مدل بازده محصول در کنترل موجودی بررسی صحت مفروضات عمومی

The literature on stochastic models for inventory control with product returns commonly makes the following simplifying assumptions: demand and returns are each a homogeneous (compound) Poisson Process, and the processes are independent of each other. In this paper, we explore the validity of these assumptions by analysing real data on return flows. In addition, we discuss practical implications of our findings and we provide insights on information management for inventory systems with return flows.

Already for a long time, companies take back products, which if in good condition go back to inventory. Furthermore, environmental consciousness, legal and economic forces have brought more attention to systems with reverse flows, and to its control. Fleischmann et al. (2002), van der Laan et al. (1999) and Inderfurth and van der Laan (2001) are recent examples of scientific literature on inventory control in case of returns. From a modelling perspective, one of the consequences of reverse flows is the loss of monotonicity of inventory levels between replenishments of new products. That is, the inventory level does not only decrease because of demand but it may also increase in case of returns. Since this makes the analysis much more difficult than traditional inventory control, authors use simplifying assumptions regarding the return process. These assumptions typically are: (1) the demand flow is a homogeneous Poisson Process; (2) the return flow is a homogeneous Poisson Process; and (3) the return process is independent of the demand process (see Fleischmann, 1997; Dekker and van der Laan, 1996). However, there is nearly no (scientific) literature on empirical analysis of data with reverse flows. Thus, in this paper, we explore the empirical validity of these common assumptions. First of all, we present a methodology to check the assumptions empirically. We describe actual practice in companies with respect to information storage on returns and inventory control. Moreover, we apply the methodology to real data and we discuss practical implications of our findings, for instance with respect to information management on inventory systems with returns. We employ data from three companies here referred to as CERN, MOC and RF. CERN, the database of the European Organization for Nuclear Research (CERN Web Communications, 2000) and RF, a refinery, regards internal material returns. MOC, a mail-order company, handles customer product returns. The remainder of the paper is organised as follows. The next section is dedicated to a survey of relevant issues concerning return handling in practice. Next, a review of the main assumptions in the literature when it comes to inventory models with return flows is presented. Then, in Section 4 the methodology is put forward and in Section 5 the data is described. The analysis can be found in Section 6. The last sections sum up the conclusions, practical implications and research needs.

7.1. Summary of findings In this paper, we explored the validity of the general assumptions in the literature on inventory modelling with product returns. We have set a framework for the statistical testing of these assumptions, i.e. whether • the demand process is an HCPP; • the return process is an HCPP; • the time elapsing between return and demand occurrences follows a negative exponential distribution. Afterwards, we used the framework with three sets of real data: Case 1. Data from an in-company warehouse with internal returns in Switzerland (CERN). Case 2. Data from a mail-order company with commercial returns in the Netherlands (referred to as MOC). Case 3. Data from an in-company warehouse in the Netherlands (referred to as RF). We found products for which the common assumptions on the theoretical models fit reasonably, as opposed to products for which they do not. Regarding the (non-)validity of the common assumptions, we empirically observed that: (A) Demand may not behave as an HCPP due to seasonality or over long periods of time (e.g. agenda and stabiliser gas—CERN). (B) In spite of a non-stationary environment, we may not reject that the return process behaves as an HCPP (e.g. large agenda—CERN). (C) In some cases we cannot reject that the time to return behaves as negative exponentially distributed (e.g. stabiliser gas and Group 1—CERN). (D) Time to return does not seem to behave as an exponential distribution due to a long tail (e.g. Group 2—CERN). (E) Time to return does not seem to behave as an exponential distribution on account of the short-lag returns (e.g. Group 3—CERN). With the developed methodology it was possible to carry out the desired testing including small (below 20) sample sizes. Only for extremely small sample sizes, the methodology does not work. It is unambiguous that in the last case, either the proposed or any other statistical framework cannot guarantee rigour. In spite of the specific sets of data, the findings and its implications are transferable to a much larger group of demand-return processes. We employed data on products of in-company warehouses (CERN and RF) with internal returns and a mail-order company with commercial returns. In case of equipment leasing, we conjecture that although the tail of the time to return may behave as an exponential, the same is unlikely to hold for the short-lag returns. In maintenance settings, we believe that the validity of assumptions depends on whether the maintenance is corrective or preventive. In the first case the research findings are likely to apply. 8. Practical implications Returns can be said to be a “necessary evil” as they complicate inventory control. Important is to know how much will come back and when. This knowledge can be used to avoid superfluous replenishment orders and outdating of products. Therefore, it is important that companies monitor returns, investigate return reasons and get an idea of the return lag. Next, companies will have to look how the lag can be shortened, especially for the long-lags. In the context of inventory control, we put forward the following suggestions: • To separate short-lag returns from long-lag returns. In the presence of the former, proceed to netting (D′=D−R), so it is as returns have never occurred. Especially for long-lag returns, monitor returns lag distributions, return rates and register return reasons. The latter helps to find return patterns that may be useful to potential shortening of the lag and to inventory control (e.g. cancellation of replenishments when many products are expected to return). • When investing on product return information (e.g. tracking and tracing) and its storage, the following questions should be taken into account: (1)Does the return lag behave as a negative exponential distribution? (2) Is the environment likely to be stationary? An exponentially distributed time to return is in itself less demanding concerning information than other distributions. In a stationary environment, high investments on tracking and tracing may not pay off. On the other hand, we conjecture that the same happens in highly unstable environments. Thus, the most gains of information are likely to be in medium well-behaved environments.