بررسی جایگزینی مشترک روش های تعیین اندازه دسته تولید در فهرست سیستم های برنامه ریزی افقی

Joint replenishment problems are commonly encountered in purchasing, manufacturing, and transportation planning. Literature evaluates various algorithmic approaches for solving the joint replenishment problem in a static environment, but their relative performance in a dynamic rolling horizon system is unknown. This research experimentally evaluates nine joint replenishment lot-sizing heuristics and policy design variables when implemented in a dynamic rolling schedule environment. The findings indicate that a single algorithm does excel on both dimensions of schedule cost and stability. Hence, management must trade off these two performance metrics when choosing the best approach for their specific problem. Generally, metaheuristics provide the best cost replenishment schedule, but forward pass based heuristics yield the most stable schedules. The results also indicate that the choice of lot-sizing heuristic is the major cost performance driver in rolling planning systems, with policy design variables (frozen interval and planning horizon length) having little impact. While the simulated annealing heuristic of Robinson et al. (2007a) is the most effective solution procedure for the static joint replenishment problem, the perturbation metaheuristic of Boctor et al. (2004) produces lower schedule costs and greater stability in rolling schedule environments.

Joint replenishment problems (JRPs) determine the time-phased replenishment schedule that minimizes sum of ordering and inventory costs for a product family. A joint ordering cost is incurred each time one or more items in the product family are replenished and an item order cost is charged for each line item replenished. Silver (1979), Stowers and Palekar (1997), and Robinson and Lawrence (2004) provide examples of joint replenishment problems in production, procurement, and transportation operations. An illustrative problem is procurement operations of a grocery chain where a family of items is sourced from a single vendor. Each replenishment order is accessed a fixed delivery charge regardless of quantity shipped, while each line item incurs a fixed cost for inventory maintenance, receipt, inspection, and put-away. The objective is to minimize sum of delivery charge, line item costs, and inventory costs for the product line recognizing that item replenishment costs are jointly linked through the shared delivery cost. This research investigates the JRP in a rolling horizon planning system with stochastic demand that is forecast. Moving closer in time, the forecast is replaced with booked customer orders as each time period enters the replenishment planning horizon. The resulting problem is a short-term, or “static”, JRP with deterministic, dynamic demand. After solving this static problem, replenishment decisions within the frozen order interval are implemented rolling through time. After a pre-specified re-planning periodicity, a new short-term plan is constructed using the updated demand received since the last planning cycle. When constructing the new replenishment plan, orders from the prior planning cycle that lay outside the frozen order interval may be rescheduled if doing so results in an improved solution for the new planning cycle. In this manner, solutions to a series of linked static planning problems are implemented rolling through time (Blackburn and Millen, 1982). Fig. 1 depicts two planning cycles and illustrates the basic definitions and concepts used in rolling horizon planning systems. Full-size image (25 K) Fig. 1. Illustration of rolling horizon planning environment. Figure options Prior research indicates that effectiveness of rolling horizon planning systems may be determined by planning horizon interval, frozen order interval, re-planning periodicity, choice of lot-sizing procedure for solving the short-term planning problem, and cost and demand factors defining the planning environment. While several researchers study performance of heuristic and optimization-based approaches for solving the static JRP, their relative performance in rolling horizon systems is not addressed. This is a major shortcoming of the literature since the best performing lot-size procedure in a static environment may not be the best performer in a rolling horizon environment. This is due to the end-of-horizon effect, where not knowing the demand beyond the planning horizon may lead to relatively poor quality short-term schedules. Even with optimal solutions to the static problems, their implementation in a rolling horizon environment provides at best a heuristic solution (Simpson, 1999). Prior research on single-item and multi-level rolling horizon problems finds that the problem’s demand pattern, cost structure, choice of lot-sizing procedure, and policy variables governing rolling schedule implementation play a significant role in determining schedule cost and stability. Hence, studying the joint replenishment problem in rolling horizon systems is well justified. This study conducts extensive computational experiments evaluating impact of rolling horizon policy variables (e.g., planning horizon and frozen interval lengths) and joint replenishment lot-sizing procedures on system cost and schedule stability. The findings indicate a tradeoff between schedule cost and stability when selecting a particular lot-sizing procedure for implementation. A single algorithm does not excel on both performance dimensions. The results provide managerial guidelines for implementing joint replenishment lot-sizing procedures in rolling horizon planning systems. The following section reviews the relevant literature on the JRP and rolling horizon planning systems. Next, the experimental design and computer simulation model is described. Research findings are discussed in Section 5 and the final section provides research conclusions and implications.

The research findings and conclusions provide several implications for both researchers and managers. Fig. 4 indicates the tradeoff between cost error and schedule instability for the JRP heuristics. FP-LV produces the most stable schedule, but has the largest cost error. In contrast, PM has the lowest cost error but at a considerably increase in schedule instability over FP-LV. SAM, which ranks a close second on cost error, has the greatest schedule instability of all the lot-sizing heuristics. Six of the heuristics have similar levels of schedule instability, but cost error varies greatly. Fig. 4 enables managers to identify the cost error and schedule stability tradeoff in order to select the heuristic that most closely meets their needs. If cost error is the primary criterion, then the PM is the best choice. However in situations where rescheduling is not desirable, the FP-E and FP-LV heuristics proved to be particularly stable in terms of product family replenishment timing.The research findings provide additional insights on cost error and schedule stability performance. The ANOVA results in Table 3 indicate that the major driver of cost performance is choice of JRP heuristic followed by the problem’s demand density and TBOItem. The policy variables (frozen interval and planning horizon length) have relatively little impact on cost performance. However, Table 7 indicates that driving factors for schedule stability are reversed. Here, the frozen interval and planning horizon length dominate, while the JRP heuristic, demand density, and TBOItem have a lesser impact on schedule stability. This research also provides new insights on applications of the JRP heuristics in static versus rolling schedule environments. While Robinson et al. (2007a, 2007b) suggest that the SAM is the most effective solution procedure for the static JRP this does not hold in rolling schedule environments. Instead, PM produces lower schedule costs, and at substantially greater schedule stability. Considering that JRP heuristics are commonly applied in rolling schedules and the importance of maintaining stable schedules, these findings are important for both researchers and practitioners. The effect of policy design variables on cost error also contradicts the results in the rolling horizon literature for multi-item systems. Shorter planning horizon and longer frozen interval length produce the least cost error. As discussed in Simpson (1999) the use of relative cost measure may explain some of this unexpected results. Suggested research extensions include development of more efficient optimization approaches for the JRP and their testing in both static and rolling schedule environments. This research should also test modified fixed cost approaches as suggested by Stadtler (2000). It is also worthwhile to consider extending the research to include capacitated variant of the JRP. The capacitated problem is frequently encountered in systems with limited shipping and/or production resources. Finally, the research findings highlight the tradeoff between schedule cost and stability. Extending the analysis to explicitly consider rescheduling cost in successive planning iterations would provide an integrated approach to evaluating both schedule cost and schedule stability. This more comprehensive treatment of the problem is well justified, but not addressed in the literature.