تعیین اندازه دسته تولید در مقابل دسته بندی در برنامه ریزی تولید و توزیع کالا فاسد شدنی

Joint production and distribution planning at the operational level has received a great deal of attention from researchers. In most industries these processes are decoupled by means of final goods inventory that allow for a separated planning of these tasks. However, for example, in the catering industry, an integrated planning framework tends to be more favorable due to the perishable nature of the products that forces a make-to-order production strategy. So far this planning problem has only been addressed by allowing the batching of orders. The main contribution of this paper is to extend this approach and prove the importance of lot sizing for make-to-order systems when perishability is explicitly considered. The value of considering lot sizing versus batching is further investigated per type of production scenario. Overall, results indicate that lot sizing is able to deliver better solutions than batching. On average, for the improved instances, the cost savings ascend to 6.5% when using lot sizing. The added flexibility of lot sizing allows for a reduction on production setup costs and both fixed and variable distribution costs. The savings derived from lot sizing are enhanced by customer oriented time windows and production systems with non-triangular setups.

Strategic, tactical and operational integration of the production and distribution processes is reported as being able to deliver better results for companies than a decoupled approach (Park, 2005 and Amorim et al., 2012). Very often this integration is driven by a management decision, rather than by an actual need of the underlying processes. However, when the final products are not allowed to be stocked due to, for example, freshness reasons this integration scenario becomes imperative. Within these three decision levels, it is on the operational one where more research needs to be conducted (Chen, 2009), since actual models fail to be accurate and detailed enough for the real-world problems. The motivation for studying the operational integrated production and distribution problem comes from very practical industry situations when it is not possible or advisable to keep final inventory decoupling these two processes. In this case, companies are forced to engage in a make-to-order production strategy. Therefore, the production for a certain demand order may only start after the order arrival. The examples found in practice are related to the computer assembly industries, the food-catering, the industrial adhesive materials or the ready-mixed concrete. The importance of a holistic vision of these processes is driven by very demanding customers requiring a product that cannot wait a long time to be delivered after production. These products, having a very short lifespan, will be called hereafter as perishable. Hence, the considered operational integrated production and distribution problem relates to the decisions on how to serve a set of customers with demand for different products. The planner has to simultaneously decide on the production planning and vehicle routing, in a setting where inventory is not allowed (i.e. no inventory is carried from one planning horizon to the subsequent). Regarding the production process, the definitions proposed by Potts and Van Wassenhove (1992) are followed, where batching is defined as the decision of whether or not to schedule similar jobs contiguously and lot sizing refers to the decision of when and how to split a production lot of identical items into sublots. Note that processing times are proportional to the quantities processed in both cases. The modelling of our problem considers a complex production system that is accurately synchronized with the distribution process to allow for as much flexibility as possible. Therefore, no specific industry constraints are modelled, but instead the formulation is as general as possible. Several parallel production lines with sequence dependent setups are taken into account. Moreover, the demand from different customers for a set of products has to be delivered within strict time windows on different routes that have to be determined together with the production planning. So far the research community has tackled this operational integrated production and distribution problem by batching orders of customers as if lot sizing decisions were never to yield a better solution. This is clearly not the case in the production planning literature where the importance of considering lot sizing and scheduling simultaneously is consensual for the multi-period setting (for example Almada-Lobo et al., 2010). By just considering batching operations one could not achieve a production plan in which a product to a given customer is processed on different lines for example. Intuitively, however, it is observable that if the requested product is strongly perishable, then it may make sense to produce it simultaneously on both lines to ship it as soon as possible. To the best of our knowledge, the incorporation of lot sizing decisions in the operational production and distribution problem has never been analyzed. Therefore, a major contribution of this paper is to evaluate whether lot sizing decisions may deliver better results than batching when this integrated problem tackles perishability. After proving that lot sizing should be considered in this problem setting, the secondary contribution is to understand the conditions that improve the benefits of lot sizing versus batching. The remainder of this paper is organized as follows. The next section reviews the literature on the operational integrated production and distribution problem. Section 3 describes the considered problem and proposes two mathematical formulations for the operational production and distribution problem of perishable goods: one considering batching and the other lot sizing. In Section 4, the results of the computational study are presented and the impact of considering lot sizing versus batching is assessed. Finally, the paper is concluded in Section 5 with the main findings and ideas for future work.

In this paper, we have analyzed the importance of considering sizing the lots (or in other words, splitting the jobs) besides pure batching at the operational production and distribution planning when considering perishability. The lot sizing decision is a counterintuitive one in make-to-order environments and this is the first time that its importance is analyzed. The logistic setting of our operational problem encompasses multiple perishable products subject to sequence dependent changeovers, which have to be delivered in a certain route by one of the available vehicles. We have developed models for integrating with accuracy both lot sizing and batching with the vehicle routing problem with time windows. In order to understand the impact of the extra flexibility coming from the possibility of splitting the lots, experiments varying different key parameters are designed and the solutions between the batching and lot sizing models are compared. Computational results for the set of systematically generated instances show that lot sizing is able to decrease the integrated production and distribution costs on very different types of instances. Both customer oriented time windows and production environments with non-triangular setups seem to favour the importance of considering lot sizing in this operational problem. Several mechanisms to improve the batching solution were found by the lot sizing model. The lot sizing solution could achieve a better performance by: reducing the number of setups, changing the sequence, reducing setup costs, reducing the number of vehicles and/or the total travelled distance.