Supply Chain Inventory Management – Independent Demand Items

Chapter 5 Vollmann, Berry, Whybark & Jacobs

Analyze the facts before making key decisions

On June 25 th , 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.

Basic Concepts

 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.

Inventory Decision Rules

 Q * is an order for a fixed quantity Q.

 S ΐ 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.

Decisions Needed in Inventory Management

 How much to order (size)  When to order (timing) using  Decision Rules Order Frequency Variable R ‡ Order Quantity Fixed Q * Variable S ΐ Q, R S, R Fixed T § where Q, T S, T

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 Turnover 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 Il valore del Safety Stock può essere determinato per migliorare alcune di queste performance

Inventory Related Costs

 Service costs – Can be estimated by the level of investment necessary to provide the desired level of service.

Cost Trade-Off

(pag. 140)  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 [1]

pag. 142 Total Annual Cost equation: TAC = [ (A/Q )numero di ordini all’anno]* C p + [ (Q/2 )quantità media in magazzino con consumo lineare]* C H Where A = Demand per year Q= quantity to be ordered C p = Cost per order or set-up (quantità fissa) C H = 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

 _________

Min TAC (una retta + un’iperbole) =>

EOQ = √2*C p *A/C H If A = 1250 units/year C p = 6.25 $/order (or setting up) C H = 25 $/unit/year ______________ EOQ = √2*6.25*1250/25 = 25 When we buy tv’s we should buy them in lots of 25.

More information

 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)* C p + (Q/2)*C H =1250/25*6.25+25/2*25=625

Example

    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?

Example (Cont.)

________________  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

Example

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) b) What is the economic lot size?

What is the total stocking cost?

Example (cont.)

a) __________________ Q * = √2*(250*180)*150/0.25 = 7348.5

b) TAC = 7348.5/2*.25 + 250*180/7348.5*150 = 918.6 + 918.6

= 1837.1

Service Level

 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 (S.L. - Example of: ”management policy regarding level of customer service”) refers to the number of units of an item demanded that can be supplied from stock currently on hand.

Order Timing Decision (Q,R) [2]

 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 is calculated using: * ) when the stock level reaches some level R. The value of R R = d + S (valori discreti) S : safety stock, may be Z σ d R = d + Z σ d (valori continui) : where d is the average demand during lead time and Z is the Z score associated with a service level (1,645 for a 95% S.L.). σ d is the standard deviation of usage (demand) during lead time.

Example Text p 147-8

Q = 5; σ d = 1.5; alla consegna) SL = 95% (probabilità che la domanda sia soddisfatta durante il periodo di rimpiazzo, cioè dall’ordine R = d + Z σ d = 5 + 1.645*1.5 = 5 + 2.5

= 7.5 (Z σ d : deviazione che taglia fuori il 5% sulla gaussiana; qui vale 2,5) Order 5 (Q) whenever the inventory level is below 7.5 (8).

So, what does this mean?

Example

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 σ d = 4*75 + (1.04)*(10 √4) = 300 + 20.8 = 321 b) Safety Stock SS = 20.8

ABC Analysis

Dollar Usage Category # of items % of items % of $ use A B 15 25 11 15 84% 15 C Total 88 128 74 100 1 100

ABC Analysis - Criticality

Criticality Category # of items % of items % of $ use II I 5 48 4 39 40% 56 III Total 75 128 57 100 4 100

ABC Analysis – Two sided view

Dollar Usage I II A B Criticality 2 1 12 19 III Total 1 15 5 25 C Total 2 5 17 69 88 48 75 128

ABC Analysis – Combined

Combined # % % Category of items of items of $ use AA BB 14 16 11 13 78% 12 CC Total 98 128 76 100 10 100

Inventory Management Policy Parameters for Multiple ABC

AA BB CC Counting Frequency Monthly Every 6 months Yearly Order quantity Safety Stock Reclassify Review Small for costly items Large for critical items Every six months Medium – EOQ based Large for critical items Every six months Large quantities Low or none Yearly