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## Chapter 11

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**Chapter 11**Inventory: Managing to Meet Demand**Learning Objectives**• Explain why businesses carry inventory. • Describe the costs associated with inventory. • Compare independent and dependent demand inventory. • Calculate days-of-supply. • Explain how a reorder point system works. • Describe the contribution made by a safety stock. • Compute the reorder point for a desired service level. • Make computations for the economic order quantity models. • Describe weaknesses of the economic order quantity. • Compute the appropriate order quantity for a fixed interval, variable quantity system. • Describe the information inputs necessary to manage dependent demand inventory. • Compute planned order releases using material requirements planning. • Explain ABC analysis. • Compute dollar days for a given inventory.**Introduction: A Balancing Act for Management**• Both the presence and absence of inventory contribute to value and to costs. • Too much inventory is an investment that will provide no return. • Too little inventory results in missed or late sales and deliveries. • Carrying the correct amount of inventory is a difficult balancing act.**Why Should Businesses Carry Inventory?**• Decoupling: Reducing the direct dependency of a process step on its predecessor. This could be in a process or in the supply chain. • Decouple customer from supplier and machine from machine • Disruptions, if decoupled, don’t have as serious of an impact • Decoupling enhances reliability and response time**Why Should Businesses Avoid Carrying Too Much Inventory?**• Inventory is an investment that should provide a financial return. • Excess inventory is an investment that provides no return. • In addition to the cost of purchasing it, inventory also has other “carrying” costs: • Cost of storage • Cost of insurance • Reduction in flexibility**Costs and Benefits**• Order cost: The fixed cost associated with ordering inventory. • Changeover (setup) cost: The cost of changing equipment from producing one product or service to another. Analogous to order cost. • Carrying cost: Costs associated with carrying inventory. Insurance, storage, opportunity cost of money tied up in inventory. • Stockout cost: Costs associated with not having inventory when a customer wants it. • Purchasing cost: Cost of purchasing the actual inventory. Sometimes quantity discounts lower this cost, but this comes at the expense of raising carrying costs. • Buying in Bulk (discounted)…..**How Many to Order:The Economic Order Quantity**• The relationships among the ordering cost, carrying costs, and total cost curve: Exhibit 11.8 Carrying Costs, Ordering Cost, and Total Cost in EOQ Ordering at this quantitywill minimize the totalcosts**Costs and Benefits**• If inventory is replenished when it reaches zero, average inventory is half the order quantity. • Order costs and carrying costs are inversely related. Large orders increase average inventory and carrying cost, but the larger the orders, the less frequently you have to order. Exhibit 11.1 Average Inventory as Q/2**Retailing and Finished-Product Inventories**• Continuous Replenishment • The delivery of inventory, frequently, and in small quantities. • Results in lower average levels of inventory. Exhibit 11.2 Frequent Small Deliveries versus Infrequent Large Deliveries**Retailing and Finished-Product Inventories: Inventory and**Time • Inventory provides a supply or coverage for a given length of time. • Days-of-supply is inventory on hand divided by average daily demand. • Stockout • An instance when demand cannot be satisfied by existing inventory. • Delays in replenishment can cause stockouts.**Retailing and Finished-Product Inventories: Days-of-Supply**Calculation Calculate days of supply when average demand is 40 gallons per day, and 60 gallons remain**Retailing and Finished-Product Inventories: Days-of-Supply**Example • If a retailer has a six-day supply of a product, how soon a stockout occurs depends on the rate demand. If the rate is “average” it will last for six days • If demand is less than average, it will last longer. • If demand is greater than average, it won’t last as long Exhibit 11.3 Example of Days’ Supply**Retailing and Finished-Product Inventories: Independent**Demand Inventories • Independent Demand Inventory is inventory whose demand is dictated by the marketplace. • Finished products • Retailer stocks • Maintenance, Repair, and Operating (MRO) Inventory (Inventory that consists of items consumed in the day-to-day activities of a business).**Dependent Demand Inventory**• Dependent demand inventory is inventory whose demand is determined by the production schedule for finished products • It usually consists of components and raw materials**Inventory Decisions**• When should it be ordered? • How many should be ordered?**Managing Independent Demand Inventory**• Service Level: Percent of orders satisfied from existing inventory. • Replenishment Lead Time: The time required to receive inventory that has been ordered. • Since there is a replenishment lead time, orders must be made before the inventory has run out. • Two general approaches: • Fixed quantity, variable interval systems • Fixed interval, variable quantity systems**Fixed Quantity, Variable Interval System: The Reorder Point**Model • Demand during the replenishment lead time is uncertain. • Assume: • Demand averages60 units per week and is normally distributed • The replenishment lead time is 2 weeks • When should inventory be reordered?**Fixed Quantity, Variable Interval System: The Reorder Point**Model If the order is placed when the on hand inventory is equal to the average demand during the replenishment lead time (120), what is the probability having enough inventory to meet demand? 50%**Fixed Quantity, Variable Interval System: The Reorder Point**Model If the order is placed when the on hand inventory is equal to 1 standard deviation above the average demand during the replenishment leadtime (132) , what is the probability of having enough inventory to meet demand? 84.13%**Fixed Quantity, Variable Interval System: The Reorder Point**Model If the order is placed when the on hand inventory is equal to 3 standard deviations above the average demand during the replenishment leadtime (132) , what is the probability of having enough inventory to meet demand? 99.87%**Fixed Quantity, Variable Interval System: The Reorder Point**Model Safety Stock: Additional inventory (above mean demand) maintained to increase service levels in response to demand variability. A safety stock of 36 units increasesthe probability of not stocking out during the replenishment lead time from 50% to 99.87%**Fixed Quantity, Variable Interval System: The Reorder Point**Model • To meet demand during the replenishment lead time, the reorder point must include a safety stock linked to demand variability. Where: ROP = Reorder Point (i.e., quantity at which more inventory is ordered) dLT = Average demand during replenishment lead time σLT = Standard deviation of demand during replenishment lead time Z = Number of standard deviations above the average demand during replenishment lead time required for desired service level.**Fixed Quantity, Variable Interval System: The Reorder Point**Model • The diagram shows how a fixed-quantity reorder point system works. • What should the reorder point be if we wanted a 99% service level? Exhibit 11.6 Reorder Point System**Fixed Quantity, Variable Interval System: The Reorder Point**Model • A service level of 99% implies an inventory level that is 2.33 standard deviations above the mean demand during the replenishment lead time. • The mean is 120 and standard deviation is 12 • ROP = 120 + 2.33(12) = 120 + 28 = 148 • A ROP of 148 would be sufficient to satisfy demand during the replenishment lead time with 99% confidence.**Fixed Quantity, Variable Interval System: The Reorder Point**Model Exhibit 11.7 ROP at 2.33s Service Levels 3σ provides 99.87% confidence 2.33σ provides 99.00% confidence 2σ provides 97.73% confidence 1σ provides 84.13% confidence The mean provides 50.00% confidence**How Many to Order:The Economic Order Quantity**The ROP tells us when to order, but the order quantity (how many?) still needs to be determined. The economic order quantity (EOQ) model is used to determine an order quantity that minimizes the sum of ordering and carrying costs. The basic EOQ model makes the following assumptions: Annual demand is known Demand is even Lead time is constant No quantity discounts Only one product is involved Orders are received in single deliveries**How Many to Order:The Economic Order Quantity**• By taking the first derivative with respect to Q of the formula for the total cost curve, we obtain the formula for the optimal Q which is the EOQ: • Step-by-Step: The Economic Order Quantity Calculation • Determine the annual demand (D) • Determine the inventory carrying cost per unit (H). If carrying costs are given as a percentage of the item value, H will be the percentage (i) multiplied by the item value (P) • Determine the cost of ordering (S) per order • Use the formula above to compute EOQ**Economic Order Quantity Calculation**2DS 2 * 600 * 13 EOQ = = = = 4800 69 . 282 H 3.25 • The University Bookstore wished to utilize the EOQ formula to determine the appropriate order quantity for its most popular backpack. Determine the EOQ given the following information: • Annual demand = 600 • Order cost = $13 per order • Carrying cost = $3.25 per unit, per year As a matter of practice we would round up to order 70 units.**Weaknesses of the EOQ Model**• The EOQ has been criticized for inflating order quantities. Many feel it underestimates carrying costs by ignoring well-accepted nonfinancial costs of carrying inventory: • Loss of flexibility • Increased quality feedback time • Increased lead times**How Many to Order: The Economic Order Quantity with Quantity**Discounts • Various modifications of the basic EOQ model are used as the assumptions are relaxed.One such commonly relaxed assumption relates to quantity discounts • If discounts are available for certain order quantities, the order quantity no longer just affects order costs and carrying costs—it also affects the cost of purchasing it. In that scenario, the total cost consists of order cost, carrying cost, and purchase cost. • Step-by-step: EOQ with quantity discounts • Compute basic EOQ. It will fall within one of the price ranges specified by the supplier. • If the EOQ falls within the cheapest price range, the EOQ is the optimal order quantity. • If the EOQ does not, all price ranges having lower prices than the range the EOQ falls in must be evaluated. • The optimal quantity will be at the lowest allowable quantity of a price range. For each quantity, compute the total cost (carrying, order, and purchase price) for the quantity at each price break.**How Many to Order: The Economic Order Quantity with Quantity**Discounts • Total cost with quantity discounts: TC = (D/Q)S + (Q/2)H + DP Where D = annual demand Q = order quantity S = cost per order H = carrying cost P = price per unit**Quantity Discount Model Calculation**Given the following quantity discount information . . . 1-20 units: $229 each 21-60 units: $210 each 61-120 units: $199 each 120 units: $175 each Order cost: $20 per order Carrying cost: $36 per unit per year Annual demand: 476 units What would the low-cost order quantity be?**Quantity Discount Model Calculation**Solution: Calculate Basic EOQ • Calculate TC for EOQ and lower priced quantities • TC at 23 units per order = $100,787.91 • TC at 61 units per order = $95,978.07 • TC at 121 units per order = $85,556.68 Order 121 units per order**Periodic Review System: An independent demand management**system that orders inventory on fixed time intervals. If the timing cannot vary, the order quantity must vary to meet demand This system is used when user needs to order at periodic intervals because of supplier shipment schedules, or needs to combine orders for different products to save on transaction costs Fixed Interval, Variable Quantity Systems**The periodic review model**Fixed Interval, Variable Quantity Systems Order quantity must be enough to cover demand until the next order arrives, here. Periodic order is placed here Order arrives here Exhibit 11.9 Periodic Review System**Fixed Interval, Variable Quantity Systems**• The order quantity must cover the expected demand during the order interval and replenishment lead time. Order Quantity = Target Inventory Level –Inventory On Hand Q = TI - A The target inventory level = Where = the average demand during the order interval and lead time SS = the safety stock OI = the number of days in the order interval LT = the number of days in the replenishment lead time**Fixed Interval, Variable Quantity Systems**• The safety stock is calculated as Where SS = the safety stock OI – the number of days in the order interval LT = the number of days in the replenishment lead time Z = the number of standard necessary for the desired confidence level σOI+LT = the standard deviation of demand over the OI and LT σt = the daily standard deviation**Step-by-Step: Determining the Order Quantity**Based on the average daily demand, determine the average demand during the order interval Based on the average daily demand, determine the average demand during the replenishment lead time Identify the Z value from Appendix B and the desired service level Determine the amount of inventory on hand currently Using formula 11.8, determine the safety stock Using formula 11.7, determine the target inventory level Using formula 11.6, determine the order quantity Fixed Interval, Variable Quantity Systems**Periodic Review Model Example**Compute safety stock • Average daily demand: 3.6 units • Replenishment lead time: 2 days • Standard deviation of demand (daily): 5 • Inventory on hand: 5 • Service level desired: 95% • Order Interval: 7 days. SS =1.645(.5)(3) =2.4675 Compute target inventory level = 32.4 + 2.4675= 34.87Round up to 35 Subtract on hand inventory Q = TI – A= 35 – 5= 30**Material Requirements Planning (MRP) is an inventory**management approach used to manage dependent demand inventory that plans order releases for the future based on production schedules. The same two questions get answered: ‘When?’ and ‘How many?’ “How many” is determined by a process called netting: computing net requirements. Net requirements are total quantity needed less on-hand inventory “When” is determined by backward scheduling, where a known completion date or due date is used to determine a start date Managing Dependent Demand Inventory:Material Requirements Planning**Netting and backward scheduling in MRP require information**that comes from master production schedules (MPS), bills of material, and inventory master files. Managing Dependent Demand Inventory:Material Requirements Planning Exhibit 11.10 Material Requirements Planning Inputs**Managing Dependent Demand Inventory:Material Requirements**Planning Master Production Schedule (MPS): A schedule of end products that must be completed in a specific time period. Exhibit 11.11 Master Production Schedule (MPS) for Staple Remover**Bill of material: A file containing information about the**materials required to produce a product or component. Managing Dependent Demand Inventory:Material Requirements Planning Exhibit 11.12 Structure for Staple Remover**Inventory master file: A file containing information about**an inventory item such as the quantity on hand, the cost, and so on. More MRP terms: Gross requirements: The total quantity needed to meet demand Beginning on-hand inventory: Inventory at the beginning of a time period Ending on hand inventory: Inventory at the end of a time period Net requirements: Gross requirements less beginning on-hand inventory Planned order receipt: The planned receipt of material that results from a planned order release Planned order release: An order planned to be released to satisfy a future net requirement Managing Dependent Demand Inventory:Material Requirements Planning**Managing Dependent Demand Inventory:Material Requirements**Planning • MRP takes individual component lead times into account to make sure that required components arrive on time Depending on how long it takes to get each one, they must be ordered here. All components must be available here If staple remover order is due here, and assembly takes one week . . . Exhibit 11.14 Time Line for Staple Remover Component Orders**Managing Dependent Demand Inventory: Material Requirements**Planning How many should be ordered (or produced) this week in order to meet the demand? How many does the MPS say I need? (usage) Exhibit 11.13 Quantity and Timing for Staple Remover Orders (Staple Remover MRP Record) How many do I already have? (Ending Inventory from previous week) How many will be left? (Beginning + Receipts - Usage) How many more do I need? (Gross Requirement - Beginning Inventory) How many will be received? (receipts)**Managing Dependent Demand Inventory: Material Requirements**Planning “Parent” Item Gross requirements for components come from “planned order release” of the parent Component Item**Managing Dependent Demand Inventory:Material Requirements**Planning If I am going to need 62 units of the “parent” in week 8…, I need to release the order (start making them) in week 7 …, so I need the component in week 7 …, And I need to order (or start making) it in week 6 (it has a 1-week lead time)**Managing Dependent Demand Inventory:Material Requirements**Planning Component Lead Time Staple Remover (parent) 1 week Outer jaw 1 week Inner jaw 1 week Connecting Pin 2 weeks Spring 2 weeks …, also, where I ordered the outer jaw one week before I needed it …, …, I have to order connecting pins two weeks before I need them.**Lot-for-lot ordering: Ordering exactly the amount of the net**requirements. Used in previous example Fixed-quantity order policy: Rather than ordering the quantity of the net requirements, orders are placed in increments of a fixed quantity. Trades off reduction in ordering costs against increases in carrying costs Managing Dependent Demand Inventory:Extended MRP