Inventory Management Chapter 13 Learning Objectives Define the

Inventory Management Chapter 13

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.

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

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

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)

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)

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.

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.

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

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 Management 10

Effective Inventory Management • Requires: 1. 2. 3. 4. A system keep track of inventory A reliable forecast of demand Knowledge of lead time and lead time variability Reasonable estimates of • holding costs • ordering costs • shortage costs 5. A classification system for inventory items MIS 373: Basic Operations Management 11

Measures of performance • Measures of performance: – Customer satisfaction • Number and quantity of backorders • Customer complaints – Inventory turnover = a ratio of (average) cost of goods sold (average) inventory investment during a period MIS 373: Basic Operations Management 12

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 Management 13

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 Management 14

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 Management 15

ABC Classification System • How to classify? # Annual demand Unit price 8 1, 000 4, 000 A 3 2, 400 500 1, 200, 000 B 6 1, 000 B 1 2, 500 360 900, 000 B 4 1, 500 150, 000 C 10 500 200 100, 000 C 9 8, 000 10 80, 000 C C items: the most with the lowest dollar value. 2 1, 000 70 70, 000 C 5 700 70 49, 000 C B items: those in between 7 200 210 42, 000 C 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 18, 800 MIS 373: Basic Operations Management Annual value Class 7, 591, 000 % of items % of value 5. 3 52. 7 31. 4 40. 8 63. 3 6. 5 100 16

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 Management 17

Inventory Models • Economic Order Quantity models: – identify the optimal order quantity • by minimizing total annual costs that vary with order size and frequency 1. 2. 3. 4. 5. 6. The basic Economic Order Quantity model (EOQ) The Quantity Discount model The Economic Production Quantity model (EPQ) Reorder Point Ordering (uncertainty, when to order) Fixed-Order-Interval model Single Period model (perishable items)

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 Management 19

The Inventory Cycle Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point Receive order Place order Receive order Time Lead time MIS 373: Basic Operations Management 20

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

Total Annual Cost • Total Cost = Annual Holding Cost + Annual Ordering Cost Q D (TC) = H + S 2 Q Average number of units in inventory Number of orders 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 22

Goal: Total Cost Minimization • The Total-Cost Curve is U-Shaped Annual Cost – There is a tradeoff between holding costs and ordering costs Holding Costs Ordering Costs Q* (optimal order quantity) MIS 373: Basic Operations Management Order Quantity (Q) 23

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 Management 24

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 Management 25

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 TCmin = 4, 800 Let’s verify whether the Q* indeed gives the lowest cost. MIS 373: Basic Operations Management 26

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

Solution • a • b • c • d Instructor Slides 28

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. 2. 3. 4. 5. 6. 7. 8. Only one item is involved Annual demand requirements are known Usage rate is constant (= even demand throughout the year) Usage occurs continually, but production occurs periodically (batch production) The production rate is constant Production rate is greater than usage rater Lead time does not vary There are no quantity discounts Instructor Slides 13 -29

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

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

EPQ Model Instructor Slides 32

EPQ – Total Cost Instructor Slides 13 -33

EPQ Optimal Batch size a. k. a Economic Produciton Quantity (EPQ) Instructor Slides 13 -34

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

Solution • a • b Instructor Slides 36

Solution • c • d Instructor Slides 37

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

When to Reorder • If delivery is not instantaneous, but there is a lead time: Order When to order? Inventory Quantity Q Lead Time Place Receive MIS 373: Basic Operations Management order Time 39

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 Management 40

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 i. Pads per year – 300 working day year – Lead time for orders is 3 working days 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 MIS 373: Basic Operations Management 41

The Inventory Cycle Q: When shall we order? A: When inventory = ROP Q: How much shall we order? A: Q = EOQ Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point ROP = Lx. D Receive order D: demand period L: Lead time in periods Place order Receive order Time Lead time MIS 373: Basic Operations Management 42

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) Recall: EOQ = 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)

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.

But demand is rarely predictable! Inventory Level When Actual Demand < Expected Demand Order Quantity Lead Time Demand ROP Inventory at time of receipt Time Place order Lead Time Receive order MIS 373: Basic Operations Management 45

But demand is rarely predictable! Inventory Level When Actual Demand > Expected Demand Order Quantity Stockout Point ROP Unfilled demand Place order Time Lead Time Receive MIS 373: Basic Operations Management order 46

But demand is rarely predictable! Inventory Level Order Quantity If ROP = expected demand, inventory left 50% of the time, stock outs 50% of the time. ROP = Expected Demand Average Uncertain Demand Time MIS 373: Basic Operations Management 47

Safety Stock Inventory Level To reduce stockouts we add safety stock Order Quantity ROP = Safety Stock + Expected LT Demand Ex Le pe De ad- cted m tim an e d Order Quantity Q = EOQ Safety Stock Place order Lead Time Receive MIS 373: Basic Operations Management order Time 48

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 lead time variability 3. The desired service level • Service level = probability of NOT stocking out • Reorder point (ROP) = Expected demand during lead time + z*σd. LT Where z = number of standard deviations σd. LT = the standard deviation of lead time demand MIS 373: Basic Operations Management 49

Reorder Point • The ROP based on a normal distribution of lead time demand Service level Risk of stockout (probability of not stockout) Safety Stock Expected ROP demand MIS 373: Basic Operations Management Z 0 Quantity Z scale 50

Recap