روش های بهینه سازی مبتنی بر شبیه سازی برای تنظیم پارامترهای برنامه ریزی تولید

This paper refers to a hierarchical production planning system in a make-to-order environment. A challenging task in this context is to determine good production parameter settings in order to benefit from established planning methods. We present a framework for hierarchical production planning which we use to identify good settings for three planning parameters, namely planned leadtimes, safety stock, and lotsizes. Within a discrete-event simulation which mimics the production system we use a mathematical optimization model for replicating the decision problem. This mathematical model is solved to optimality using a standard optimization engine. We use data referring to four different demand market situations in order to derive general statements concerning the quality and sensitivity of the three analyzed planning parameters. For exploring the parameter space we follow the concept of simulation-based optimization. We compare the performance of six different optimization methods to a kind of systematic enumeration of parameter combinations. We show that among these a search procedure based on the idea of Variable Neighborhood Search (VNS) leads to the best results in this context.

Manufacturing companies are often faced with challenging market situations concerning product complexity and changing demand situations. Their customers frequently emphasize on logistics performance (e.g. service levels, delivery leadtimes, average lateness) in addition to product quality. In order to remain competitive various decisions, which are strongly influencing each other although referring to different planning levels, have to be made carefully. Tasks like capacity planning, order release, lotsizing, and scheduling are often mentioned to be typical challenges in this context (see Stadtler and Kilger, 2005 and Schuh, 2006). Different decision levels usually refer to different time horizons and aggregation degrees. This is mainly induced by an increasing level of uncertainty involved in longer planning horizons. Coordination between decisions taken on different levels can be approached by implementing a hierarchical planning system (cf. Hax and Meal, 1975, Sitompul and Aghezzaf, 2011, Hopp and Spearman, 2000 and Schneeweiss, 2003). We present such a system in the context of make-to-order production. Our experimental framework has been implemented based on data from the automotive supplier industry. However, it is not restricted to this business area, but could also be used to model make-to-order manufacturing environments from other industries. The main driver in make-to-order manufacturing systems are customer orders, which means that production processes are always triggered by the given demand. Important components of hierarchical planning system for make-to-order production systems are aggregate planning, Master Production Scheduling (MPS) and Material Requirements Planning (MRP). Within our framework for aggregate planning we use a linear model, solve it to optimality and derive the master plan. The performance of such a planning framework of course is highly influenced by the setting chosen for the inherent parameters. Thus, parameter tuning is a crucial issue in this context. Since MPS is already solved exactly, we have to take care about MRP related parameters that have to be optimized in order to ensure a well performing system. In this study we consider planned leadtimes, safety stock, and lotsizes as most relevant for our investigations. In this study we use the term planned leadtimes for the number of time periods to insert between the due date and the start date of a production order in addition to known processing times. Thus, the release date of a production order i with planned leadtime plt i and estimated processing time t i is (plti+ti)(plti+ti) periods ahead of its due date. Of course both customer orders and production replenishment orders are triggered by this parameter. The arising trade-off refers to short planned leadtimes with more variable workload on the shopfloor, and long ones leading to an increased level of work-in-process (cf. Teo et al., 2011). Since we are investigating a setting with stochastic influences we also use safety stocks to increase service levels. Safety stocks used within the MRP concept have a somehow similar impact as planned leadtimes since both of them are intended to reduce the risk of stock-out situations. Clearly, here we observe a trade-off between increased service level and high inventory levels. Increased lotsizes also lead to higher inventories but reduce the number of set-ups. In our framework the settings specified during the planning steps are used for execution on the simulated shopfloor where we are able to measure a number of performance indicators. The impact of parameter settings is examined on a combined objective function consisting of service- and inventory level. For this purpose we have to find a method able to search the parameter space efficiently. Of course using the stand-alone simulation for some trial-and-error experiments would be insufficient to find satisfying results. An analytical model on the other hand covering all stochastic and non-linear dependencies of the given problem would be far too complex to be solved in acceptable amount of time (see Almeder et al., 2009). The concept of simulation-based optimization, where the simulation is embedded into a superordinate search procedure seems to be most appropriate here (cf. Köchel and Nieländer, 2005). This leads us to a further contribution of this work which is the identification of methods for searching the parameter space efficiently. Different simulation-based optimization methods, where the output of the simulation triggers a superordinate search procedure, are compared. Also a commercial software add-on is subject to our evaluations. The performance of these methods is evaluated based on results from a systematic enumeration of parameter combinations. This paper is organized as follows. The upcoming section is dedicated to related literature. Section 3 describes the experimental framework used as input for the parameter optimization procedures. The latter are described in Section 4. Results are provided in Section 5. Conclusions and further research are summed up in Section 6.

In this paper we investigated methods for finding good settings for planning parameters in a make-to-order environment. We presented a simulation-optimization framework going align with the concept of hierarchical planning. In this framework production plans are executed on a shop floor where performance indicators are measured and used for the parameter optimization. MPS is regularly calculated by an embedded optimizer, so we concentrate on MRP parameters, namely planned leadtime, safety stocks and lotsizes. Since we wanted to analyze the impact of all three parameters simultaneously we needed an efficient method to search the arising huge parameter space. For this purpose we proposed six simulation-based optimization methods which we evaluated compared to a systematic enumeration of parameter settings. We identified a procedure based on the VNS concept as most robust, and thus most favorable in this context. Based on the results found by the VNS algorithm for four different demand scenarios we analyzed the impact of the three investigated parameters on an objective function covering service- and inventory level. We provided managerial recommendations for identifying good parameter settings in the context of robust production planning. For instance, we found that for the given setting and the underlying assumptions it seems that safety stocks need not increase with rising demand volatility, as is usually postulated in the literature. Concerning further research it would be worthwhile to relax the assumption that production orders for all products are triggered by an identical parameter setting. Since this extension would lead to a considerably increased solution space it cannot be expected to apply this directly to larger real world scenarios. One might be able to generate decision rules in order to find reasonable good parameter settings depending on the characteristic of the demand and the production environment. Also the inclusion of more planning parameters and an analysis of their mutual influences might lead to valuable managerial insights. Referring to the presented framework it would be interesting to extract more subproblems (in addition to the MPS) and try to solve them to optimality. One possibility would be to tackle the lotsizing problem by an additional optimization method. Since we face a multi-level capacitated lotsizing problem (MLCLSP) here, we would have to use an appropriate (meta)heuristical approach.