ABSTRACT
This thesis studies some Economic Production Quantity (EPQ) models of deteriorating items that
exhibit delay in deterioration with reliability consideration. Two modifications to existing
models are presented; the first modification assumes a constant demand both before and after
deterioration begins, while the second modification assumes a linearly time dependent demand
after deterioration begins. The unit cost of production of an item is assumed to be directly related
to the process reliability and inversely related to the demand rates. Numerical examples are given
to illustrate the applications of the models.
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TABLE OF CONTENTS
COVER PAGE
FLY PAGE
TITLE PAGE
DEDICATION ………………………………………………………………………………………………………………… i
DECLARATION ……………………………………………………………………………………………………………. ii
CERTIFICATION …………………………………………………………………………………………………………. iii
ACKNOWLEDGEMENT ……………………………………………………………………………………………….. iv
ABSTRACT ……………………………………………………………………………………………………………….. ..vi
TABLE OF CONTENTS ……………………………………………………………………………………………….. vii
CHAPTER ONE: GENERAL INTRODUCTION
1.0 INTRODUCTION …………………………………………………………………………………………………. 1
1.1 Components of Inventory Models …………………………………………………………………………….. 2
1.2 A Generalized Inventory Model ……………………………………………………………………………….. 3
1.3 Types of Inventory Models ……………………………………………………………………………………… 4
1.3.1 Deterministic demand ………………………………………………………………………………………. 4
1.3.2 Stochastic demand …………………………………………………………………………………………… 5
1.3.3 Deterministic continuous-review model ………………………………………………………………. 5
1.3.3.1 The basic EPQ model ……………………………………………………………………………………. 6
1.3.4 Deterministic periodic-review model ………………………………………………………………….. 7
1.3.5 A stochastic continuous-review model ………………………………………………………………… 8
1.3.5.1 Choosing the order quantity Q………………………………………………………………………… 9
1.3.6 Stochastic periodic-review models ……………………………………………………………………. 10
1.4 Order Point and Safety Stock …………………………………………………………………………………. 10
1.5 The Finite Production Rate Models with Deterioration ………………………………………………. 11
1.6 The Inventory Models with Delayed in Deterioration ………………………………………………… 12
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1.7 Justification for the Research …………………………………………………………………………………. 13
1.8 The Problem Studied in this Thesis …………………………………………………………………………. 14
1.9 Limitation …………………………………………………………………………………………………………… 15
1.10 Research Methodology …………………………………………………………………………………………. 16
1.11 Research Aims and Objectives……………………………………………………………………………….. 16
1.12 Outline of the Thesis ……………………………………………………………………………………………. 17
1.13 Definitions of Some Basic Terms …………………………………………………………………………… 18
CHAPTER TWO: LITERATURE REVIEW
2.0 INTRODUCTION: ………………………………………………………………………………………………. 21
2.1 The Basic Economic Order Quantity ………………………………………………………………………. 21
2.2 EPQ or Lot Size Inventory Models with Constant Deterioration ………………………………….. 21
2.3 Inventory Model for Non-Instantaneous Deteriorating Items……………………………………….. 22
2.4 Inventory Model with Process Reliability(Quality Assurance) …………………………………….. 24
2.5 Deteriorating Inventory Models with Varying Demand Rate ……………………………………….. 25
2.6 Inventory Models with Imperfect Quality ………………………………………………………………… 26
2.7 Other EPQ Inventory Models ………………………………………………………………………………… 28
CHAPTER THREE: AN EPQ MODEL FOR ITEMS THAT EXHIBIT DELAY IN
DETERIORATION WITH RELIABILITY CONSIDERATION AND CONSTANT
DEMAND
3.0 INTRODUCTION: ………………………………………………………………………………………………. 29
3.1 Notation and Assumptions …………………………………………………………………………………….. 29
3.2 The Mathematical Model ………………………………………………………………………………………. 31
3.3 Results Obtained from the Model …………………………………………………………………………… 38
3.3.1 Numerical examples ………………………………………………………………………………………. 38
3.3.2 Sensitivity analysis ………………………………………………………………………………………… 39
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CHAPTER FOUR: AN EPQ MODEL FOR DELAYED DETERIORATING WITH
RELIABILITY CONSIDERATION AND LINEAR DEMAND
4.0 INTRODUCTION ……………………………………………………………………………………………….. 40
4.1 Notation and Assumptions …………………………………………………………………………………….. 40
4.2 The Mathematical Model ………………………………………………………………………………………. 41
4.3 Results Obtained from the Model …………………………………………………………………………….. 48
4.3.1 Numerical examples ………………………………………………………………………………………. 49
4.3.2 Sensitivity analysis ………………………………………………………………………………………… 50
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATIONS
5.1 SUMMARY ……………………………………………………………………………………………………….. 51
5.2 CONCLUSION …………………………………………………………………………………………………… 51
5.3 RECOMMENDATIONS ………………………………………………………………………………………. 53
5.4 RESEARCH EXTENSIONS …………………………………………………………………………………. 53
REFERENCES …………………………………………………………………………………………………………….. 54
1
CHAPTER ONE
GENERAL INTRODUCTION
1.0. INTRODUCTION
Inventory consists of materials, commodities, products, etc, which are usually carried in stock in
order to be consumed or benefited from when needed. An Economic Order Quantity (EOQ)
model sometimes referred to as Economic Order Lot-size model is an inventory control model,
which determines the optimal quantity to be ordered so as to meet a deterministic demand over a
planned period of time in order to minimize cost. An Economic Production Quantity (EPQ) or
Economic Production Lot-size model is an inventory control model which determines the
optimal quantity to be produced so as to meet a deterministic demand with the objective of
minimizing cost. Thus, EPQ model is an offshoot of the well known EOQ model.
In several articles in the literature on inventory models (focusing on EOQ and EPQ), it is
assumed that items can be stored for a long period of time for future use without spoilage.
However, it is a general knowledge that almost all items on inventory deteriorate over time.
Deterioration can be referred to as depression in quality/quantity of items kept on inventory for
certain purpose. An item on inventory becomes reliable, if it satisfies the probability that it will
adequately perform its specified purpose, for a specified period of time, under specified
environmental conditions. Thus reliability is influenced by the decisions made during the design
and manufacturing of the product.
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In this thesis, we study some EPQ models of deteriorating items which exhibit delay in
deterioration with reliability consideration. These are items which do not start deteriorating
immediately they are stored, until later. Such items include potatoes, yam, bread, cakes, to name
a few. Two modifications to existing models are presented; the first modification assumes a
constant demand both before and after deterioration begins, while the second assumes a linearly
time dependent demand after deterioration commences.
1.1 COMPONENTS OF INVENTORY MODELS
The profit of a production is affected by the policies on inventory; as such the choice among
inventory policies depends upon their relative profitability. Profitability is determined by the
following factors: the costs of ordering or production set-up costs (in case of production),
shortage costs, holding costs, salvage costs, revenues and discount rates.
• Cost of Ordering: This is the cost of placing an order to an outside supplier or releasing a
production order to a manufacturing shop.
• Set-up cost: This is the cost incurred in preparing a machine or process for manufacturing
an order. It includes the design cost, location of machinery, employee hiring, research
and development expenses, and labor cost for cleaning and changing tools or holders.
• Shortage Cost: Shortage cost (sometimes called the unsatisfied demand cost) is incurred
when the amount of the commodity required (demand) exceeds the available stock.
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• Holding Cost: Holding cost (sometimes called the storage cost) represents all the costs of
capital tied up, space, insurance, protection, and taxes attributed to storage. The holding
cost can be assessed either continuously or on a period-by-period basis.
• Salvage Value: Salvage value of an item is the value of a leftover item when no further
inventory is desired. The salvage value represents the disposal value of the item to the
firm, perhaps through a discounted sale. The negative of the salvage value is called the
salvage cost. If there is a cost associated with the disposal of an item, the salvage cost
may be positive.
• Revenue: Revenue may or may not be included in the model. If both the price and the
demand for the product are established by the market and so are outside the control of the
company, the revenue from sales (assuming demand is met) is independent of the firm’s
inventory policy and may be neglected. However, if revenue is not neglected in the
model, the loss in revenue must then be included in the shortage cost whenever the firm
cannot meet the demand and the sale is lost.
• Discount Rate: discount rate takes into account the time value of money. When a firm
ties up capital in inventory, the firm is prevented from using this money for alternative
purposes.
1.2 A GENERALIZED INVENTORY MODEL
The ultimate objective of an inventory model is to answer two questions.
1. How much to order/produce?
2. When to order/produce?
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The answer to the first question (how much to order/produce) is expressed in terms of what we
call the order/production quantity and the second question (when-to-order/produce) is the
inventory level at which a new order/product should be placed/produced usually expressed in
terms of re-order point.
According to Hadley and Whitin (1963), one can summarize the total cost of a general inventory
model as a function of its principal components in the following manner:
Total inventory cost = purchasing cost + setup cost (or ordering cost) + holding cost
+ shortage cost (if shortages are allowed)
1.3 TYPES OF INVENTORY MODELS
Basically, all inventory models (EOQ/EPQ) are classified into two categories:
Deterministic model and
Stochastic model
1.3.1 DETERMINISTIC DEMAND
This is a situation where by the demand rate is known with certainty. It can be further classified
into uniform (constant) demand and time-dependent demand. The time-dependent demand is also
classified into discrete time dependent demand and continuous time dependent demand. The
time-dependent demand may be:
o linearly increasing given by (t) a bt ; a 0, b 0 ,
o linearly decreasing given by (t) a bt ; a 0, b 0 ,
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o it may be exponentially increasing given by (t) aebt ; a 0, b 0 , or
o exponentially decreasing with ( ) ; 0, 0 t aebt a b and so on.
1.3.2 STOCHASTIC DEMAND
This is a situation where by the demand rate follows a statistical distribution which may be a
known probability distribution or an arbitrary probability distribution.
Inventory models can also be classified based on their current mode of supervision: periodic
review and continuous review. In periodic review, the level of the inventory is to be checked at
discrete intervals, e.g., at an interval of one month, and decisions on ordering are to be made only
at these times (an interval of one month) even if the inventory level is below the reorder point
between the current and preceding review times. In continuous review, placement of an order is
done as soon as the stock level falls down to the prescribed reorder point. (Hillier and
Lieberman, 2001)
1.3.3 DETERMINISTIC CONTINUOUS-REVIEW MODEL
Manufacturers/producers, retailers as well as wholesalers face a common inventory scenario; that
items in stock are exhausted/drained over time and they are refilled/replaced by the arrival of
new manufactured items. An inventory control model describing such situation in a production
environment is the economic production quantity (EPQ) model, which is sometimes referred to
as the production lot-size model.
In the EPQ model, the demand rate is constant. The inventory is replenished when required by
producing a batch of fixed size (Q units), where all Q units are produced at the desired time. For
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this case of basic economic production quantity (EPQ) model, the following costs are
considered:
K = set-up cost per production run
c= unit cost of the item
h= inventory carrying cost in a production cycle.
The main objective is either to minimize the total inventory cost per unit time or to maximize the
profit. (Paknejad et al., 1995)
1.3.3.1 THE BASIC EPQ MODEL
The basic EPQ model is an offshoot of the well known Economic Order Quantity (EOQ) model
and the two (EPQ and EOQ) have similar assumptions. The EPQ as an inventory control model
is usually based on the following assumptions:
i. Constant deterministic demand rate per unit time.
ii. If inventory level drops to 0, then the production quantity (Q) to replenish inventory is
produced all at once.
iii. Planned shortages are not permitted.
The total cost of production per unit time T is computed from the following components.
Production cost per cycle =K+cQ.
The average inventory level during a cycle is Q/2 units, and the corresponding cost is hQ/2 per
unit time. Since the cycle length is Q/a,
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Holding cost per cycle
2
2
hQ
a
Then,
Total cost per cycle
2
2
K cQ hQ
a
And so, the total cost per unit time T is
2 2
2
K cQ hQ a aK hQ T ac
Q a Q
The value of Q, say Q*, that minimizes T is found by setting the first derivative of T with respect
to Q to zero (provided that the second derivative is positive).
i.e. 2 0
2
dT aK h
dQ Q
giving Q* 2aK
h
(1.1)
which is the well-known EPQ formula. The corresponding cycle time, say t*, is
t*
Q* 2K
a ah
(1.2)
(Nahmias, 2009)
1.3.4 DETERMINISTIC PERIODIC-REVIEW MODEL
The assumptions in the basic EPQ model are not always realistic. This is why several authors
modified the model over time to reflect several realistic scenarios. When the assumption of
constant demand is relaxed for instance i.e. when the amounts that need to be withdrawn from
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inventory are allowed to vary from period to period, the EPQ formula no longer ensures a
minimum-cost solution, for all cycles.
Suppose planning is to be done for the next n periods regarding how much (if any) to produce to
replenish inventory at the beginning of each of the periods. The demands for the respective
periods are known (but not the same in every period) and are denoted by
= demand in period , for = 1,2,3,…,
The EPQ in this case is given by
* 2 i
i
Q rK
h
for = 1,2,3,…, (1.3)
and
*
* 2 i
i
i i
t Q K
r rh
for = 1,2,3,…, (1.4)
(Hadley and Whitin, 1963; Hillier and Lieberman, 2001)
1.3.5 A STOCHASTIC CONTINUOUS-REVIEW MODEL
In a stochastic continuous-review inventory system for a particular item, there are two factors to
be considered, namely:
R = reorder point,
Q = order quantity.
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For a retailer or wholesaler (or a manufacturer replenishing its raw materials inventory from a
supplier), the purchase order for Q units of the product is the order quantity. On the other hand,
for a manufacturer managing its finished products on inventory, the production run of size Q is
the order quantity.
Inventory policy based on these factors (R and Q) is as follows: an order for Q more units is to be
placed to replenish the inventory, if the inventory level of the product drops to R units. Such a
policy is sometimes called reorder point, order quantity policy or (R, Q) policy. [Consequently,
the overall model might be referred to as the (R, Q) model. Other modifications such as (Q, R)
model, (Q, R) policy, and so on, are also used.] (Paknejad et al., 1995)
1.3.5.1 CHOOSING THE ORDER QUANTITY Q
The approach used in formulating Q for stochastic continuous-review model is as follows:
Total cost=setup cost + purchase cost + holding cost +shortage cost
2 2
2 2
hR p Q R T K cQ
a a
(1.5)
where p is the shortage.
Total cost per unit time T(Q,R) is given as
2 2
,
2 2
aK hR p Q R T Q R ac
Q Q Q
(1.6)
taking the partial derivative of (1.6) with respect to Q and R and set the result to zero, we have
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R* 2aK p and Q* 2aK p h
h p h h p
(1.7)
(Ra’afat, 1991)
1.3.6 STOCHASTIC PERIODIC-REVIEW MODELS
This is a situation when we assume that the demand is uncertain. However, in contrast to the
continuous-review inventory system, we now assume that the system is only being monitored
periodically. At the end of each period, when the current inventory level is determined, a
decision is made on how much to order (if any) to replenish inventory for the next period. Each
of these decisions takes into account the planning for multiple periods into the future.
1.4 ORDER POINT AND SAFETY STOCK
The economic production quantity model indicates how many units to produce. Practitioners are
also concerned with the order point. This quantity reflects the level of inventory that triggers the
start of set up for additional units.
Determination of the order point is based on three factors:
usage (quantity of inventory used or sold each day),
lead time (is the time it takes from the start of set up to when the goods are produced),
and
safety stock (The quantity of inventory kept on hand by a company in the event of
fluctuating usage or unusual delays in lead time).
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Order point=(usage per unit time lead time)+safety stock
If usage per unit time is entirely constant and lead time is known with certainty, the order point is
equal to usage per unit time multiplied by lead time:
Order point=usage per unit timelead time
i.e. there is no need for safety stock. Note that in the EPQ case, lead time is zero and safety stock
is also zero, so the addition of these two in the basic EPQ model is one of the ways in which the
model is modified to reflect some realistic situations. (Ra’afat, 1991)
1.5 THE FINITE PRODUCTION RATE MODELS WITH DETERIORATION
Misra (1975) developed the first production lot size model in which both a constant and variable
rate of deterioration were considered and obtained approximate expressions for the production
lot size with no backlogging. For the case of Weibull distribution deterioration, no closed
expression for the lot size and the average total cost was possible. However, for the case of
exponential distribution (i.e. constant deterioration rate), through a series of approximations,
Misra (1975) calculated the optimal production lot size to be
0.5
3
1
C
Q = 1 + Q ,
Cp E
d
, with
0.5
2
1
2C
Q
C p d E
dp
,
where
E Q is the production lot size for items without decay,
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p is the constant production rate,
is the constant rate of decay,
d is the constant demand rate and
1 2 3 C , C , and C are inventory carrying cost, ordering cost and deteriorating cost respectively.
Shah and Jaiswal (1976) derived results similar to those of Misra (1975) for a constant
deterioration rate and extended the model to include backlogging. By assuming the average
carrying inventory to be approximately one-half the maximum level of inventory and using the
same notation with Misra, they obtained the following expression for the production lot size as a
function of inventory cycle time: Q p ln l d exp T l ,
p
where T is the
inventory cycle time.
1.6 THE INVENTORY MODELS WITH DELAY IN DETERIORATION
In the EOQ model with constant rate of deterioration, many authors assume that deterioration of
the items start from the instance of their arrival in stock. As a matter of fact, many items (for
example, firsthand vegetables, fruits, and some items produced in industry like bread, cakes, etc)
have a span of maintaining fresh quality or original condition. During that period, there is no
deterioration occurring, but after sometime, deterioration begins. Thus it is important to consider
inventory problems for non-instantaneous deteriorating items. Ouyang et al. (2006) developed an
EOQ model for non-instantaneous deteriorating items with permissible delay in payments and
where the demand before deterioration starts is the same as that after deterioration begins. Musa
13
and Sani (2012) developed an EOQ inventory model for delayed deteriorating items under
permissible delay in payments but where the demand before deterioration starts is different from
that after deterioration starts. Thus, this paper is a generalization of Ouyang et al. (2006).
Similarly, in the context of EPQ model, many authors assume that deterioration start
immediately after production, but this is not the usual situation. Some items (for example; bread,
cakes, etc) have a span of maintaining their original condition. Hence, it is important to consider
inventory problems of delayed deteriorating items. Sugapriya and Jeyaraman (2008a) developed
a model to determine a common production cycle time for an economic production quantity
model of non-instantaneous deteriorating items allowing price discount and permissible delay in
payments. Sugapriya and Jeyaraman (2008b) also developed an EPQ model for noninstantaneous
deteriorating items in which production and demand rate are constant, holding cost
varies with time, completely deteriorated units are discarded, partially deteriorated items are sold
with some discount and no shortage is allowed. Baraya and Sani (2011) developed an EPQ
model for delayed deteriorating items with stock-dependent demand rate and linear time
dependent holding cost.
1.7 JUSTIFICATION FOR THE RESEARCH
The economic production quantity (EPQ) model has been widely used in practice because of its
simplicity. However, there are some drawbacks in the assumptions of the original EPQ model
and many authors have tried to improve it with different assumptions. The assumption of the
unconstrained production period length is one of these shortcomings. The classical EPQ model
assumes that production period length is unconstrained. However, in real production
14
environment, this assumption is not always tenable because, it can often be observed that the
production period length is constrained due to some technical services reasons. Hence, the
inventory policy determined by the conventional model would be inappropriate.
Reliability of an item is the probability that it will adequately perform its specified purpose for a
specified period of time under specified environmental conditions. Product reliability is
influenced by the decisions made during the design and manufacturing of the product. This
implies that reliability can be viewed as a link to integrate the different stages of manufacturing –
design, engineering, production, marketing, and post sale service – in an effective manner. As
such reliability is very important in the context of new products. Recently research articles,
emphasize the growing importance of this subject to both consumer and producer (Cheng, 1991).
Objective determination of reliability costs will help manufacturers plan operations more
effectively since an accurate knowledge of reliability costs allows more accurate profit
expectations which may, in turn, lead to some marketing advantages (Cheng, 1991).
In case of demand of an item, it is natural that the higher the price of an item the lower the
demand and the lower the price of an item the higher the demand of such item, i.e. the unit cost
of an item is inversely related to the demand of the product. In general the unit cost of production
is directly proportional to the reliability of the product and inversely related to the demand of the
product.
1.8 THE PROBLEM STUDIED IN THIS THESIS
EPQ model has been widely used for more than four decades as an important tool to control
inventory. However, as already indicated, EPQ model did not represent the real world problem in
some situations. The analysis for finding an EPQ therefore has several weaknesses. This is why,
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many authors had to make extensions or modifications in several aspects of the original EPQ
model. The quality assurance (reliability) is one good aspect that could be added to the EPQ
model since quality assurance plays an important role in the demand of an item in the market.
Quality assurance was incorporated in the models of many authors such as Cheng (1991) and
Tripathy et al. (2003).
Musa and Sani (2009) developed an EOQ model for items that exhibit delay in deterioration. The
non-instantaneous deterioration (delay in deterioration) is a situation where items do not start
deteriorating immediately they are stocked. During this period, before deterioration sets in,
depletion of inventory is dependent on demand only. As deterioration sets-in depletion is then
dependent on both demand and deterioration. The items that exhibit delay in deterioration
include farm produce such as fruits, potatoes etc. or even fashion goods such as cars, fabrics etc.
In this thesis, we intend to make an extension of Musa and Sani (2009) but in the context of EPQ
by assuming the unit cost of production of an item to be directly related to reliability (quality
assurances in producing the item) and inversely related to demand rates. This is a reasonable
assumption because the higher the reliability of an item the higher the price is in many cases, and
the lower the reliability of the item the lower the price is in many cases. Also, the higher the
price of an item the lower the demand of such item, and the lower the price of the item the higher
the demand of such item in many cases.
1.9 LIMITATION
The applicability of the study is limited to items with delay in deterioration, where the unit cost
of production is directly related to reliability and it is inversely related to quantity demanded.
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1.10 RESEARCH METHODOLOGY
The approach we use in this study will start with the review of existing literature in both
Economic Order Quantity (EOQ) model and Economic Production Quantity (EPQ) model. It will
also review literature on constant demand, varying demand, constant deterioration, varying
deterioration and reliability consideration in EPQ models. Mathematical modeling will then be
used to derive the mathematical relationship for the required models under the stated
assumptions after which numerical examples will be used to show the application of the models.
Sensitivity analyses will also be conducted to see the effect of changes in some of the
parameters.
1.11 RESEARCH AIMS AND OBJECTIVES
The aim of this research is to develop economic production quantity models for items which
exhibit delayed deterioration with quality assurance consideration.
The objectives of this research are:
To investigate the effect of quality assurance (reliability) in the EPQ inventory model of
items that exhibit delayed deterioration;
To develop an EPQ model of items which exhibit delayed deterioration with quality
assurance consideration and constant demand;
To develop an EPQ model of items which exhibit delayed deterioration with quality
assurance consideration and linear demand (after deterioration begins).
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1.12 OUTLINE OF THE THESIS
Chapter one deals with the general introduction of the thesis. It starts with the introduction of
inventory control theory, components of inventory, generalized inventory model and basic
classification of inventories. The chapter goes ahead to discuss the Economic Production
Quantity (EPQ) model and some other models that depend on it. The justification of reliability
consideration, problem studied, methodology, objectives of the study and limitations of the study
are also stated in the chapter.
Chapter two surveys the existing literature on Inventory Management and Control and
particularly the deteriorating inventory. It covers various inventory related problems especially
the EOQ/EPQ where EOQ/EPQ models are discussed under different mathematical assumptions.
These include inventory models for constant deteriorating items and inventory models for noninstantaneous
(delayed) deteriorating items, inventory models for deteriorating items with
process reliability, inventory models for items with constant demand, inventory models for items
with varying demand, inventory models for deteriorating items with varying demand and
inventory models with imperfect quality.
Chapter three contains development of the mathematical model (EPQ) on items that exhibit
delay in deterioration with reliability consideration and constant demand (both before and after
deterioration sets-in). It is assumed in the model that the unit cost of production is directly
related to reliability of the product and inversely related to the rates of demand. The chapter then
gives some numerical examples to show how the model is applied. The chapter also gives a
sensitivity analysis of some important parameters.
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Chapter four contains development of the EPQ model of items that exhibit delay in deterioration
with reliability consideration but where the demand rate after deterioration sets-in is linearly time
dependent. Numerical examples are also given to illustrate the application of the model. The
chapter also gives a sensitivity analysis of some important parameters.
Chapter five gives the summary of the thesis, contribution of the thesis to research on inventory
of deteriorating items and it gives a conclusion of the work. Possible areas of interest where the
research could be extended are also given and this is in addition to further recommendations
given.
1.13 DEFINITIONS OF SOME BASIC TERMS: The following are the definitions of some
of the technical terms we will frequently use in this thesis.
Backlogging: This is the process of holding customer orders to be filled later when they
cannot be settled immediately because of stockouts.
Backorder: A customer order that cannot be filled when presented, and for which the customer
is prepared to wait for some time.
Backorder cost: The cost of handling the backorder (special handling, follow-ups etc.) plus
whatever loss of goodwill occurs as a result of having to backorder an item.
Demand rate: This is also called the usage rate. It is the number of units demanded by
customers of production departments per unit of time. The demand may be constant (static)
or variable (dynamic).
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Instantaneous inventory receipt: This is the inventory that is received or obtained at one point
in time and not over a period of time.
Inventory Turnover (or stock turn): This is a ratio showing how many times a company’s
inventory is sold and replaced over a period.
Lead time: This is the time between ordering a replenishment of an item and actually
receiving the item into inventory. The lead-time can be either deterministic (constant or
variable) or probabilistic.
Instantaneous delivery: If the lead time of an item is zero, then we have a special case of
instantaneous delivery where there is no need for placing an order in advance. This occurs in
many cases in production industries when the production run is so planned that new items
produced become available just as old items finish. This is clearly seen in a bakery for
instance. In our own study, we consider the lead time to be zero; therefore we have a case of
Instantaneous delivery.
Inventory cycle: This is made up of the activities of sensing a need for ordering materials,
placing an order, lead time for getting the material delivered, receiving the material and using
it.
Inventory level: This refers to the amount of materials on hand in inventory that is ready for
use, i.e. the current amount of a product that a business has in stock.
Inventory carrying (holding) cost: This is the cost a business incurs over a certain period of
time, to hold and store its inventory.
Order quantity: This is the quantity of material produced each time inventory is replenished.
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Planned shortages: This is a situation where stock outs are planned.
Set-up cost: This is the cost incurred in preparing a machine or processing for manufacturing
an order. It includes the design cost, moving of machinery, employee hiring, research and
development expenses, and labor cost for cleaning and changing tools or holders.
Time horizon: The period over which the inventory level will be controlled is called the time
horizon. It can be finite or infinite depending on the nature of demand.
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