مشکل تعیین اندازه دسته تولید : یک پژوهش دوران سومی

This paper provides a survey of literature reviews in the area of lot sizing. Its intention is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. We first develop the methodology of this review and then descriptively analyze the sample. Subsequently, a content-related classification scheme for lot sizing models is developed, and the reviews contained in our sample are discussed in light of this classification scheme. Our analysis shows that various extensions of Harris' lot size model were developed over the years, such as lot sizing models that include multi-stage inventory systems, incentives, or productivity issues. The aims of our tertiary study are the following: firstly, it helps primary researchers to position their own work in the literature, to reproduce the development of different types of lot sizing problems, and to find starting points if they intend to work in a new research direction. Secondly, the study identifies several topics that offer opportunities for future secondary research.

Since the publishing of Ford Whitman Harris' (1913) seminal paper, the lot sizing problem, which aims at determining economic (production or order) lot sizes by balancing inventory and setup or order costs, has received wide attention both in the academic literature and in practice. According to Google Scholar, the reprint of the original article that appeared in Operations Research in 1990 has been cited 660 times, while Scopus lists 214 citations of the original article. The search term “lot size” (“EOQ”, “EPQ”) results in more than 40,300 (34,100, 32,000) hits in Google Scholar and more than 2400 (1450, 1070) document results in Scopus.1 These numbers illustrate impressively how the results of Harris' work have disseminated over the last 100 years.2 Curiously enough, Harris' paper was cited with an incorrect year of publication for many years, and further it was only very infrequently considered in the literature for almost 70 years after its appearance (cf. Erlenkotter, 1989 and Erlenkotter, 1990). For a comparison between Harris' lot size formula and Kelvin's Law that was published already in 1881, the reader is referred to Roach (2005). The attention the lot sizing problem has received is not surprising given the importance of inventories in the global economy. The management of inventories is among the most important operational activities of industrial and trading companies. Inventory levels and structures may directly influence customer service in terms of product availability and delivery speed, which are both indispensable elements for competitiveness in developed economies (see Vastag and Montabon, 2001). In addition, managing inventories efficiently may lead to significant cost reductions. According to the US Census Bureau (2013), the present value of inventory in the United States exceeds $1.6 trillion, which illustrates the enormous potential a reduction in inventories may have on individual companies and an economy as a whole. The Economic Order Quantity (EOQ) model proposed by Harris is a simple and efficient tool to avoid excessive inventory build-up in companies, and its robustness has frequently been confirmed in the literature (e.g., Lowe and Schwarz, 1983, Dobson, 1988 and Stadtler, 2007). An almost uncountable number of extensions of the basic model exists, which include multi-stage production systems (e.g., Bogaschewsky et al., 2001 and Glock, 2011), worker learning (see Jaber and Bonney, 1999 and Glock and Jaber, 2013), or the determination of safety stocks (e.g., Hadley and Whitin, 1963 and Glock and Ries, 2013), among others. A comprehensive review on the lot sizing problem has not been conducted so far. The lack of such an overview is, according to Williams and Tokar (2008), “a handicap to the advancement of theory and practice in inventory management“. Although reviewing all extensions of Harris' model would be a project too ambitious to accomplish, the existing literature permits the identification of popular research streams, whose analysis and synthesis may help researchers in identifying relevant works in the area of lot sizing. In this line of thought, this paper presents the results of a tertiary study on the lot sizing problem. In this study, review papers on lot sizing-related topics are identified in a systematic search of the literature and evaluated with the help of a structured framework. The intention of this paper is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. Thus, this tertiary study presents an overview that may support primary researchers in positioning their own work in the literature, in reproducing the development of different types of lot sizing problems, and in finding starting points if they intend to work in a new research direction. In addition, this study also derives suggestions for reviewing the literature in the area of lot sizing, which may be of help for future secondary research. The remainder of the paper is structured as follows: the next section describes the methodology of the tertiary study and descriptively evaluates the sample. Section 2 also presents Harris' seminal EOQ model and develops a classification scheme for lot sizing models. Section 3 assigns the identified reviews to the categories of the framework developed in Section 2 and discusses major findings of the reviews. Section 4 concludes this paper and provides suggestions for future research.

The intention of this paper was to develop an overview of major streams of research that emerged from Harris' (1913) seminal lot size model and to highlight major advances that were made in the respective research streams. For this purpose, we conducted a tertiary study on the lot sizing problem by systematically reviewing and evaluating literature reviews that appeared in this area. Since many different technical classification schemes of lot sizing models were suggested in the literature, we deductively derived a content-related classification scheme from our sample. This could be interpreted as a comprehensive description of generic modeling approaches, which facilitates illustrating the main features of different models from a content-related perspective. Our analysis showed that various extensions of Harris' model were developed over the years, such as lot sizing models that include scheduling, incentives or productivity issues. Another aspect that became apparent from our review is that recent research seems to have a special focus on the modeling of complex inventory systems. These systems, which may include multiple production stages within companies or across company borders, parallel machines, or capacity constraints, result in complex models and therefore require sophisticated solution procedures. Some authors have laid a focus on the development of meta-heuristics, which proved to be suitable methods for solving such inventory systems in many cases. Moreover, the consideration of uncertainty and other performance-related factors in inventory management becomes more apparent by using dynamic or stochastic approaches and by developing extended models. The results of this tertiary study can be summarized as follows. First, to the best of the authors' knowledge, no comprehensive review of literature reviews in lot sizing exists, which highlights the original contribution of this paper. It extends the existing literature on lot sizing by giving a broad overview of the research field and by synthesizing findings of reviews (secondary research) that have been published in this field of research. In addition, a content-related and technical classification of lot sizing problems was developed and major achievements that have been accomplished in lot sizing were discussed. This paper may support both primary and secondary researchers in future works. Our review of literature reviews gives guidance to primary researchers as it helps researchers in positioning their own work in the literature and in finding starting points if they intend to work in a new research direction. It facilitates getting access to a certain research topic, in this case the area of lot sizing, as it identifies different streams of research that emerged from the seminal lot size model proposed by Harris. This paper further contributes to the development of secondary research as it allows assessing the status quo of lot sizing reviews, and as it classifies existing reviews and synthesizes their findings. In addition, the content discussion shows which major achievements have been accomplished in the respective areas of lot sizing research, which helps scientists in identifying which topics should be addressed in future secondary studies. For example, our review methodology did not find a review that focuses on sustainability or pricing issues in lot sizing, although we can observe an increasing number of primary works on these topics. In addition, only one review focusing on learning and forgetting in lot sizing could be found, which was published in 1999 ( Jaber and Bonney, 1999). This indicates that these topics may be worth being investigated in a secondary study. Finally, an evaluation of the sample showed that most of the reviews that have been published on lot sizing problems did not use an established methodology for conducting reviews, and that sample generation and selection could not be reproduced in many cases. In fact, only 3 out of 52 reviews could be categorized as systematic reviews (Bakker et al., 2012, Glock, 2012 and Williams and Tokar, 2008). We therefore recommend that future research in this area should be oriented at established methodologies for systematic literature reviews and meta-analyses, such as the one of Cooper (2010), Tranfield et al. (2003) or Rhoades (2011). This tertiary study could also serve as a guideline for the application of systematic reviewing techniques in the area of inventory modeling, which is of increasing relevance in the scientific literature. This review also has limitations. First, the search strategy was limited to articles published in peer-reviewed journals, which may have led to publication bias as well as overestimation effects (Neely et al., 2010). Including other types of publications, such as conference proceedings or books, could result in a broader picture of developments in the area of lot sizing. Second, the review was restricted to literature reviews, and primary studies were excluded from the survey. As a result, only research streams have been discussed in this paper that have been evaluated in literature reviews before. Finally, assigning the literature reviews to content categories and technical categories involved some amount of judgment, which might have biased the analysis. These and other limiting factors could be addressed in an extension of this paper.