order) 5.Fixed-Order-Interval model 6.Single Period model (perishable items) MIS 373: Basic Operations Management20

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BASIC EOQ MODEL The basic EOQ model: used to find a fixed order quantity that will minimize total annual inventory costs continuous monitoring system Assumptions: 1.Only one product is involved 2.Annual demand requirements are known 3.Demand is even throughout the year 4.Lead time does not vary 5.Each order is received in a single delivery 6.There are no quantity discounts MIS 373: Basic Operations Management21

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THE INVENTORY CYCLE MIS 373: Basic Operations Management Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time 22

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TOTAL ANNUAL COST Total Cost = Annual Holding Cost + Annual Ordering Cost (TC) where Q = order quantity in units H = holding (carrying) cost per unit, usually per year D = demand, usually in units per year S = ordering cost per order MIS 373: Basic Operations Management = Q H+ D S 2Q Number of orders Average number of units in inventory 23

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GOAL: TOTAL COST MINIMIZATION The Total-Cost Curve is U-Shaped There is a tradeoff between holding costs and ordering costs MIS 373: Basic Operations Management Order Quantity (Q) Ordering Costs Q* Annual Cost ( optimal order quantity) Holding Costs 24

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DERIVING EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal. MIS 373: Basic Operations Management25

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EXAMPLE: DERIVING EOQ Tire distributer D (Demand)=9,600 tires per year H (Holding cost)=$16 per unit per year S (Ordering cost) = $75 per order MIS 373: Basic Operations Management26

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EXAMPLE: DERIVING EOQ D (Demand)=9,600 tires per year H (Holding cost)=$16 per unit per year S (Ordering cost) = $75 per order Q*=300 tires TC min = 4,800 MIS 373: Basic Operations Management27 Let’s verify whether the Q* indeed gives the lowest cost.

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WHEN TO REORDER If delivery is not instantaneous, but there is a lead time: When to order? MIS 373: Basic Operations Management28 Receive order Time Inventory Order Quantity Q Lead Time Place order

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WHEN TO REORDER EOQ answers the “how much” question The reorder-point (ROP) tells “when” to order Reorder-Point When the quantity on hand of an item drops to this amount (quantity- trigger), the item is reordered. Determinants of the Reorder-Point 1.The rate of demand 2.The lead time 3.The extent of demand and/or lead time variability 4.The degree of stockout risk acceptable to management MIS 373: Basic Operations Management29

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REORDER-POINT ROP = (Demand per day) * (Lead time for a new order in days) = d * L where d = (Demand per year) / (Number of working days in a year) Example: Demand = 12,000 iPads per year 300 working day year Lead time for orders is 3 working days MIS 373: Basic Operations Management In other words, the manager should place the order when only 120 units left in the inventory. d = 12,000 / 300 = 40 units ROP = d * L = 40 units per day * 3 days of leading time = 120 units 30

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THE INVENTORY CYCLE MIS 373: Basic Operations Management Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time 31 ROP = LxD D: demand per period L: Lead time in periods Q: When shall we order? A: When inventory = ROP Q: How much shall we order? A: Q = EOQ

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EXERCISE: EOQ & ROP Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size? (Assuming that the lead time to receive cars is 10 days and that there are 365 working days in a year) ROP = ( Demand per day ) * ( Lead time for a new order in days ) = d * L where d = (Demand per year) / (Number of working days in a year) EOQ = Recall:

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EXERCISE: EOQ & ROP Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size? Since d is given in years, first convert: 5000/365 =13.7 cars per working day So, ROP = 13.7 * 10 = 137 So, when the number of cars on the lot reaches 137, order 548 more cars.

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BUT DEMAND IS RARELY PREDICTABLE! MIS 373: Basic Operations Management34 Time Inventory Level Order Quantity Demand??? Receive order Place order Lead Time

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BUT DEMAND IS RARELY PREDICTABLE! MIS 373: Basic Operations Management35 Time Inventory Level Order Quantity Receive order Place order Lead Time Inventory at time of receipt ROP Lead Time Demand When Actual Demand < Expected Demand

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BUT DEMAND IS RARELY PREDICTABLE! MIS 373: Basic Operations Management36 Time Inventory Level Order Quantity Receive order Place order Lead Time ROP When Actual Demand > Expected Demand Unfilled demand Stockout Point

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BUT DEMAND IS RARELY PREDICTABLE! MIS 373: Basic Operations Management37 Time Inventory Level Order Quantity ROP = Expected Demand Average If ROP = expected demand, inventory left 50% of the time, stock outs 50% of the time. Uncertain Demand

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SAFETY STOCK MIS 373: Basic Operations Management38 Time Inventory Level Order Quantity Expected Lead-time Demand To reduce stockouts we add safety stock Receive order Place order Lead Time Order Quantity Q = EOQ ROP = Safety Stock + Expected LT Demand Expected LT Demand Safety Stock

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HOW MUCH SAFETY STOCK? The amount of safety stock that is appropriate for a given situation depends upon: 1.The average demand rate and average lead time 2.Demand and lead time variability 3.The desired service level Service level = probability of NOT stocking out Reorder point (ROP) = Expected demand during lead time + z*σ dLT Where z = number of standard deviations σ dLT = the standard deviation of lead time demand MIS 373: Basic Operations Management39

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REORDER POINT The ROP based on a normal distribution of lead time demand MIS 373: Basic Operations Management40 Safety Stock Risk of stockout ROP Quantity Expected demand Service level (probability of not stockout) Z scale Z 0

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Z TABLE http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf Other variations of Z table http://2.bp.blogspot.com/- afjxDroAfuY/UNIjs9kL_YI/AAAAAAAAASY/3gBDkp7r_H8/s1600/normTab.jpeghttp://2.bp.blogspot.com/- afjxDroAfuY/UNIjs9kL_YI/AAAAAAAAASY/3gBDkp7r_H8/s1600/normTab.jpeg https://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/file s/lesson17/TopOfNormalBTable.gifhttps://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/file s/lesson17/TopOfNormalBTable.gif How to use Z table: 1.Decide the desired service level 2.Look up the smallest number in the Z table that is greater than the service level 3.Use the row of the number to identify the first two digits of the z 4.Use the column of the number to identify the second decimal point Q1: what is the z for a 99% service level? Q2: what is the z for a 10% risk of stockout?

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FIXED-ORDER-INTERVAL MODEL The fixed-order-interval (FOI) model is used when orders must be placed at fixed time intervals (weekly, twice a month, etc.): The timing of orders is set. The question, then, at each order point, is how much to order. Fixed-interval ordering systems are widely used by retail businesses. If demand is variable, the order size will tend to vary from cycle to cycle. This is quite different from an EOQ/ROP approach in which the order size generally remains fixed from cycle to cycle, while the length of the cycle varies. MIS 373: Basic Operations Management42

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FIXED-ORDER-INTERVAL MODEL Reasons for Using the Fixed-Order-Interval Model A supplier's policy might encourage orders at fixed intervals. Grouping orders for items from the same supplier can produce savings in shipping costs. Some situations do not readily lend themselves to continuous monitoring of inventory levels. Many retail operations (e.g., drugstores, small grocery stores) fall into this category. The alternative for them is to use fixed-interval ordering, which requires only periodic checks of inventory levels. MIS 373: Basic Operations Management43

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MIS 373: Basic Operations Management44 fixed-quantity ordering fixed-interval ordering LT: Lead Time OI: Order Interval The same quantity same length Different quantity

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FIXED-ORDER-INTERVAL MODEL Order size in the fixed-interval model is determined by the following computation: MIS 373: Basic Operations Management45 Amount to order Expected demand during protection interval Safety stock Amount on hand at reorder time = + − Q = + − A

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EXAMPLE: FIXED-ORDER- INTERVAL MODEL MIS 373: Basic Operations Management46 Q = + − A = + − 71 = 222 units

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KEY POINTS All businesses carry inventories, which are goods held for future use or potential future use. Inventory represents money that is tied up in goods or materials. Effective inventory decisions depend on having good inventory records, good cost information, and good estimates of demand. The decision of how much inventory to have on hand reflects a trade-off, for example, how much money to tie up in inventory versus having it available for other uses. Factors related to the decision include purchase costs, holding costs, ordering costs, shortage and backlog costs, available space to store the inventory, and the return that can be had from other uses of the money. As with other areas of operations, variations are present and must be taken into account. Uncertainties can be offset to some degree by holding safety stock, although that adds to the cost of holding inventory. MIS 373: Basic Operations Management47

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