Chapter 6 Inventory Control Models Presented by: Jeniel Pascual & Caleb Costales Learning Objectives After completing this chapter, students will be able to: • Understand the importance of inventory control. • Understand the various types of inventory related decisions. • Use the economic order quantity (EOQ) to determine how much to order. • Compute the reorder point (ROP) in determining when to order more inventory. • Handle inventory problems that allow non-instantaneous receipt. • Handle inventory problems that allow quantity discounts. Learning Objectives After completing this chapter, students will be able to: • Understand the use of safety stock. • Compute single period inventory quantities using marginal analysis. • Understand the importance of ABC analysis. • Describe the use of material requirements planning in solving dependent-demand inventory problems. • Discuss just-in-time inventory concepts to reduce inventory levels and costs. • Discuss enterprise resource planning systems. Inventory as an Important Asset -Inventory is one of the most expensive and important assets to many companies.. Inventory -Inventory is any stored resource that is used to satisfy a current or a future need. Examples: 1. 2. 3. Raw materials, work-in-process, and ﬁnished goods. -Studying how organizations control their inventory is equivalent to studying how they achieve their objectives by supplying goods and services to their customers. -Inventory is the common thread that ties all the functions and departments of the organization together. Inventory -Lower inventory levels • Can reduce costs • May result in stockouts (frequent inventory outages) and dissatisﬁed customers -Companies must make the balance between low and high inventory levels. -Cost minimization is the major factor in obtaining this delicate balance. Inventory Planning & Control (Figure 6.1) Five Uses of Inventory 1. The decoupling function o Reduces delays and improves efﬁciency o A buffer between stages 2. Storing resources o Seasonal products stored to satisfy off-season demand o Materials stored as raw materials, work-in-process, or ﬁnished goods o Labour can be stored as a component of partially completed subassemblies 3. Irregular supply and demand o Not constant over time o Inventory used to buffer the variability Five Uses of Inventory 4. Quantity discounts o Lower prices may be available for larger orders o Higher storage and holding costs (spoilage, damaged stock, theft, insurance…) o By investing in more inventory, you will have less cash to invest elsewhere! 5. Avoiding stockouts and shortages o Stockouts may result in lost sales o Dissatisﬁed customers may choose to buy from another supplier o Loss of goodwill Inventory Decisions ECONOMIC ORDER QUANTITY (EOQ) 2 Fundamental Decisions 1. How much to order 2. When to order REORDER POINT (ROP) -A major objective in controlling inventory is to minimize total inventory costs. 1. Cost of the items- (purchase cost or material cost) 2. Cost of ordering- (often involves personnel time) 3. Cost of carrying, or holding, inventory- (taxes, insurance, cost of capital…) 4. Cost of stockouts- (lost sales and goodwill that result from not having the items available for the customers) Inventory Cost Factors Inventory Cost Factors (Table 6.1) • Ordering costs are generally independent of order quantity o Many involve personnel time o The amount of work is the same no matter the size of the order • Holding costs generally vary with the amount of inventory or order size o Labour, space, and other costs increase with order size o Cost of items purchased can vary with quantity discounts Economic Order Quantity Economic order quantity (EOQ) model o One of the oldest and most commonly known inventory control techniques o Easy to use o Several important assumptions limits the applicability of this model • Objective is to minimise total cost of inventory *Lead time = the time between the placement of the order and the receipt of the order Economic Order Quantity Assumptions: 1. Demand is known and constant over time 2. Lead time* is known and constant 3. Receipt of inventory is instantaneous (arrives in one batch, at one point in time!) 4. Purchase cost (= cost of the inventory!) per unit is constant throughout the year (Quantity discounts are not possible!) 5. The only variable costs are ordering cost and holding or carrying cost, and these are constant throughout the year 6. Orders are placed so that stockouts or shortages are avoided completely If this amount is 1,000 bananas, all 1,000 bananas arrive at one time when an order is received. The inventory level jumps from 0 to 1,000 bananas (Q). Inventory Usage Over Time Inventory Costs in the EOQ Situation Based on our assumptions - if we minimise the sum of the ordering and carrying costs we are minimising the total costs • Annual ordering cost is number of orders per year times cost of placing each order • Annual carrying cost is the average inventory times carrying cost per unit per year Inventory Costs in the EOQ Situation Inventory Costs in the EOQ Situation Inventory Costs in the EOQ Situation Inventory Costs in the EOQ Situation Total Cost as a Function of Order Quantity: Finding the EOQ When the EOQ assumptions are met, total cost is minimised when: Annual ordering cost = Annual holding cost Economic Order Quantity (EOQ) Model Equation summary: Sumco Pump Company Example Sumco, a company that sells pump housings to other manufacturers, would like to reduce its inventory cost by determining the optimal number of pump housings to obtain per order. The annual demand is 1,000 units, the ordering cost is $10 per order, and the average carrying cost per unit per year is $0.50. Using these ﬁgures, if the EOQ assumptions are met, we can Calculate the optimal number of units per order: Sumco Pump Company Example Reduce inventory costs by ﬁnding optimal order quantity Sumco Pump Company Example The total annual inventory cost is the sum of the ordering costs and the carrying costs: Number of orders per year = (D÷Q) = 5 Average inventory (Q÷2) = 100 Sumco Pump Company Example Sensitivity Analysis with the EOQ Model • The EOQ model assumes that all input values are ﬁxed and known with certainty. • Values are estimated or may change • Sensitivity analysis determines the effects of these changes • Because the EOQ is a square root, changes in the inputs (D; Co; Ch) result in relatively minor changes in the optimal order quantity Sensitivity Analysis with the EOQ Model For example, if Co were to increase by a factor of 4, the EOQ would only increase by a factor of 2. Consider the Sumco example just presented. The EOQ for this company is as follows: In general, the EOQ changes by the square root of the change to any of the inputs! Reorder Point: Determining When To Order • Next decision is “When to order” • The time between placing an order and its receipt is called the lead time (L) or delivery time • “On hand” and “on order” inventory must be available to meet demand during lead the total of these is called “inventory position” • Generally the “when to order” decision is usually expressed in terms of a reorder point (ROP; inventory position at which an order should be placed) d = Demand per day L = Lead time for a new order in days Procomp’s Computer Chips Example D = Annual demand = 8,000 d = Daily demand = 40 units L = Delivery in 3 working days An order for the EOQ (400) is placed when the inventory reaches 120 units The order arrives 3 days later just as the inventory is depleted to 0! Reorder Point Graphs Q = 400 d; = 40 units; L = Delivery in 3 working days; ROP = d * L = 120 ROP < Q 120 < 400 d = Demand per day L = Lead time for a new order in days Procomp’s Computer Chips Example Suppose the lead time for Procomp Computer Chips was 12 days instead of 3 days. How would this affect the “reorder point”? Annual demand = 8,000 Daily demand = 40 units Delivery in three twelve working days d = Demand per day L = Lead time for a new order in days Procomp’s Computer Chips Example Annual demand = 8,000 Daily demand = 40 units Delivery in three twelve working days New order placed when inventory = 80 and one order is in transit! Reorder Point Graphs Q = 400; d = 40 units; L = Delivery in 12 working days; ROP = d * L = 480 ROP > Q 480 > 400 Reorder Point Graphs EOQ Without Instantaneous Receipt • When a ﬁrm receives its inventory over a period of time, a new model is needed that does not require the “instantaneous inventory receipt assumption”! • This new model is applicable when inventory continuously ﬂows or builds up over a period of time after an order has been placed or when units are produced and sold simultaneously. •Under these circumstances, the daily demand rate (d) must be taken into account. EOQ Without Instantaneous Receipt The production run model eliminates the instantaneous receipt assumption. Production run model: This graph shows inventory levels as a function of time. Model especially suited to the production environment! Annual Carrying Cost for Production Run Model • In the production process, instead of having an ordering cost, there will be a setup cost -Cost of setting up the production facility to manufacture the desired product! • Salaries and wages of employees responsible for setting up the equipment • Engineering and design costs of making the setup • Paperwork, supplies, utilities … Annual Carrying Cost for Production Run Model So how can we derive the optimal production quantity? • We need to set our “setup costs” equal to “carrying costs” and then solve for the “order quantity”. • Let’s start by developing the expression for carrying cost! Annual Carrying Cost for Production Run Model As with the EOQ model, the carrying costs of the production run model are based on the average inventory, and the average inventory is one-half the maximum inventory level. p = daily production rate d = daily demand rate t = length of production run in days Annual Carrying Cost for Production Run Model Annual Carrying Cost for Production Run Model Annual Carrying Cost for Production Run Model When a product is produced over time, setup cost replaces ordering cost: Both of these are independent of the size of the order and the size of the production run! This cost is simply the number of orders (or production runs) times the ordering cost (setup cost). Annual Carrying Cost for Production Run Model Production Run Model Brown Manufacturing Example Brown Manufacturing produces commercial refrigeration units in batches. The ﬁrm’s estimated demand for the year is 10,000 units. It costs about $100 to set up the manufacturing process, and the carrying cost is about 50 cents per unit per year. When the production process has been set up, 80 refrigeration units can be manufactured daily. The demand during the production period has traditionally been 60 units each day. Brown operates its refrigeration unit production area 167 days per year. How many units should Brown produce in each batch? How long should the production part of the cycle last? Brown Manufacturing Example Produces commercial refrigeration units in batches: How many units should Brown produce in each batch? How long should the production part of the cycle last? Brown Manufacturing Example Brown Manufacturing Example Brown Manufacturing Example If Q* = 4,000 units and we know that 80 units can be produced daily, the length of each production cycle will be days. When Brown decides to produce refrigeration units, the equipment will be set up to manufacture the units for a 50-day time span. -The number of production runs per year will be D/Q = 10,000/4,000 = 2.5. -The average number of production runs per year is 2.5. -There will be 3 production runs in one year with some inventory carried to the next year -Therefore only 2 production runs are needed in the second year. Quantity Discount Models In developing the EOQ model, we assumed that quantity discounts were not available. -However, many companies do offer quantity discounts. -If such a discount is possible, but all of the other EOQ assumptions are met, it is possible to ﬁnd the quantity that minimises the total inventory cost by using the EOQ model and making some adjustments Quantity Discount Models • When quantity discounts are available the basic EOQ model is adjusted by adding in the “purchase or materials cost” Quantity Discount Models Quantity Discount Models Quantity Discount Models •Overall our objective is to minimise the total cost. • Because the unit cost (4.75) for the third discount is lowest, we might be tempted to order 2,000 units or more to take advantage of the lower material cost. • Placing an order for that quantity with the greatest discount cost might not minimise the total inventory cost. • As the discount quantity goes up, the material cost goes down, but the carrying cost increases because the orders are large. • Key trade-off when considering quantity discounts is between the reduced material cost and the increased carrying cost! Quantity Discount Models Brass Department Store Example Brass Department Store stocks toy race cars. Recently, the store was given a quantity discount schedule for the cars. The ordering cost is $49 per order, the annual demand is 5,000 race cars, and the inventory carrying charge as a percentage of cost, I, is 20%. Brass Department Store Example Toy race cars: Quantity discounts available Brass Department Store Example Brass Department Store Example Brass Department Store Example Brass Department Store stocks toy race cars. Recently, the store was given a quantity discount schedule for the cars. The ordering cost is $49 per order, the annual demand is 5,000 race cars, and the inventory carrying charge as a percentage of cost, I, is 20%. Brass Department Store Example Brass Department Store Example Brass Department Store Example