ATG 312 Inventory Systems hapter 20 Economic-Order-Quantity Decision Model The economic-order-quantity (EOQ) is a decision model that calculates the optimal quantity of inventory to order under a restrictive set of assumptions. The simplest version of this model incorporates only ordering costs and carrying costs into the calculations. The EOQ minimizes the relevant ordering costs and carrying costs. Relevant total costs = Relevant ordering costs + Relevant carrying costs 2 Assumptions The same fixed quantity is ordered at each reorder point. Demand, ordering costs, and carrying costs are known with certainty. Purchase-order lead time the time between placing of an order and its delivery is also known with certainty. Purchasing costs per unit are unaffected by the quantity ordered. Data required: Expected demand Price Ordering cost arrying costs 3 4 PLANNING AND ONTROL OF STOKS 1. Reasons for holding stocks Transaction motive (e.g. special sale) Precautionary motive (e.g. strike ) Speculative motive (e.g. new tax charge of goods) 2. Relevant costs required for determining EOQ Holding costs Ordering costs PLANNING AND ONTROL OF STOKS 3. Holding costs Opportunity cost of investment in stocks Incremental insurance costs Incremental warehouse and storage costs Incremental material handling costs osts of deterioration and obsolete stocks 4. Ordering costs Incremental clerical costs of preparing a purchase order, receiving deliveries and paying invoices. 1
EOQ (economic order quantity) Holding costs can be minimised by placing many small orders i.e. holding low stock levels, but then ordering costs are large. Determining the EOQ (Tabulation method) onversely ordering costs can be minimised by placing few large orders, but then holding costs are large. At a particular order quantity the combined annual holding and ordering cost is a minimum the EOQ EOQ can be done three ways Tabulation method Graphical method Formula method Economic order quantity (graphical method) EOQ formula method (example) Q used instead of EOQ Example 1: Prasan s demand for computer paper is 7,000 cartons per year. The cost of each carton is $70 and carrying cost is $3.50 per carton. A price increase of $10 per carton has recently been announced that will take effect next year. The Prasan budget for next year also includes an increase in carrying costs to $6.40 per carton. In addition, a study of the demand for computer printouts indicates that Prasan will use 7,200 cartons of paper next year. It costs $10 to place an order for paper. a) alculate the economic order quantity for the current budget year. b) Determine the EOQ for the next budget year. 2(7,000 units )($10) $3.50 = 200 cartons 2
2(7,200 units )($10) $6.40 = 150 cartons Example 2 Jenifer Louise sells packages of blank video tapes. Jenifer Louise purchases packages of video tapes from Amanda, Inc., at $15 per package. Annual demand is 12,844 packages. Jenifer Louise requires a 15% annual return on investment. Jenifer Louise additional data: Relevant ordering cots per purchase order $209 Relevant other carrying costs $3.25 per unit Required: What is the economic-order-quantity? 2(12,844 units )($209) $5.50 = 988 cartons Please note: Relevant carrying costs per package per year: Required annual return on investment (15% $15) = $2.25 + Relevant other costs of $3.25 = $5.50 Other factors in calculating EOQ Lead time Safety stocks Rate of usage of inventory during lead time Reorder points and safety stock Having determined the EOQ, we next need to determine how often to order. This requires calculation of the reorder point and level of safety stock. Aim is to minimise holding costs while avoiding stock-out costs Reorder point: point to reorder inventory or to initiate production of new inventory depends on: 1. EOQ (or economic batch size) 2. Lead time: time between order and receipt/ production of inventory 3. Rate of usage of inventory during lead time onstant rate of usage If usage rate and lead time known with certainty; no safety stock is required to protect against stock-out and reorder point is: Reorder point = Lead time average usage per period Eg: EOQ = 1,000 units; Lead time is 2 weeks; average usage per week is 200 units Reorder point = 2 weeks 200 units = 400 units Business should reorder 1,000 units whenever inventory level reaches 400 units 3
Variable rate of usage If usage fluctuates (usually the case); then safety stock (buffer to meet demand) is required to minimise risk of stock-out Safety stock = maximum expected usage in period (average usage per period) Reorder point = (Lead time average usage per period) + safety stock Eg: From before: maximum demand per week = 300 units (average demand is 200 per week) Safety stock = 600 units 400 units = 200 units Reorder point = 400 units + 200 units = 600 units Business should reorder 1,000 units when inventory level reaches 600 units. Determining when to place the order 1. Assume: EOQ = 600 units; Lead time = 2 wks; Usage per wk = 120 units 2. Re-order point = 2 weeks 120 units = 240 units. With an EOQ of 600 units orders will be placed at fiveweekly intervals. Uncertain demand If weekly demand exceeds 120 units there will be a stock-out. 1. Therefore safety stocks are maintained and re-order point is: (Average usage during average lead time) + (Safety stocks) JIT purchasing and production JIT Purchasing Supplier Minimise EOQ JIT Production Raw Materials Store WIP Finished Goods Store ustomer JIT purchasing EOQ 2DO H From EOQ formula: EOQ decreases if: 1. ost of placing an order decreases; and/or 2. ost of holding inventory increases Holding costs generally more difficult than ordering costs to reduce If good relationship with supplier (long-term) ordering costs can become minimal As ordering cost (O) approaches zero in formula; EOQ approaches 0 (in reality to 1 unit per order) onditions for JIT purchasing Reliable supplier (can t afford stock-outs as whole factory could stop). Long-term relationships must be beneficial to both parties (may not be the cheapest supplier). Geographically close (realistic transport time) eg Japanese model where main factory is surrounded by satellite supplier factories. JIT production If production process uses advanced manufacturing technology (AMT) JIT can also be used in production (AMT also called flexible manufacturing technology - FMT). EOQ 2DB H Economically worthwhile (inventory value must be sufficient that delivery costs per order aren t excessive). 4
JIT production inventory levels But JIT production does not mean that zero inventories will be held as customers may still require immediate supply of products (i.e. can t usually make to order have to have a minimum level of finished goods inventories to avoid stockout costs). Workshop Evans ompany has the following information: Annual demand 4,000 units Order size 1,000 units Ordering cost per order $500 arrying costs per unit for one year $50 Lead time (maximum 20 days) 10 days Maximum daily use 25 units Work year 250 days Required: a. Determine the economic order quantity for Evans. b. What is the annual savings to Evans ompany if it was to change from an order size of 1,000 to the economic order quantity? c. What is the reorder point? d. What is the safety stock needed to prevent stockouts? entennial Manufacturing ompany estimates that it will consume 400,000 units of Part 101 in the coming year. The ordering cost for this unit is $3.20. What would be the carrying costs per unit if the EOQ model indicates that it is optimal to place exactly 50 orders for the upcoming year? Lemmons orporation estimates that it will consume 400,000 units of Part 303 in the coming year. The ordering cost for this unit is $3.20. Lemmons orporation wants to maintain a safety stock of 1,000 units, and its factory operates 200 days per year. What is the order point if the lead time is 2 days? Delectable Delights manufactures a special blend of beef marinade. The company buys one of the spices used in the marinade in 10-pound bags that cost $5 each. The company uses 50,000 of the bags per year, and usage occurs evenly throughout the year. The average cost to carry a 10-pound bag in inventory per year is $1. The cost to place an order is $12. 1. Determine the economic order quantity for the spice in terms of 10 pound bags. 2. If the company works 250 days per year, on average how many bags of spice are used per working day? 3. If the lead time for an order is normally five working days, determine the reorder point. 4. If the company normally carries 50 bags as safety stock, determine the reorder point for the spice. Reed orporation produces lawn chairs. In order to produce the frames for the furniture, special equipment must be set up. The setup cost per frame is $50. The cost of carrying frames in inventory is $4 per frame per year. The company produces 10,000 lawn chairs per year. 1. ompute the number of frames that should be produced per setup in order to minimize total setup and carrying costs. 2. ompute the total setup and carrying costs associated with the economic order quantity? 5