HANDOUT week 9 inventory management.pdf

1 WEEK 9 INVENTORY MANAGEMENT Concept of Inventory Management Inventory cost Economic order quantity (EOQ) Re-Order point (ROP)  2 Introduction Inventory can be one of the mo...

1 WEEK 9 INVENTORY MANAGEMENT Concept of Inventory Management Inventory cost Economic order quantity (EOQ) Re-Order point (ROP)  2 Introduction Inventory can be one of the most expensive assets of an organization Inventory management policy affects how efficiently a firm deploys its assets in producing goods and services. Management must reduce inventory levels yet avoid stockouts The right amount of inventory supports manufacturing, logistics, and other functions. But excessive inventory is a sign of poor inventory management that creates an unnecessary waste of scarce resources. Primary functions of inventory are To service the market (downstream players) To buffer from uncertainty in the marketplace  3 Types of inventory Four broad categories of inventories Raw materials Items that are bought from suppliers to use in the production of a product. Work-in-process (WIP) inventory 공정중 재고 Partially processed materials not yet ready for sales so that is in production process Finished goods inventory Completed products ready for shipment so items that are ready for sale to customers Maintenance, repair & operating (MRO) 소모성 자재 - Materials & supplies used in producing products e.g. spare parts, tools, cleaning supplies, safety equipment, and other consumables necessary to keep the business running smoothly  4 Concepts of Inventory Management Inventory turnover or turnover ratio 재고회전율 Measures how many times inventory “turns” in an accounting period Calculated by dividing the cost of revenue (cost of goods sold) by average inventory. Higher ratios being better Cost of goods sold 매출원가 Inventory turn over (ratio) = Average inventory at cost  5 Inventory cost Ordering costs 주문비용 This refers to the transaction costs associated with replenishing inventories. This is a direct variable costs for placing an order. It includes the expenses incurred in placing and receiving orders from suppliers For example, order preparation, order transmittal, order receiving, and accounts payments Holding (carrying) costs 유지 (보유) 비용 Costs incurred for holding inventory in storage Opportunity cost (including cost of capital). Storage and warehouse management. Taxes and insurance. Obsolescence, spoilage & shrinkage. Material handling, tracking and management.  6 Inventory cost Stockout Cost 품절비용 It refers to the costs incurred when a company does not have inventory available to meet demand. Example of self-service retailing A consumer who can’t locate an item simply leave the store. This is the cost of a lost sale (e.g., lost profit). The consumer never returns to the store, and so the company loses future sales and profits. Example of manufacturing If a production plant runs out of a component part, the resulting cost is the opportunity cost of having the production line shut down. Stockouts also cause disruptions of materials flows in the supply chain  7 Economic Order Quantity Economic Order Quantity (EOQ) Model The basic order decision is to determine the optimal order size This is a deterministic model When the order size for an item is small Orders have to be placed on a frequent basis, causing high annual order costs You have a low average inventory level, resulting in low annual inventory holding costs. When the order size for an item is large Orders are placed less frequently, causing lower annual order costs High average inventory levels for this item, resulting in higher annual cost to hold the inventory.  8 Economic Order Quantity Economic Order Quantity (EOQ) Model The order size needs to minimizes total annual inventory costs—that is, the sum of the annual order cost and the annual inventory holding cost So, this is a quantitative decision model based on the trade-off between annual inventory holding costs & annual order costs. Remember Order cost (set up cost) is associated with placing an order. sometimes called setup cost. Holding Cost (carrying cost) is cost incurred for holding inventory in storage.  9 Economic Order Quantity Assumptions of the EOQ Model 1) Demand must be known & constant e.g., if there are 365 days per year and the annual demand is known to be 730 units, then daily usage must be exactly 2 units throughout the entire year (730/365=2) 2) Lead time is known & constant e.g,. if the delivery lead time is known to be 10 days, every delivery will arrive exactly ten days after the order is placed) 3) Replenishment 보충 is instantaneous (The entire order is delivered at one time and partial shipments are not allowed) 4) Price is constant (Quantity or price discounts are not allowed) 5) Holding cost is known & constant 6) Ordering cost is known & constant 7) Stock-outs are not allowed (Inventory must be available at all times)  10 Total Annual Inventory Cost (TAIC) 연간총재고비용 TAIC = Annual Purchase Cost 연간 구입비용 + Annual Holding Cost 연간보유비용 + Annual Order Cost 연간주문비용 Annual Purchase Cost (APC) = annual demand * purchase cost per unit = R*C (연간 구입비용=연간수요*단위당 가격) Annual Holding Cost (AHC) = average inventory hold across the year * annual holding cost per unit = (Q/2)*(k*C) (연간 보유비용=연평균재고수준*단위당 보유비용) Annual Order Cost (AOC) = (R/Q)*S (연간 주문비용=연주문횟수*주문 당 주문비용) Where, R = annual demand C = unit value (purchase cost per unit) Q = order quantity S = cost of placing per order (set up cost) k = holding rate (holding cost in percentage), where annual holding cost per unit = k × C  11 Economic Order Quantity Total Annual Inventory Cost (TAIC) formula TAIC = APC + AHC + AOC TAIC = (R*C) + [(Q/2)*(k*C)] + [(R/Q)*S] EOQ Cost Trade-Offs  12 Economic Order Quantity The optimum Q (the EOQ) – method 1 R, C, k, and S are deterministic (i.e., assumed to be constant terms) Q is the only unknown variable By taking the first derivative of TAIC with respect to Q and then setting it equal to zero TAIC = (R*C) + [(Q/2)*(k*C)] + [(R/Q)*S] Set,  13 Economic Order Quantity The annual purchase cost drops off after the first derivative is taken. The managerial implication here is that purchase cost does not affect the order decision if there is no quantity discount (the annual purchase cost remains constant regardless of the order size, as long as the same annual quantity is purchased) Thus, the annual purchase cost is ignored in the EOQ model  14 Economic Order Quantity The optimum Q (the EOQ) – method 2 Making Annual Holding Cost (AHC) = Annual Order Cost (AOC) Recall, AHC = average inventory hold across the year * annual holding cost per unit = (Q/2)*(k*C) Annual Order Cost (AOC) = (R/Q)*S (Q/2)*(k*C) = (R/Q)*S (Q*K*C)/2=(R*S)/Q Q2*K*C = 2R*S Q2 = 2R*S/K*C Q=  15 EOQ Exercise The LV Corporation purchases a critical component from one of its key suppliers. The operations manager wants to determine the economic order quantity, along with when to reorder, to ensure the annual inventory cost is minimized. The following information was obtained from historical data. Annual requirements (R) = 7,200 units Cost of placing an order (set up cost) (S) = $100 per order Holding rate (k) = 20% Unit cost (C) = $20 per unit Order lead time (LT) = 6 days Number of days per year = 360 days  16 EOQ Exercise A) = √1,440,000/4 = √ 360000 = 600 units The annual purchase cost= R*C=7,200units*$20=$144,000 The annual holding cost=Q/2*k*C=(600/2)*0.20*$20=$1,200 The annual order cost=R/Q*S=(7,200/600)*$100=$1,200. In EOQ, the annual holding cost equals the annual order cost The total annual inventory cost =$144,000+$1,200+$1,200 = $146,400  17 EOQ Exercise At time 0, firm starts with a complete order of 600 units The inventory is consumed at a steady rate of 20 units per day On the 24th day, the reorder point (ROP) of 120 is reached and the firm places its first order of 600 units. It arrives six days later (on the 30th day). The 120 units of inventory are totally consumed immediately prior to the arrival of the first order. The vertical line on the 30th day shows that all 600 units are received (the instantaneous replenishment). A total of twelve orders (including the initial 600 units) will be placed during the year to satisfy the annual requirement of 7,200 units.  18 EOQ Exercise EOQ - Quantity Discount model The Quantity Discount model (Price Break Model) It allows purchase quantity discounts. It considers the trade-off between larger quantities of the price discount vs. the higher inventory holding cost For example, a supplier may offer a price of $5 per unit for orders up to 200 units, $4.50 per unit for orders between 201 and 500 units, $4 per unit for orders of more than 500 units. This creates an incentive for the buyer to purchase in larger quantities if the savings is greater than the extra cost of holding larger inventory levels. Unlike the EOQ model, the annual purchase cost now becomes an important factor EOQ - Quantity Discount model The purchase price per unit, C, is no longer fixed, as assumed in the classical EOQ model derivations. The total annual inventory cost must now include the annual purchase cost, which varies depending on the order quantity. Total annual inventory cost = annual purchase cost + annual holding cost + annual order cost TAIC = APC + AHC + AOC = (R*C) + [(Q/2)*(k*C)] + [(R/Q)*S] This model creates cost curves for each price level so no single curve fits all purchase quantities. Total annual inventory cost curve combines these curves. Price break point 단가변경점: minimum quantity for discount 최소주문량 Each price level has EOQ, not always feasible due to quantity range. Optimal order quantity locates at feasible EOQ or price break point. EOQ - Quantity Discount model Two-step procedure Step1 – exercise 1 (EOQ at the Lowest Price Level Is the Optimal Order Quantity) Starting with the lowest purchase price, compute the EOQ for each price level until a feasible EOQ is found. If the feasible EOQ found is for the lowest purchase price, this is the optimal order quantity with its the lowest point on the total annual inventory cost curve. If the feasible EOQ is not associated with the lowest price level, proceed to step 2. Step 2 – exercise 2 (the Optimal Order Quantity Is at the Price Break Point) Compute the total annual inventory cost for the feasible EOQ found in step 1, and for all the price break points at each lower price level. Price break points above the feasible EOQ will result in higher total annual inventory cost, thus need not be evaluated. The order quantity that yields the lowest total annual inventory cost is the optimal order quantity.  22 Quantity Discount model Exercise 1 The K Corporation purchases a component from a supplier who offers quantity discounts to encourage larger order quantities. The supply chain manager of the company wants to determine the optimal order quantity to ensure the total annual inventory cost is minimized. The company’s annual demand forecast for the item is 7,290 units, the order cost is $20 per order, and the annual holding rate is 25 percent. The price schedule for the item is: Q1) What is the optimal order quantity that will minimize the total annual inventory cost for this component? Q2) what is the minimum total annual inventory cost?  23 Quantity Discount model Exercise 1 A1) Find the first feasible EOQ starting with the lowest price level This is a feasible EOQ because order size of 540 units falls within the order quantity range for the price level of $4.00 per unit. Thus, 540 units is the optimal order quantity. A2) The minimum total annual inventory cost is The annual holding cost equals the annual order cost because the optimal order quantity falls on an EOQ. Quantity Discount model Exercise 1 The TAIC of $29,700 corresponds to the EOQ of 540, not the price break quantity of 501 Quantity Discount model Exercise 2 The S Corporation purchases one of its crucial components from a supplier who offers quantity discounts to encourage larger order quantities. The supply chain manager of the company wants to determine the optimal order quantity to minimize the total annual inventory cost. The company’s annual demand forecast for the item is 1,000 units, its order cost is $20 per order, and its annual holding rate is 25 percent. The price schedule is: Q1) What is the optimal order quantity that will minimize the total annual inventory cost? Q2) what is the total annual inventory cost? Quantity Discount model Exercise 2 Find the first feasible EOQ starting with the lowest price level This quantity is infeasible because an order quantity of 200 units does not fall within the required order quantity range to qualify for the $4 price level (the unit price for an order quantity of 200 units is $5) This quantity is also infeasible This order quantity is the first feasible EOQ because a 179-unit order quantity corresponds to the correct price level of $5 per unit. Quantity Discount model Exercise 2 Find the total annual inventory costs for the first feasible EOQ found in step 1 and for the price break points at each lower price level The optimal order quantity is 501 units, which qualifies for the deepest discount Quantity Discount model Exercise 2 Total Annual Inventory Cost Where the Optimal Order Quantity is at the price break point  29 Reorder point The Statistical Reorder Point (ROP) This refers to the lowest inventory level at which a new order must be placed to avoid a stockout. Since the demand and delivery lead time tend to vary, safety stock is required. In-stock probability is commonly referred to as the service level. ROP = Average demand during the order’s delivery lead time + Safety stock We have two models Model 1. ROP with probabilistic (unknown) demand and constant lead time Model 2. ROP with constant demand and probabilistic (unknown) lead time  30 ROP 1 - Probabilistic Demand and Constant Lead Time This model is to Determine the lowest inventory level at which a new order should be placed This assumes that Lead time is constant Demand during delivery lead time is unknown (but normally distributed) In this model The average demand during the lead time is represented by μ The standard deviation formula is Safety stock is (x − μ) = ZσdLT (σdLT is the standard deviation of demand during the delivery lead time) ROP is represented by x = μ + ZσdLT The probability of stockout is represented by α The probability that inventory is sufficient to cover demand is (1 − α).  31 ROP 1 - Probabilistic Demand and Constant Lead Time The relationship of Safety Stock to the Probability of a Stockout  32 ROP 1 - Probabilistic Demand and Constant Lead Time Z-value can be determined from the standardized normal curve (see the Z-table) For example A 97.5 percent service level (α = 2.5%) corresponds to the Z-value of 1.96. The middle of the normal curve, where the reorder point equals the average demand μ, the required safety stock is 0 and the probability of stockout would be 50% The statistical reorder point (x) can be calculated as the average demand during the order’s delivery lead time plus the desired safety stock  33 ROP1 exercise L Inc., stocks a crucial part that has a normally distributed demand during the reorder period. Past demand shows that the average demand during lead time (μ) for the part is 550 units The standard deviation of demand during lead time (σdLT) is 40 units. The supply chain manager wants to Q1) determine the safety stock and statistical reorder point that result in 5 percent stockouts or a service level of 95 percent. Q2) the manager wants to know the additional safety stock required to attain a 99 percent service level  34 A) Calculating the Statistical Reorder Point – model 1 The normal distribution Z-table shows that a 95 percent service level (5 percent stockouts allowed) corresponds to a Z-value of 1.65 standard deviations above the Average. The required safety stock is (x - μ) = ZσdLT = 1.65 * 40 = 66 units The ROP for Q1 ROP = + ZσdLT = 550 + 66 units = 616 units This means the manager must reorder the part from their supplier when their current stock level reaches 616 units. The ROP for Q2 The required safety stock at a 99 percent service level = ZσdLT = 2.33 * 40 = 93 units. The additional safety stock compared to the 95 percent service level is 27 units.  35 ROP 2 - constant demand and probabilistic lead time Model 2. Statistical ROP with constant demand and probabilistic lead time This assumes that The demand of a product is constant The lead time is unknown (but is normally distributed) The safety stock is used to buffer against variations in the lead time instead of demand The safety stock = daily demand * σLT (the standard deviation of lead time in days) ROP = the average demand during the order’s delivery lead time + Safety stock The reorder point in this case is ROP = (daily demand * average lead time in days) + (daily demand * σLT)  36 ROP 2 - exercise The A Store has an exclusive contract with B Electronics to sell their most popular electronic pens. The demand of this e-pen is very stable at 120 units per day. However, the delivery lead times vary and can be specified by a normal distribution with a mean lead time of 8 days and a standard deviation of 2 days. The supply chain manager at A desires to Q1) calculate the safety stock Q2) calculate reorder point for a 95 percent service level  37 ROP 2 - exercise Daily demand (d) = 120 units. Average lead time ( ) = 8 days. Standard deviation of lead time (σLT) = 2 days. A service level of 95 percent yields a Z=1.65 (the Z-table) Required safety stock = d * ZσLT = 120 units * 1.65 * 2 = 396 units. ROP = (d * ) + (d * ZσLT) = (120 * 8) + 396 = 1,356 units. B must order more e-pens from A when its current inventory reaches 1,356 units