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Inventory Management Chapter 13

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Learning Objectives Define the term inventory List the different types of inventory Describe the main functions of inventory Discuss the main requirements for effective 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 the economic production quantity model and solve typical problems Describe the quantity discount model and solve typical problems Describe reorder point models and solve typical problems.

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From the video, what are the elements relevant to inventory management? Inventory Management at Cox Hardware

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Inventory Definition – A stock or store of goods – Dependent demand items Items that are subassemblies or component parts to be used in the production of finished goods. – Independent demand items Items that are ready to be sold or used Inventories are a vital part of business: – necessary for operations – contribute to customer satisfaction

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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)

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Discussion Which of them are dependent demand items and independent demand items? – 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)

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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.

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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.

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Objectives of Inventory Control Inventory management has two main concerns: 1.Satisfactory 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

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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 Management10

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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 Management11

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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 12 Measures of performance

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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 Management13 Inventory Counting Systems

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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 Management14

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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 Management15 ABC Classification System

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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 valueClass% of items % of value 81,0004,0004,000,000A , ,200,000B ,000 1,000,000B 12, ,000B 41, ,000C ,000C 98, ,000C 21, ,000C ,000C ,000C 18,8007,591, ABC Classification System

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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 Management17

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Inventory Models Economic Order Quantity 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)

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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 Management19

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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 20

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Discussion What costs are associated with this model? – (Hint: Recall the 5 types of costs) Purchase cost Holding (carrying) cost Ordering cost Setup cost Shortage cost (Backorder/Backlog cost) Instructor Slides 21

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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 22

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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 23

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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 Management24

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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 Management25

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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 Management26 Let’s verify whether the Q* indeed gives the lowest cost.

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Exercise A local distributor for a national tire company expects to sell approximately 9,600 tires per year. Annual carrying cost is $16 per tire, and ordering cost is $75 per order. The distributor operates 288 working days a year. a. What is the optimal order size? b. How many times per year the store reorder? c. What is the length of an order cycle? d. What is the total annual cost if EOQ is placed? Instructor Slides 27

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Solution a b c d Instructor Slides 28

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Economic Production Quantity (EPQ) The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate) – Assumptions 1.Only one item is involved 2.Annual demand requirements are known 3.Usage rate is constant (= even demand throughout the year) 4.Usage occurs continually, but production occurs periodically (batch production) 5.The production rate is constant 6.Production rate is greater than usage rater 7.Lead time does not vary 8.There are no quantity discounts Instructor Slides 13-29

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EPQ: Inventory Cycle Instructor Slides Q QpQp I max Production and usage Production and usage Production and usage Usage only Usage only Cumulative production Amount on hand Time 13-30

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Discussion What costs are associated with this model? – (Hint: Recall the 5 types of costs) Purchase cost Holding (carrying) cost Ordering cost Setup cost Shortage cost (Backorder/Backlog cost) Our decision making in EPQ model is to determine the size of order (Q) each time. Why? Instructor Slides 31

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EPQ Model Instructor Slides 32

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EPQ – Total Cost Instructor Slides 13-33

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EPQ Instructor Slides Optimal Batch size a.k.a Economic Produciton Quantity (EPQ)

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Exercise A toy manufacturer uses 48,000 wheels per year for toy trucks. The firm produces its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost is $45 per production run. The firm operates 240 days per year. a. What is the optimal batch size? b. What is the total annual cost if EPQ is produced each run? c. What is cycle time (production stage + usage stage)? d. What is the production cycle time? Instructor Slides 35

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Solution a b Instructor Slides 36

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Solution c d Instructor Slides 37

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Quantity Discount Model Quantity discount – Price reduction for larger orders offered to customers to induce them to buy in large quantities Instructor Slides 13-38

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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 Management39 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 Management40

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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 41

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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 42 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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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: Exercise: EOQ & ROP

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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. Exercise: EOQ & ROP

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But demand is rarely predictable! MIS 373: Basic Operations Management45 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 Management46 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 Management47 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 Management48 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 Management49

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Reorder Point The ROP based on a normal distribution of lead time demand MIS 373: Basic Operations Management50 Safety Stock Risk of stockout ROP Quantity Expected demand Service level (probability of not stockout) Z scale Z 0

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