Chapter 12 Inventory Management

Reasons to Hold Inventory Meet unexpected demand Smooth seasonal or cyclical demand Meet variations in customer demand Take advantage of price discounts Hedge against price increases Quantity discounts

Inventory Costs Carrying Cost Cost of holding an item in inventory, May include cost of obsolescence Ordering Cost Cost of replenishing inventory Shortage Cost Temporary or permanent loss of sales when demand cannot be met

Inventory Control Systems Continuous system (fixed-order- quantity) Constant amount ordered when inventory declines to predetermined level Periodic system (fixed-time-period) Order placed for variable amount after fixed passage of time

Assumptions of Basic Economic Order Quantity Model Demand is known with certainty and is constant over time Demand is known with certainty and is constant over time No shortages are allowed No shortages are allowed Lead time for the receipt of orders is constant Lead time for the receipt of orders is constant The order quantity is received all at once The order quantity is received all at once

The Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0

When to Order Reorder Point is the level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

Reorder Point Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = yards/day Lead time = L = 10 days R = dL = (32.154)(10) = yards

Safety Stocks Safety stock Safety stock buffer added to on hand inventory during lead time buffer added to on hand inventory during lead time Stockout Stockout an inventory shortage an inventory shortage Service level Service level probability that the inventory available during lead time will meet demand probability that the inventory available during lead time will meet demand

Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 TC = + CoDQCoDQ CcQ2CcQ2 =- + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 =- + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

EOQ Cost Model Slope = 0 Total Cost Order Quantity, Q Annual cost ($) Minimum total cost Optimal order Q opt Q opt Carrying Cost = CcQCcQ22CcQCcQ222 Ordering Cost = CoDCoDQQCoDCoDQQQ

EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 (150)(10,000)2,000(0.75)(2,000)2 TC min = $750 + $750 = $1,500 Orders per year =D/Q opt =10,000/2,000 =5 orders/year Order cycle time =311 days/(D/Q opt ) =311/5 =62.2 store days

EOQ with Noninstantaneous Receipt Q(1-d/p) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average

EOQ with Noninstantaneous Receipt p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - Qpdp Average inventory level = 1 - Q2 dp TC = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

Quantity Discounts Price per unit decreases as order quantity increases Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

Quantity Discounts Price per unit decreases as order quantity increases Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand ORDER SIZEPRICE $

Quantity Discount Model Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 )

Quantity Discount Model Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 )