13 Inventory Management Inventory Independent Demand Dependent Demand

13 Inventory Management

Inventory Independent Demand Dependent Demand A C(2) B(4) D(2) E(1) D(3) F(2) Independent demand is uncertain. Dependent demand is certain.

Inventory Models n Independent demand – finished goods, items that are ready to be sold n n E. g. a computer Dependent demand – components of finished products n E. g. parts that make up the computer

Types of Inventories n Raw materials & purchased parts Partially completed goods called n Finished-goods inventories n work in progress n (manufacturing firms) or merchandise (retail stores)

Types of Inventories (Cont’d) n n Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers

Functions of Inventory n n n To meet anticipated demand To smooth production requirements To protect against stock-outs

Functions of Inventory (Cont’d) n n n To help hedge against price increases To permit operations To take advantage of quantity discounts

Objective of Inventory Control n To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds n Level of customer service n Costs of ordering and carrying inventory

Effective Inventory Management n A system to keep track of inventory n A reliable forecast of demand n Knowledge of lead times n Reasonable estimates of n n Holding costs n Ordering costs n Shortage costs A classification system

Inventory Counting Systems n Periodic System Physical count of items made at periodic intervals n Perpetual Inventory System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

Inventory Counting Systems n n (Cont’d) Two-Bin System - Two containers of inventory; reorder when the first is empty Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached 0 214800 232087768

Key Inventory Terms n Lead time: time interval between ordering and receiving the order n Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year n Ordering costs: costs of ordering and receiving inventory n Shortage costs: costs when demand exceeds supply

ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - mod. important C - least important High Annual $ value of items A B C Low High Percentage of Items

Economic Order Quantity Models n Economic order quantity (EOQ) model n The order size that minimizes total annual cost n Economic production model n Quantity discount model

Assumptions of EOQ Model n n n n Only one product is involved Annual demand requirements known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery Inventory Level = 0 when new order just arrived There are no quantity discounts

The Inventory Cycle Q Quantity on hand Profile of Inventory Level Over Time Usage rate Reorder point Receive order Place Receive order Lead time Place Receive order Time

Total Cost Annual Total cost = carrying + ordering cost TC = Q H 2 + DS Q

Annual Cost Minimization Goal Ordering Costs QO (optimal order quantity) Order Quantity (Q)

Minimum Total Cost The total cost curve reaches its minimum where the Carrying Cost = Ordering Cost Q H 2 = DS Q

Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Economic Production Quantity (EPQ) n Assumptions n n n n Only one product is involved Annual demand requirements are known Usage rate is constant Usage occurs continually, but production occurs periodically The production rate is constant Lead time does not vary There are no quantity discounts 12 -21

EPQ: Inventory Profile Q Q* Production and usage Usage only Production and usage Cumulative production Imax Amount on hand Time 12 -22

Quantity Discount Model n Quantity discount n Price reduction offered to customers for placing large orders 12 -23

Quantity Discounts 12 -24

Quantity Discounts 12 -25

When to Reorder with EOQ Ordering n Reorder Point - When the quantity on n Safety Stock - Stock that is held in n Service Level - Probability that demand hand of an item drops to this amount, the item is reordered excess of expected demand due to variable demand rate and/or lead time. will not exceed supply during lead time.

Determinants of the Reorder Point n n The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)

Safety Stock reduce risk of stockout during lead time

Reorder Point The ROP based on a normal Distribution of lead time demand Service level Risk of a stockout Probability of no stockout Expected demand 0 ROP Quantity Safety stock z z-scale

Single Period Model n Single period model: model for ordering n Shortage cost: generally the unrealized n Excess cost: difference between of perishables and other items with limited useful lives profits per unit purchase cost and salvage value of items left over at the end of a period

Single Period Model n Continuous stocking levels n n n Identifies optimal stocking levels Optimal stocking level balances unit shortage and excess cost Discrete stocking levels n n Service levels are discrete rather than continuous Desired service level is equaled or exceeded

Optimal Stocking Level Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit Ce Cs Service Level Quantity So Balance point

Example 15 n n Ce = $0. 20 per unit Cs = $0. 60 per unit Service level = Cs/(Cs+Ce) =. 6/(. 6+. 2) Service level =. 75 C e Service Level = 75% Stockout risk = 1. 00 – 0. 75 = 0. 25 Quantity Cs

Operations Strategy n Too much inventory n n Tends to hide problems Easier to live with problems than to eliminate them Costly to maintain Wise strategy n n Reduce lot sizes Reduce safety stock