Costs involved in Inventory Models Ordering (Setup) cost Unit purchasing (Production) cost Holding (Carrying) cost Shortage (Penalty) cost Revenue (Selling price)
Basic EOQ Model EOQ: Economic Order Quantity Assumptions of EOQ models: –Demand is constant (unvarying ), expressed as annual demand (units per year ). –Models use continuous review, not periodic review. –Lead time is constant & known. –Quantity discounts are not possible. –2 variable costs: setup cost and holding cost.
Inventory Levels Inventory vs. time. Inventory ( Q ) time Usage rate (D) Cycle time (T) Lead time ( L, l ) Reorder Point (ROP)
Symbols in EOQ models Order quantity:Q Optimal order quantity: Q* Annual demand (units):D Setup cost per order:K Holding cost (per unit):H
Total Cost vs. Order Quantity. Annual Cost Order Quantity Holding cost curve Setup cost curve Combined curve: holding & setup. Minimum annual cost Optimal order quantity We’ll find an equation for this amount
Annual setup cost: equation What is related to it? Annual setup cost = DQDQ K * Q, K, & D demand / quantity per order = # of orders. # of orders * K = annual setup cost.
Annual holding cost: equation. Q: order quantityQ & H. inventory is replenished precisely when no inventory remains. Average inventory = Q time Constant slope Q/2
Annual holding cost: equation. Q time Annual holding cost = Q2Q2 H *
Finding where they are equal. The minimum cost of the system will be found where ASC = AHC. AHC = Q2Q2 H * ASC = DQDQ K *
Solve for Q The minimum cost of the system will be found where ASC = AHC. Q2Q2 H * DQDQ K * =
Solve for Q The minimum cost of the system will be found where ASC = AHC. Q2Q2 H 2DK =
Solve for Q The optimal order quantity that results in the lowest system cost is called Q* Q* H 2DK =
Holding costs Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs: cQ 2 H c =
Holding costs Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs: i * cQ 2 H f =
Holding costs Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs: sQ 2 H s =
Total holding costs Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs: ( s + i c ) Q 2 H t =
Other factors (lurking in the shadows) Unit cost (production cost): cost per unit to buy the inventory: symbol “c” Annual unit cost = cD
Other factors (lurking in the shadows) Revenue: profit per unit of inventory sold: symbol “r” Annual revenue = rD
Total Cost of the System ( s + i c ) Q 2 Total cost = cD + + DK Q Cost of the products Cost of ordering Cost of inventory
Determine reorder point Demand is constant. Lead time is known. Qtime ROP L Q LTLT =
MS Excel example (Go to it)
Preview of Thurs.: 2 other models (ind. D) Production Order Quantity Model Quantity Discount Model Homework: due Thursday p. 470, #1, 2, 4 - turn in ON PAPER (preferably computer printouts, each on 1 sheet of paper that can be understood by someone who WASN’T there when you set it up.)