0 Production and Operations Management Norman Gaither Greg Frazier Slides Prepared by John Loucks  1999 South-Western College Publishing

1 Chapter 10 Independent Demand Inventory Systems

2 OverviewOverview l Opposing Views of Inventories l Nature of Inventories l Fixed Order Quantity Systems l Fixed Order Period Systems l Other Inventory Models l Some Realities of Inventory Planning l Wrap-Up: What World-Class Producers Do

3 Opposing Views of Inventory l Why Do We Want to Hold Inventory l Why Do We Not Want to Hold Inventory

4 Why Do We Want to Hold Inventory l Improve customer service l Reduce certain costs such as l ordering costs l stockout costs l acquisition costs l start-up quality costs l Contribute to the efficient and effective operation of the production system

5 Why We Do Not Want to Hold Inventory l Certain costs increase such as l carrying costs l cost of customer responsiveness l cost of coordinating production l cost of diluted return on investment l reduced-capacity costs l large-lot quality cost l cost of production problems

6 Nature of Inventory l Two Fundamental Inventory Decisions l Terminology of Inventories l Independent Demand Inventory Systems l Dependent Demand Inventory Systems l Inventory Costs

7 Two Fundamental Inventory Decisions l How much to order of each material when orders are placed with either outside suppliers or production departments within organizations l When to place the orders

8 Independent Demand Inventory Systems l Demand for an item carried in inventory is independent of the demand for any other item in inventory l Finished goods inventory is an example l Demands are estimated from forecasts (Chapter 3) and/or customer orders

9 Dependent Demand Inventory Systems l Items whose demand depends on the demands for other items l For example, the demand for raw materials and components can be calculated from the demand for finished goods l Therefore the systems used to manage these inventories (Chapter 11) are different from those used to manage independent demand items

1010 Inventory Costs l Costs associated with ordering too much (represented by carrying costs) l Costs associated with ordering too little (represented by ordering costs) l These costs are opposing costs, i.e., as one increases the other decreases l... more

1 Inventory Costs (continued) l The sum of the two costs is the total stocking cost (TSC) l When plotted against order quantity, the TSC decreases to a minimum cost and then increases l This cost behavior is the basis for answering the first fundamental question: how much to order l It is known as the economic order quantity (EOQ)

1212 Fixed Order Quantity Systems l Behavior of Economic Order Quantity (EOQ) Systems l Determining Order Quantities l Determining Order Points

1313 Behavior of EOQ Systems l As demand for the inventoried item occurs, the inventory level drops l When the inventory level drops to a critical point, the order point, the ordering process is triggered l The amount ordered each time an order is placed is fixed or constant l When the ordered quantity is received, the inventory level increases l... more

1414 Behavior of EOQ Systems l An application of this type system is the two-bin system l A perpetual inventory accounting system is usually associated with this type of system

1515 Determining Order Quantities l Basic EOQ l EOQ for Production Lots l EOQ with Quantity Discounts

1616 Model I: Basic EOQ l Typical assumptions made l annual demand (D), carrying cost (C) and ordering cost (S) can be estimated l average inventory level is the fixed order quantity (Q) divided by 2 which implies l no safety stock l orders are received all at once l demand occurs at a uniform rate l no inventory when an order arrives l... more

1717 Model I: Basic EOQ l Assumptions (continued) l Stockout, customer responsiveness, and other costs are inconsequential l acquisition cost is fixed, i.e., no quantity discounts l Annual carrying cost = average inventory level X carrying cost = (Q/2)C l Annual ordering cost = average number of orders per year X ordering cost = (D/Q)S l... more

1818 Model I: Basic EOQ l Total annual stocking cost (TSC) = annual carrying cost + annual ordering cost = (Q/2)C + (D/Q)S l The order quantity where the TSC is at a minimum (EOQ) can be found using calculus (take the first derivative, set it equal to zero and solve for Q)

1919 Model II: EOQ for Production Lots l Used to determine the order size, production lot, if an item is produced at one stage of production, stored in inventory, and then sent to the next stage or the customer l Differs from Model I because orders are assumed to be supplied or produced at a uniform rate (p) rate rather than the order being received all at once l... more

2020 Model II: EOQ for Production Lots l It is also assumed that the supply rate, p, is greater than the demand rate, d l The change in maximum inventory level requires modification of the TSC equation l TSC = (Q/2)[(p-d)/p]C + (D/Q)S l The optimization results in

2121 Model III: EOQ with Quantity Discounts l Under quantity discounts, a supplier offers a lower unit price if larger quantities are ordered at one time l This is presented as a price or discount schedule, i.e., a certain unit price over a certain order quantity range l This means this model differs from Model I because the acquisition cost (ac) may vary with the quantity ordered, i.e., it is not necessarily constant l... more

2 Model III: EOQ with Quantity Discounts l Under this condition, acquisition cost becomes an incremental cost and must be considered in the determination of the EOQ l The total annual material costs (TMC) = Total annual stocking costs (TSC) + annual acquisition cost TSC = (Q/2)C + (D/Q)S + (D)ac TSC = (Q/2)C + (D/Q)S + (D)ac l... more

2323 Model III: EOQ with Quantity Discounts To find the EOQ, the following procedure is used: 1. Compute the EOQ using the lowest acquisition cost (ac). If the resulting EOQ is feasible, i.e., that quantity can be purchased at the acquisition cost used, it is optimal. Otherwise, go on to Step 2

2424 Model III: EOQ with Quantity Discounts 2. Using the EOQ from Step 1 and the discount schedule, find the acquisition cost that should have been used and compute a new EOQ. This new EOQ should be feasible. 3. Compute the TMC for the EOQ found in Step 2 4. Compute the TMC for all quantities greater than Step 2’s EOQ where a discount is offered. Select the quantity with the lowest TMC

2525 Determining Order Points l Basis for Setting the Order Point l DDLT Distributions l Setting Order Points

2626 Basis for Setting the Order Point l In the fixed order quantity system, the ordering process is triggered when the inventory level drops to a critical point, the order point l This starts the lead time for the item. l Lead time is the time to complete all activities associated with placing, filling and receiving the order. l... more

2727 Basis for Setting the Order Point l During the lead time, customers continue to draw down the inventory l It is during this period that the inventory is vulnerable to stockout (run out of inventory) l Customer service level is the probability that a stockout will not occur during the lead time l... more

2828 Basis for Setting the Order Point l Thus, the order point is set based on l the demand during lead time (DDLT) and l the desired customer service level l Order point (OP) = Expected demand during lead time (EDDLT) + Safety stock (SS) l The amount of safety stock needed is based on the degree of uncertainty in the DDLT and the customer service level desired

2929 DDLT Distributions l If there is variability in the DDLT, the DDLT is expressed as a distribution l discrete l continuous l In a discrete DDLT distribution, values (demands) can only be integers l A continuous DDLT distribution is appropriate when the demand is very high

3030 Setting Order Point for a Discrete DDLT Distribution l Assume a probability distribution of actual DDLTs is given or can be developed from a frequency distribution l Starting with the lowest DDLT, accumulate the probabilities. These are the service levels for DDLTs l Select the DDLT that will provide the desired customer level as the order point

3131 Setting Order Point for a Continuous DDLT Distribution l Assume that the lead time (LT) is constant Assume that the demand per day is normally distributed with the mean (d ) and the standard deviation (  d ) Assume that the demand per day is normally distributed with the mean (d ) and the standard deviation (  d ) l The DDLT distribution is developed by “adding” together the daily demand distributions across the lead time l... more

3232 Setting Order Point for a Continuous DDLT Distribution l The resulting DDLT distribution is a normal distribution with the following parameters: EDDLT = LT(d ) EDDLT = LT(d )  DDLT =  DDLT =

3 Setting Order Point for a Continuous DDLT Distribution l The customer service level is converted into a Z value using the normal distribution table The safety stock is computed by multiplying the Z value by  DDLT. The safety stock is computed by multiplying the Z value by  DDLT. l The order point is set using OP = EDDLT + SS, or by substitution OP = LT(d ) + Z ( ) OP = LT(d ) + Z ( )

3434 Auto Zone sells auto parts and supplies including a popular multi-grade motor oil. When the stock of this oil drops to 20 gallons, a replenishment order is placed. The store manager is concerned that sales are being lost due to stockouts while waiting for an order. It has been determined that lead time demand is normally distributed with a mean of 15 gallons and a standard deviation of 6 gallons. The manager would like to know the probability of a stockout during lead time. Example: Setting Order Points

3535 l EDDLT = 15 gallons  DDLT = 6 gallons  DDLT = 6 gallons OP = EDDLT + Z(  DDLT ) 20 = 15 + Z(6) 5 = Z(6) 5 = Z(6) Z = 5/6 Z = 5/6 Z =.833 Z =.833

3636 Example: Setting Order Points l Standard Normal Distribution Area =.2967 Area =.5 Area =.2033 z

3737 Example: Setting Order Points l The Standard Normal table shows an area of.2967 for the region between the z = 0 line and the z =.833 line. The shaded tail area is = The probability of a stockout during lead time is.2033.

3838 Fixed Order Period Systems l Behavior of Economic Order Period (EOP) Systems l Economic Order Period Model

3939 Behavior of Economic Order Period Systems l As demand for the inventoried item occurs, the inventory level drops l When a prescribed period of time (EOP) has elapsed, the ordering process is triggered, i.e., the time between orders is fixed or constant l At that time the order quantity is determined using order quantity = upper inventory target - inventory level + EDDLT l... more

4040 Behavior of Economic Order Period Systems l After the lead time elapses, the ordered quantity is received, and the inventory level increases l The upper inventory level may be determined by the amount of space allocated to an item l This system is used where it is desirable to physically count inventory each time an order is placed

4141 Determining the EOP l Using an approach similar to that used to derive EOQ, the optimal value of the fixed time between orders is derived to be

4242 Other Inventory Models l Hybrid Inventory Models l Single-Period Inventory Models

4343 Hybrid Inventory Models l Optional replenishment model l Similar to the fixed order period model l Unless inventory has dropped below a prescribed level when the order period has elapsed, no order is placed l Protects against placing very small orders l Attractive when review and ordering costs are large l... more

4 Hybrid Inventory Models l Base stock model l Start with a certain inventory level l Whenever a withdrawal is made, an order of equal size is placed l Ensures that inventory maintained at an approximately constant level l Appropriate for very expensive items with small ordering costs

4545 Single Period Inventory Models l Order quantity decision covers only one period l Appropriate for perishable items, e.g., fashion goods, certain foods, magazines l Payoff tables may be used to analyze the decision under uncertainty l... more

4646 Single Period Inventory Models l One of the following rules can be used in the analysis l greatest profit l least total expected long and short costs l least total expected costs

4747 Some Realities of Inventory Planning l ABC Classification l EOQ and Uncertainty l Dynamics of Inventory Planning

4848 ABC Classification l Start with the inventoried items ranked by dollar value in inventory in descending order l Plot the cumulative dollar value in inventory versus the cumulative items in inventory l... more

4949 ABC Classification l Typical observations l A small percentage of the items (Class A) make up a large percentage of the inventory value l A large percentage of the items (Class C) make up a small percentage of the inventory value l These classifications determine how much attention should be given to controlling the inventory of different items

5050 EOQ and Uncertainty l The TSC and TMC curves are relatively flat, therefore moving left or right of the optimal order quantity on the order quantity axis has little effect on the costs l Estimation errors of the values of parameter used to compute an EOQ usually do not have a significant impact on total costs l... more

5151 EOQ and Uncertainty l Many costs are not directly incorporated in the EOQ and EOP formulas, but could be important factors l Emergency procedures to replenish inventories quickly should be established

5252 Dynamics of Inventory Planning l Continually review ordering practices and decisions l Modify to fit the firm’s demand and supply patterns l Constraints, such as storage capacity and available funds, can impact inventory planning l Computers and information technology are used extensively in inventory planning

5353 Wrap-Up: World-Class Practice l Inventory cycle is the central focus of independent demand inventory systems l Production planning and control systems are changing to support lean inventory strategies l Information systems electronically link supply chain

5454 End of Chapter 10