IM 322 Inventory Management -1- Chapter 3 Economic Order Quantity Model (EOQ) Textbook: Donald Waters, Inventory Control and Management, 2 nd ed
Chapter Outline 2
Quantitative Inventory management Quantitative Inventory management answers two primary questions: How much to order: Order Quantity or Economic Order Quantity (EOQ) When to order: Reorder point 3
Typical pattern of stock level over time Inventory level Reorder point Q 1 Q 2 0 Lead Time Lead Time 4 Time
Economic Order Quantity (EOQ) ปร มาณการส งซ ออย างประหย ด Idealized stock To find the fixed order size that minimizes costs Basis of most independent demand Order quantity, Q Inventory Level Demand rate Reorder point, R 5 0 Lead time Order placedorder receipt Lead time Order placed Order receipt Time
Basic Economic Order Quantity (EOQ) ปร มาณการส งซ ออย างประหย ด Model Assumptions Demand is known exactly, is continuous and is constant over time All costs are known exactly and do not vary Ex: holding cost, purchase price, and reorder costs do not vary with the quantity ordered No shortages are allowed Lead time is constant 6
Pressures for Low Inventories When keeping inventory, there are always some cost incurred Inventory holding cost (or carrying cost) The variable cost of keeping items on hand $/ unit-period Inventory holding cost generally includes: Interest of opportunity cost Storage and handling costs (e.g., electricity, utilities, documentation, labor costs) Tax, insurance, and shrinkage 7
Pressures for High Inventory Customer service Reorder or Ordering cost ($ / order) Setup cost Transportation cost Payment to suppliers Labor and equipment utilization 8
Variables used in the analysis Unit Cost (UC) Price charged by the suppliers for one unit of item, or Total cost to organization of acquiring one unit $ / unit Reorder cost (RC) Cost of placing a routine order $ / order, $/setup Holding cost (HC) Cost of holding one unit of the item in stock for one period of time $ / unit-period Shortage cost (SC) Cost of having a shortage and not being able to meet demand from stock $ / unit-period 9
Variables used in the analysis Order quantity (Q) Fixed order size Cycle time (T) Time between two consecutive replenishment Depends on Q Demand (D) The number of units to be supplied from stock in a given time period Basic EOQ assumes known constant demand 10
Derivation of the EOQ EOQ: the lot size or order size that minimizes total annual inventory holding and ordering cost Under basic EOQ Amount entering stock in cycle, Q = Amount leaving stock in cycle, D x T Total cost per cycle = Unit cost component Reorder Cost component + + Holding Cost component 11
Derivation of the EOQ Slope = 0 Total Cost Minimum total cost Holding Cost Reorder Cost Optimal order Q o 12
Ex 1: Carpet Sales The I-75 Carpet store stocks carpet in its warehouse and sells it through a showroom. The store keeps several brands and styles of carpet in stock; however, its bigger seller is the BIG C carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, an annual carrying cost of $0.75 per yard, and an ordering cost of $150. The store would like to know the number of orders that will be made annually and the time between orders given that the store is open every except Sunday, Thanksgiving Day and Christmas Day. 13
Adjusting EOQ 14
Sensitivity Analysis Use estimates of relevant costs Ignore uncertainty in demand What happen if the holding / ordering cost is off by 20%, 30%? Consider 4 cases of variations of the model parameters. 1. Both ordering and carrying costs are 10% less than the original estimates 2. Both are 10% higher 3. Ordering cost is 10% higher and carrying cost is10% lower 4. Ordering cost is 10% lower and carrying cost is 10% higher Determine EOQ in each case. Remark on the sensitivity of Q on the estimated total cost. 15
Adding Finite Lead Time 16
Reorder Level Additional assumption: Lead time is known and constant No need to carrying stock from one cycle to the next So each order should be scheduled to arrive as existing stock runs out Reorder level = demand during lead time = lead time x demand per unit tim ROL = LT x D Revisit Ex 1: Carpet Sell. Given that product lead time is 5 days. Calculate reorder level (ROL) 17
Reorder Level with Longer Lead Time When lead time is longer than the stock cycle There is always one order outstanding. Example: when it is time to place order B, there is one order, A outstanding and due to arrive before B. The stock on hand plus the outstanding order must be enough to last until B arrive or equal the lead time demand ROL Stock on hand ROL = LT x D + Stock on order = LT x D - Stock on order 18
Reorder Level with Longer Lead Time When lead time is very long Several orders are outstanding at anytime When lead time is between n and n+1 cycle length n x T < LT < (n+1) x T There are n orders outstanding ROL = Lead time demand - Stock on order = LT x D - n x Q o 19
Ex 2 Demand for an item is steady at 1,200 units a year with an ordering cost of $16 and holding cost of $0.24 per unit per year. Describe a appropriate ordering policy if the lead time is constant at (a) (b) (c) 3 months 9 months 18 months 20
Discussion Questions What are the benefit of short lead times? How can these be achieved in practice? 21
EOQ. Derivation
EX1 Carpet Sales