University of Illinois at Chicago
College of Business Administration
Department of Information & Decision Sciences
IDS 532 -- DM&IS II
Decision Models & Information Systems II -- Operations Management
Textbook: Markland, Vickery & Davis, 2nd ed. ("MVD")
Prof. Stanley L. Sclove
NOTES TO ACCOMPANY MVD CH. 12
INVENTORY FOR INDEPENDENT DEMAND
These notes Copyright © 1998 Stanley Louis Sclove
12.0. Introduction
12.1. Independent and Dependent Demand
12.2. Basic Inventory Concepts
12.2.1. Types of Inventories
12.2.2. How to Measure Inventory
12.2.3. Reasons for Holding Inventories
12.2.4. Inventory Costs
12.2.5. Classifying Inventory Items
12.2.6. Inventory Records
12.2.7. Objectives of Inventory Control
12.3. How Much to Order: Economic Order Quantity Models
12.3.1. Economic Order Quantity: Constant Demand, No Shortages
12.3.2. Economic Order Quantity: Constant Demand, Shortages Allowed
12.3.3. Economic Order Quantity: Uniform Replenishment Rate, Constant Demand, No Shortages
12.3.4. Economic Order Quantity: Quantity Discounts
12.3.5. Sensitivity Analysis for the EOQ Model
12.4. When to Order: The Continuous Review System
12.4.1. Determining the Reorder Point
12.4.2. Service Levels, Safety Stock, and Shortages
12.5. When to Order: The Periodic Review System
12.6. Comparing the Continuous Review and Periodic Review Systems
12.0. Introduction
TERMS AND DEFINITIONS
The root "ven" of the word "inventory" refers to motion (coming and going); so "inventory" literally means the amount of goods coming
in. In the business context it refers to goods on hand, waiting to be used or sold.
The ideal would be to get just enough goods there just when they are needed,
so that there would be no need to use space to store extra items.
This ideal is called "just-in-time" inventory control.
Since it has usually proved impossible or impractical to attain this ideal, the
costs defined in this chapter are pertinent.
12.1. Independent and Dependent Demand
12.2. Basic Inventory Concepts
12.2.1. Types of Inventories
12.2.2. How to Measure Inventory
12.2.3. Reasons for Holding Inventories
12.2.4. Inventory Costs
12.2.5. Classifying Inventory Items
12.2.6. Inventory Records
12.2.7. Objectives of Inventory Control
12.3. How Much to Order: Economic Order Quantity Models
12.3.1. Economic Order Quantity: Constant Demand, No Shortages
CALCULATING ANNUAL ORDERING AND HOLDING COSTS
The basic cost formula is developed. It consists of annual ordering cost plus annual holding cost. The quantity ordered is denoted by Q. The larger Q is, the smaller the annual ordering cost, but the larger the annual holding cost, so there is a trade-off.
SEEKING THE BEST REORDER POLICY
A spreadsheet can be used.
A first column can be either a range of values of Q or a range of values of N.
Personally, I suggest N, since it is easier to guess a suitable range for N than for Q.
Subsequent columns contain the order cost, the holding cost, and their sum.
THE ECONOMIC ORDER QUANTITY MODEL
AHO stands for Annual Holding and Order Costs.
The AHO function takes the form a/Q + bQ + c with a,b,c>0.
Consequenty, the following fact can be used in this and related
problems: A function a/x + bx + c with a,b,c>0 is minimized at x*
= sqrt(a/b). Also, a/x* = bx*.
This fact is used to derive the EOQ formula for Q*. The related
formula for N*, the optimal number of times to order, is discussed.
The lead time is the time between when an order is placed and
when it arrives. One must allow for lead-time demand.
12.3.2. Economic Order Quantity: Constant Demand, Shortages Allowed
THE EOQ MODEL WITH BACKLOGGING
Backlogging means stockout orders will eventually be filled.
12.3.3. Economic Order Quantity: Uniform Replenishment Rate, Constant Demand, No Shortages
THE PRODUCTION LOT SIZE MODEL
The determination of how much to produce is treated as a problem
where inventory arrives steadily.
12.3.4. Economic Order Quantity: Quantity Discounts
If a supplier offers a discount for buying a large quantity, you must compute the Total Cost when taking advantage of the discount to see whether it is really the less expensive option.
12.3.5. Sensitivity Analysis for the EOQ Model
12.4. When to Order: The Continuous Review System
12.4.1. Determining the Reorder Point
12.4.2. Service Levels, Safety Stock, and Shortages
INVENTORY, PROBABILISTIC DEMAND
Probabilistic demand is incorporated into the evaluation of
various alternative inventory control schemes.
The basic question is: How much inventory should a firm hold
to provide reasonable protection against uncertainty? There is
uncertainty in (1) the demand and (2) the lead-time (time between
placing and receiving the order).
THE REORDER POINT-REORDER QUANTITY MODEL
To review the standard (r,Q) model, note that the symbol r
denotes the reorder level (that is, the reorder point, ROP); Q denotes the reorder quantity.
The reorder quantity Q is determined as the EOQ.
The reorder level r would be set equal to the lead-time demand
if demand were known with certainty. If demand is uncertain, the
approach is to choose r large enough so that the stockout
probability is small enough.
CHOICE OF r
If r is too small, stockouts can occur; if; if r is too
large, too much safety stock is carried.
CHOICE OF r; UNIFORM LEAD-TIME DEMAND
The idea of stockout probability, p(s), helps define r. First
a uniform lead-time demand is investigated.
SELECTING A PROBABILITY OF STOCKING OUT
AVERAGE STOCKOUTS PER YEAR This is dependent upon the number of
orders per year as wellas the probability of a stockout per order.
THE BINOMIAL DISTRIBUTION AND THE NUMBER OF STOCKOUTS The
binomial distribution can be used to calculate the probability of any
given number of stockouts.
EFFECT OF ORDER SIZE ON STOCKOUTS As order quantity (Q)
increases, the average number of stockouts per year decreases.
CHOICE of r: NORMAL LEAD-TIME DEMAND
The normal approximation of lead time is investigated. Changing
the lead-time distribution changes the relation between r and the stock-out probability.
EXPECTED ANNUAL COST OF SAFETY STOCK
Associated with various choices for r will be a safety stock and a related expected annual holding cost.
USING SIMULATION TO CHOOSE r and Q
Simulation can be used on inventory problems.
12.5. When to Order: The Periodic Review System
12.6. Comparing the Continuous Review and Periodic Review Systems
latest revision 22-July-1998