Introduction
Inventory management is one of the
most fundamental and challenging activities for any company dealing with
raw materials, work-in-process and/or finished goods. Since
organizations usually make a significant investment in inventories, the
correct management of this tied-up capital provides a very important
opportunity for business improvements. Under these circumstances,
scientific methods for inventory decisions can be decisive to achieve a
significant competitive advantage in today’s business world. On the one
hand, there is a wish to make large replenishment orders to get trade
credit benefits and volume discounts, to reduce production costs by
means of long production runs and economies of scale, and to increase
sales by providing a high customer service level. On the other hand,
there is a wish to keep stock levels down to avoid the risk of suffering
financial difficulty as a result of low or tight liquidity and to avoid
excessive costs incurred for keeping and managing large inventories. In
order to balance these and other conflicting goals, novel approaches are
required to provide an answer to at least the following three questions:
- How often should the inventory status be reviewed and determined?
- When should an order be placed?
- How large should the order quantity be?
One way to tackle these issues is to use an inventory model as a
decision-support tool. Generally speaking, inventory models are
approximations or simplifications of real inventory management systems.
It does not reflect every aspect of reality in a particular context.
However, they can be useful for decision-making processes. Despite all
the effort invested in research, there is still a lack of research on
inventory management where useful endeavors may result not only in a
significant improvement to companies but to society in general. The
evidence supporting this is overwhelming. In the agricultural industry,
for example, post-harvest losses are significant and unavoidable
[1]. Roughly, one-third of food
produced for human consumption is globally lost or wasted throughout the
food supply chain, which is about 1.3 billion tons per year and has a
negative impact on economic development and on the environment
[2]. In the grocery retailing
industry, perishable products within the grocery-food category account
for approximately 50% of total supermarkets sales
[3-5], and the losses of these kinds
of products due to inventory spoilage at the retail level are
susceptible to range from 5% to 22.8%
[2, 6]. While reducing perishable
inventory waste 20% can increase total store profit by 33%
[7], mismanagement of perishable
products can represent a major threat to the profitability of companies
in the grocery retailing industry [8].
Therefore, finding suitable inventory management policies has always
been of great importance to both researchers and practitioners.
The mathematical modeling of inventory systems has its roots in the
Economic Order Quantity Model (EOQ) proposed by
Harris [9] in 1913, which assists in
determining the optimal number of units to order with a view to
minimizing the total cost associated with the purchase, delivery and
storage of the product. However, in the EOQ model, many of its basic
assumptions are far removed from practice. When, for example,
deterioration has a significant economic impact within inventory
systems, the common assumption of unlimited shelf life for lot-size
determination becomes very inaccurate. A challenging task for this class
of items is to maintain product availability while avoiding excessive
product loss so that effective inventory management is possible. Because
achieving this effectiveness represents a formidable challenge to both
academics and practitioners, the study of inventory systems dealing with
deteriorating products is still one of the most important research areas
that emerged from the first EOQ model.
This research aims to gain a more in-depth understanding of the state of
the inventory modeling literature stream for deteriorating items. This
responds to the need for evaluating what the lot-sizing theory applied
for perishable products has collectively accomplished and what
directions might be fruitful for future research. In general, the
identification, evaluation, and interpretation of existing knowledge in
literature reviews is an essential part of all kinds of research
processes. This is frequently pointed out by textbooks on research
methodologies [10-12], as well as
methodological articles in high impact journals
[13,
14]. In particular, since the last
literature reviews on deteriorating inventory modeling
[15-17], more than 300 papers have
been recorded over the last years. This not only raises concerns about
the state of art of this research stream but justifies the need to
provide a starting point for research by
identifying patterns, themes, and
issues from the existing body of recorded documents.
Since the earliest works on deteriorating inventory modeling during the
decades of the 50’s and 60’s [18-20],
many studies have been published every year. The first review on this
research area was developed by Nahmias
[21] in 1982. This review discussed the relevant literature dealing
with the inventory problem of finding suitable ordering policies for
either fixed or random lifetime items. Next, nine years later, and
following the classification scheme of
Silver [22],
Raafat [23] reviewed the advances of
deteriorating inventory literature but limited to those studies that
investigated the effect of deterioration as a function of the on-hand
inventory level . Then, in the year 2001,
Goyal and Giri [24] extended
Raafat [23] but included inventory
models subject to fixed lifetime items. After that, in the year 2012,
Bakker, Riezebos [15] updated
Goyal and Giri [24] by providing an
overview and classification very close to that of Goyal and Giri’s to
facilitate comparisons between them. Finally,
Janssen, Claus [17] updated
Bakker, Riezebos [15] by analyzing
relevant papers from 2012 to 2015 and by discussing new topics. Unlike
all the previous reviews mentioned, they included newsvendor and
transport models. Apart from this stream of surveys, there are other
works that have been reported in the literature. However, some of them
only focused on specific topics of deteriorating inventory modeling
[25-30], and others followed a
different classification and/or analysis approach
[16,
25].
In this paper, we complement and update the surveys in
[15, 17,
24]. As in these works, we discuss the
basic features, extensions and generalization of new reported published
literature in the mathematical deteriorating inventory modeling (in our
case, 167 papers from 2016 to 2018). However, our scope is broader and
does not only include a classification of the new reported literature
since the work of Janssen, Claus
[17], but also includes a relevant sample of published papers from
2001 to 2015. To keep the scope of this research treatable, we limited
ourselves to inventory models dealing with products which naturally
undergo physical degradation. This includes most inventory models with
fixed and random lifetime products, and even some models for seasonal
products.
The remainder of this paper is organized as follows. In Section 2, we
first describe the research materials and methodology utilized to search
and select the papers included in our review. Next, in Section 3, we
provide the different categories upon which our thorough evaluation of
the selected literature is conducted. Discussions are then presented in
Section 4, while conclusions and future research opportunities are given
in Section 5.