Inventory Management

UGBA 141Spring 2014

Why Hold Inventory?

• Customer Service• Demand-Supply Decoupling• Protection Against Uncertainties• Decoupling of Successive

Manufacturing Stages• Economies of Scale

Types of Inventory

• Raw materials and purchased parts• Work-in-process (WIP)• Pipeline (or in-transit)inventory• Spare parts inventory• Cycle stock• Safety stock• Facilitating and support stock

Importance of Inventory Investment

• Inventories constitute a significant portion of manufacturing or retail firm’s assets

• Well-managed inventories can be a competitive weapon

Inventory at Major Corporations

Company Ann. Sales Inventory TurnsHP 120.3 bill. 6.3 bill.

19.1Dell 62.1 bill. 1.4 bill. 44.4Wal-Mart 469.0 bill. 43.8 bill. 10.7Target 73.3 bill. 7.9 bill. 9.3

Inventory plays a key role in Supply Chain Management…

• As supply chains become more decentralized and more global:– goods are transported more frequently and

further• how much inventory and where?• in what quantities to produce and transport?

• As competitive pressures increase:– need to drive down costs and– need to improve customer service

Inventory Costs

• Opportunity costs of capital• Other holding costs• Procurement costs• Setup costs• Shortage costs

Issues in Designing an Inventory Control System

• Strategic:– What level of service to provide

• Operational:– Sourcing

• Tactical– How frequently to monitor the inventory for re-ordering– How often to order– How much to order– What mode of transport

Inventory Control Models

• Single-stage settings– Retailer– Wholesaler– Single manufacturing stage within larger system

• Multi-stage manufacturing and assembly

Building Blocks: Single Stage

• Economic Order Quantity (EOQ) Model– Main tradeoff is between setup costs and cost of

holding inventory• Continuous Review (Q,R) Model– Adds a reorder point, R, to the EOQ model to allow for

uncertainty during delivery leadtime• Newsvendor Model (already covered)– For seasonal goods with little value at end of season

• Periodic Review (P,T) Model– Constant reorder cycle T (to be decided) with order-up-

to level (P) that accounts for uncertain demand

Economic Order Quantity (EOQ)

• Scenario:– Known, constant demand– Product will be sold indefinitely– “Setup” (volume-independent) cost incurred for

each order– Inventory holding costs incurred based on the

average inventory level– Choose an order quantity that minimizes total

setup and inventory costs per unit time

Economic Order Quantity ModelInventory

Q

time

EOQ Cost Function

• Notation:D: annual demandS: fixed cost (setup cost) per order C: unit procurement or production costi: annual inventory holding cost rate Q: order quantity (decision)

Interpretations of Costs

• Setup cost– cost incurred, independent of volume– examples?

• Annual inventory holding cost rate– fraction of item value– includes cost of physical storage, opportunity cost

of capital, obsolescence, etc.

EOQ Cost Function, cont.• Number of orders per year: D/Q• Average inventory: Q/2 (why?)• Total annual cost =

• Optimal quantity =

Cost Function• Total Cost

total cost

setup cost inv. cost

Order Quantity

Example: Real scenario with disguised numbers

• A factory of a multi-national company in Mexico, just across the border from Texas, produces family of similar electronic components for automobiles that are assembled at an assembly plant in Texas that operates 2 shifts each day.

• The multinational company is required to provide vendor-managed inventory services (delivery, consignment, etc.)

Example, cont.

• The usage of components within a 4-hour period has a Normal distribution with a mean of about 250 and a standard deviation of 20, and each component has a value of about $100.

• The company uses an annual inventory holding cost rate of 50% and operates 250 days per year.

Example, cont.

• It costs about $100 for transporting one truckload from one location to the other, and takes four hours including delays at the border.

• The automobile assembly plant charges $200 for each unit short of satisfying demand on time. (many analogous situations in various industries)

For EOQ: ignore demand uncertainty

Continuous Review (Q,R) Model

• For products with stable mean demand but random fluctuations– Examples:

• Takes into account positive delivery lead time and demand uncertainty by adding another control knob: R (reorder point)

Inventory DynamicsInventory

Q

R

LTime

What the idea?

• Will not run out while inventory is above the reorder point if R > 0, but may run out between time of order placement and when it arrives.

• Set R so that the probability of running out during the lead time is small.

• Probability of NOT running out is called the service level.

Computing R (for Demand with Normal Distribution)

• R = mean demand during the lead time + z * standard deviation of demand during the lead time

= mLT + z sLT where z is the number of standard deviations

from the mean

Service Level vs. z

Service Level z80% 0.8590% 1.28

95% 1.6598% 2.06

99% 2.3399.5% 2.58

99.9% 3.09

Reorder Point vs. Service Level

R

80 90 100 service level

What’s the Right Service Level?

• What are the costs and benefits of increasing the reorder point by one unit?– Costs: On average, need to hold an extra unit of

inventory for an entire ordering cycle– Benefits: Prevent a shortage if demand during the

lead time exceeds the current reorder point.

(Will return to this point in more detail later)

Numerical Example

Periodic Review “Order-up-to” System

• For products with stable mean demand but random fluctuations

• For situations in which you cannot justify continuous monitoring of inventory or immediate ordering upon reaching R

• For situations in which it is administratively or economically sensible to check inventory levels and reorder several products at the same time

How System Operates• Every P time units an order is placed (P may be

decided)• Delivery lead time is L time units• Order up to T (quantity to be decided):

Order enough so that on-hand inventory plus on-order inventory less backorders is equal to T Equivalently, order quantity =• T - on-hand - on-order + backorders

Equivalently, order what you sold since the last time you ordered

Inventory Dynamics

Deciding P

• Can use EOQ model, but convert order quantity to “time between orders”

Setting T

• Same as newsvendor model except that we must consider demand distribution during P + L time units– P+L time units elapse from time of order to time of

receipt• If demand in each time unit is Normal with mean m

and standard deviation s and demands are independent, then demand during P+L time units Normal with mean (P+L)m and standard deviation

Calculating for Normal Dist’n

Numerical Example

Observations

• Average ordering frequency is the same in (Q,R) and (T,P) models

• For (Q,R) system, order quantity is fixed, but order timing fluctuates

• For Periodic Review system, order timing is fixed but order quantity fluctuates– easier to coordinate procurement of multiple products

from same supplier– easier for supplier to know when to expect an order– but transportation needs fluctuate

Practical Aspects--Estimating the Demand Distribution

• Tendency to underestimate the uncertainty or variability

• Difficult to estimate extreme values• Lost sales are usually not observed

so demand data may be censored• With new products, useful

historical data may not be available

Practical Aspects: Estimating Costs

• Setup costs are not distinguished in financial statements or engineering reports: need to investigate what really changes if number of setups changes

• Shortage costs may be difficult to estimate: need to include long-run loss of goodwill in addition to immediate loss of profits

Practical Aspects: Setting Service Levels

• Marketing always wants high service levels, so to provide the right incentives, it may be necessary to charge them for the inventory

• Selecting different service levels by product category, or even by specific product, can save a lot of money without serious adverse effects on the perceived service level

Take-Aways

• Inventory as a financial asset, competitive weapon

• Inventory-related costs• Service level concepts; economic tradeoffs

in setting service level• 4 models for setting control knobs for

single-stage inventory systems

Hint for Sport Obermeyer Case

• Focus is often on expected number of shortages but you may also want to know expected number of leftovers

• Spreadsheet titled expected_overage.xls on B-space will help you calculate this value for a newsvendor setting (one-time purchase for a short-lifecycle product) if demand is Normally distributed and you set the order quantity z standard deviations above the mean