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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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**Inventory Management at Cox Hardware**

From the video, what are the elements relevant to inventory management? https://www.youtube.com/watch?v=q3B3gwgWrnw

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**Inventory Definition Inventories are a vital part of business:**

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:**

To meet anticipated customer demand 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. To decouple operations Buffers between operations 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:**

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. 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 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. 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: Satisfactory Level of customer service Having the right goods available in the right quantity in the right place at the right time 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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**MIS 373: Basic Operations Management**

Inventory Management Management has two basic functions concerning inventory: Establish a system for tracking items in inventory Make decisions about When to order How much to order MIS 373: Basic Operations Management

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**Effective Inventory Management**

Requires: 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 A classification system for inventory items MIS 373: Basic Operations Management

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**Measures of performance**

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

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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 Management

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**MIS 373: Basic Operations Management**

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

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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 Management

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**ABC Classification System**

How to classify? For each item, multiply annual volume by unit price to get the annual dollar value. Arrange annual values in descending order. A items: the few with the highest annual dollar value C items: the most with the lowest dollar value. B items: those in between # Annual demand Unit price Annual value Class % of items % of value 8 1,000 4,000 4,000,000 A 5.3 52.7 3 2,400 500 1,200,000 B 31.4 40.8 6 1,000,000 1 2,500 360 900,000 4 1,500 100 150,000 C 63.3 6.5 10 200 100,000 9 8,000 80,000 2 70 70,000 5 700 49,000 7 210 42,000 18,800 7,591,000 MIS 373: Basic Operations Management

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**ABC Classification: 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

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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 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)

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**MIS 373: Basic Operations Management**

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: Only one product is involved Annual demand requirements are known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts MIS 373: Basic Operations Management

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**Profile of Inventory Level Over Time**

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

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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

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**MIS 373: Basic Operations Management**

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 = Q H + D S 2 Average number of units in inventory Number of orders MIS 373: Basic Operations Management

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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 Order Quantity (Q) Ordering Costs Q* Annual Cost (optimal order quantity) Holding Costs MIS 373: Basic Operations Management

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**MIS 373: Basic Operations Management**

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. 𝑇 𝐶 ′ = 𝐻 2 + −1 𝐷𝑆 𝑄 2 =0 → 𝐷𝑆 𝑄 2 = 𝐻 → 𝐷𝑆 𝑄 = 𝐻𝑄 2 𝑄 ∗ = 2𝐷𝑆 𝐻 = 2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 MIS 373: Basic Operations Management

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**MIS 373: Basic Operations Management**

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 𝑄 ∗ = 2𝐷𝑆 𝐻 = 2∗9,600∗ =300 𝑡𝑖𝑟𝑒𝑠 𝑇𝐶= 𝑄 2 𝐻+ 𝐷 𝑄 𝑆= ∗16+ 9, ∗75=2,400+2,400=4,800 MIS 373: Basic Operations Management

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

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

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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

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Solution a b c d Instructor Slides

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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 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 13-29 Instructor Slides

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**EPQ: Inventory Cycle Q Qp Imax 13-30 Time Production and usage Usage**

only Cumulative production Amount on hand Time 13-30 Instructor Slides

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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

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EPQ Model Instructor Slides

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EPQ – Total Cost 13-33 Instructor Slides

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

Instructor Slides

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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

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Solution a b Instructor Slides

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Solution c d Instructor Slides

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**Quantity Discount Model**

Price reduction for larger orders offered to customers to induce them to buy in large quantities 13-38 Instructor Slides

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**MIS 373: Basic Operations Management**

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

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**MIS 373: Basic Operations Management**

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 The rate of demand The lead time The extent of demand and/or lead time variability The degree of stockout risk acceptable to management MIS 373: Basic Operations Management

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**MIS 373: Basic Operations Management**

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 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

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**Profile of Inventory Level Over Time**

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 Quantity on hand Q Receive order Place Lead time Reorder point Usage rate Time ROP = LxD D: demand per period L: Lead time in periods MIS 373: Basic Operations Management

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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) Recall: 𝑄 ∗ = 2𝐷𝑆 𝐻 = 2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 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)

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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!**

Inventory Level When Actual Demand < Expected Demand Order Quantity Lead Time Demand ROP Inventory at time of receipt Time Place order Receive order Lead Time MIS 373: Basic Operations Management

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**But demand is rarely predictable!**

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

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**But demand is rarely predictable!**

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

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**MIS 373: Basic Operations Management**

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

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How Much Safety Stock? The amount of safety stock that is appropriate for a given situation depends upon: The average demand rate and average lead time Demand and lead time variability The desired service level Service level = probability of NOT stocking out Reorder point (ROP) = Expected demand during lead time + z*σdLT Where z = number of standard deviations σdLT = the standard deviation of lead time demand MIS 373: Basic Operations Management

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**(probability of not stockout)**

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

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Recap

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