Supply Chain Inventory Management – Independent Demand Items
Chapter 5 Vollmann, Berry, Whybark & Jacobs
Analyze the facts before making key decisions
On June 25th, 1876 General George Armstrong Custer received information that a significant number of Indians were gathering at Little Big Horn. Without analyzing the facts, he decided to ride out with 250 men to “surround” almost 3000 Indians….
What items have independent demand?
Items found at many points in the supply chain such as:
Finished Goods Inventories in factories, warehouses, distribution centers, spare-parts inventories, office supplies, maintenance materials.
Independent demand: the demand is primarily influenced by factors outside the company‟s decisions. These external factors induce random variation in the demand for such items. Thus demand will be projections of historical patterns. These forecasts estimate the average usage rate and a pattern of random variation.
Functions of Inventory
Transit stock: depends on the time to transport goods from one location to another (also called pipeline inventories). It can be modified by speeding the means of transportation or decreasing the distance between places. Cycle Stock: exists whenever orders are made in larger quantities than needed to satisfy immediate requirements.
Functions of Inventory
Safety Stock: provides protection against irregularities or uncertainties in an item demand or supply (when demand exceeds forecast or when re-supply time is longer than anticipated. Anticipation Stock: is needed for products with seasonal patterns of demand and uniform supply.
Decisions Needed in Inventory Management
How much to order (size) When to order (timing) using Decision Rules Order Quantity Order Frequency Fixed Q* Variable Sΐ Variable R‡ Q, R S, R
Fixed T§ where
Inventory Decision Rules
Q* is an order for a fixed quantity Q. Sΐ is an order up to a fixed expected opening inventory quantity S. R‡ Place an order when the inventory balance drops to R. T§ place an order every T periods.
Inventory System Performance
Inventory turnover – Annual Sales volume divided by the average annual inventory investment. DELL DATA January „03 Inv 1/02 – 278 Inv 1/03 – 306 Sales in 02/03 = 35404
35404/(306+278)/2 = 121/yr
Inventory System Performance
Fill Rate – Customer service performance metric – the percentage of units immediately available when requested by the customer. Percentage of different items that were available Number of times shortages occurred in a time period Length of time before an item was available
Inventory Related Costs
Order preparation costs. – Search for variable costs associated with the elaboration of the order. Inventory Carrying costs – Cost of capital + taxes + insurance + obsolescence + shelf life + storage space + pilferage Shortage costs – they tend to be more difficult to measure (not high unless goodwill is lost).
Inventory Related Costs
Service costs – Can be estimated by the level of investment necessary to provide the desired level of service.
Incremental Inventory Costs
Does the cost represent an actual out-ofpocket expenditure or a foregone profit? Does the cost actually vary with the decision being made? (i.e. purchase cost fixed or variable? – discounts)
Order quantity decisions primarily affect the amount of inventory held in cycle stocks at various points along the supply chain. Large order quantities mean orders placed infrequently and lead to low annual costs of preparing replenishment orders but means higher cycle inventory costs of carrying excessive inventory.
Economic Order Quantity Model 
Total Annual Cost equation: TAC = (A/Q)* Cp + (Q/2)*CH Where A = Demand per year Q= quantity to be ordered Cp = Cost per order or set-up CH = Cost per unit/unit-of-time
First part of the expression is the cost of ordering and
the second is the inventory carrying cost.
Optimum value for t.v. example
_________ EOQ = √2*Cp*A/CH
If A = 1250 units/year Cp = 6.25 $/order (or setting up) CH = 25 $/unit/year ______________ EOQ = √2*6.25*1250/25 = 25 When we buy tv‟s we should buy them in lots of 25.
Number of orders: NO NO = Demand/EOQ = 1250/25 = 50 orders/year (one every week) Time between orders TBO TBO = 1/NO = EOQ/Demand The rule is Q,T. Buy 25 units every week. Total cost/year = TAC = (A/Q)* Cp + (Q/2)*CH=1250/25*6.25+25/2*25=625
A major equipment producer sells 4000 units of its $90/unit product per year. Ordering costs are $30 and holding costs are 8% of the product unit value per year. Each items requires 5 square meters for storage (product cannot be piled on top of each other) and there is currently space in the warehouse. The space available is of size 20 by 40 meters to store the items. a) What lot size should he use? b) What should be the total stocking costs per year? c) Does he need additional space? How much, if any?
________________ a) Q* = √2*4000*30/(.08*90) = 182.6 b) TSC = 4000/182.6*30 + 182.6/2*(.08*90) = 652.6 + 652.6
c) Area = 182.6*5 = 912.9
Area = 20*40 = 800 Additional area needed = 112.9 m2
A firm manufactures a part which it uses in a downstream operation. The parts are needed at a rate of 180 parts per day. Set up costs is $150 and the carrying cost is $0.25 per unit per year. The firm operates 250 days per year. a) What is the economic lot size? b) What is the total stocking cost?
__________________ Q* = √2*(250*180)*150/0.25 = 7348.5 TAC = 7348.5/2*.25 + 250*180/7348.5*150 = 918.6 + 918.6 = 1837.1
Safety stock can be defined as the amount of product that is carried in addition to the expected demand to provide a specified level of protection against a stock-out. Service Level refers to the number of units of an item demanded that can be supplied from stock currently on hand.
Order Timing Decision (Q,R) 
In this case we will order Q (quantity fixed) when the inventory level reaches R (reorder point). Factors: Demand rate, lead time to replenish inventory, amount of uncertainty in the demand rate, and management policy regarding level of customer service.
Probability of stock-out criterion
The system perpetually monitors the inventory level and places a new order (equal to Q*) when the stock level reaches some level R. The value of R is calculated using: R=d+S (EDDLT + SS) R = d + Zσd where d is the average demand during lead time Z is the Z score associated with a service level (1.645 for a 95% S.L.). σd is the standard deviation of usage during lead time.
Example Text p 147-8
Q = 5; σd = 1.5; SL = 95%
R = d + Z σd = 5 + 1.645*1.5 = 5 + 2.5 = 7.5 Order 5 (Q) whenever the inventory level is below 7.5 (8). So, what does this mean?
Customer Service Criterion
The number of units short in one year (time period) is equal to the percentage short times the annual demand. (1 – SL) * D This is equal to the number of units short per order (σd E(Z)) times the number of orders per year (time period). σd E(Z) [D/Q] SL = σd E(Z)/Q E(Z) = Q(1- SL)/σd
Example Text (p148-9)
Q = 5; σd = 1.5 SL = 95%
E(Z) = Q(1 - .05)/σd = 5*.05/1.5 = .167 From the tables Z = 0.6
R = d + Zσd = 5 + 0.6*1.5 = 5 + 0.9 = 5.9 Order 5 when the inventory level reaches 5.9
A service station is located right across campus. His gas sales have been going down. To improve his sales he is considering utilizing some available space to place some soda vending machines. When he orders, he usually orders 10 cases (240 cans). He estimates that the daily demand can be approximated by a Normal distribution with a mean of 75 cans and a standard deviation of 10 cans. He also feels that an 85% (very sophisticated gas station owner) service level would be adequate. His soda supplier promises that his lead time will be exactly 4 days. a) What should his reorder point be? b) What is the safety stock?
Solution in terms of probability of stock-out
a) N(75, 10) Time period correction factor N(75*4, 10√4) p.149
R = d + Z σd = 4*75 + (1.04)*(10 √4) = 300 + 20.8 = 321
b) Safety Stock SS = 20.8
D = annual demand 1000 units LT=15days Q = 200 units Service Level = 95 % (.95) Working days/yr = 250 σd=50 units Average demand/day=1000/250 = 4 units/day R = d + Z σd = 4*15 + Z(50) E(Z)=(1-.95)200/50 = 0.2 from tables Z = 0.49 R = 4(15) + 0.49*50 = 84.5 R = 4(15) + 1.645*50 = 142.25
Policy: When inventory level gets to 85 or less then order 200. What is the expected number of units short per order? E(Z) σd = 0.2 * 50 = 10 How many orders per year? (1000/200)= 5 Total number of units short? 10*5 = 50 (Service level is 95%; 950/1000)
Dollar Usage Category # of items % of items % of $ use A 15 11 84% B 25 15 15 C 88 74 1 Total 128 100 100
ABC Analysis - Criticality
Criticality Category # of items % of items % of $ use I 5 4 40% II 48 39 56 III 75 57 4 Total 128 100 100
ABC Analysis – Two sided view
Dollar Usage A B C Total Criticality I II III Total 2 12 1 15 1 19 5 25 2 17 69 88 5 48 75 128
ABC Analysis – Combined
Combined # Category of items AA 14 BB 16 CC 98 Total 128 % % of items of $ use 11 78% 13 12 76 10 100 100
Inventory Management Policy Parameters for Multiple ABC
AA BB CC
Order quantity Safety Stock Reclassify Review
Every 6 months
Small for Medium – costly items EOQ based Large for Large for critical critical items items Every six Every six months months
Large quantities Low or none