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:
  1. How often should the inventory status be reviewed and determined?
  2. When should an order be placed?
  3. 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.