In practice, deterministic, multi‐period lot‐sizing models are implemented in rolling schedules since this allows the revision of decisions beyond the frozen horizon. Thus, rolling schedules are able to take realizations and updated forecasts of uncertain data (e.g., customer demands) into account. Furthermore, it is common to hold safety stocks to ensure given service levels (e.g., fill rate). As we will show, this approach, implemented in rolling schedules, often results in increased setup and holding costs while (over‐)accomplishing given fill rates. A well‐known alternative to deterministic planning models are stochastic, static, multi‐period planning models used in the static uncertainty strategy, which results in stable plans. However, these models have a lack of flexibility to react to the realization of uncertain data. As a result, actual costs may differ widely from planned costs, and downside deviations of actual fill rates from those given are very high. We propose a new strategy, namely the stabilized cycle. This combines and expands upon ideas from the literature for minimizing setup and holding costs in rolling schedules, while controlling actual product‐specific fill rates for a finite reporting period. A computational study with a multi‐item capacitated medium‐term production planning model has been executed in rolling schedules. On the one hand, it demonstrates that the stabilized‐cycle strategy yields a good compromise between costs and downside deviations. Furthermore, the stabilized‐cycle strategy weakly dominates the order‐based strategy for both constant and seasonal demands.
Little research has been done on hierarchical production planning systems (HPPS) in the context of rolling schedules with service-level constraints. Here, we adapt the stabilized-cycle strategy, which has initially been created for the master planning level (Meistering and Stadtler in Prod Oper Manag 26:2247-2265, to a two-level, multi-item, capacitated (short-medium-term) HPPS with demand uncertainty. For each planning level, we present extensions for mixedinteger programming models from literature (CLSP-L, PLSP) and introduce anticipation functions, as well as linking constraints. In a computational study, we analyze the performance of the HPPS with different rolling schedule strategies: the period-based, the order-based, and the stabilized-cycle strategy. It turns out that the stabilized-cycle strategy dominates the period-based strategy for all studied instances. For some instances, the stabilized-cycle strategy even dominates the order-based strategy; while in remaining instances, the stabilized-cycle strategy provides non-dominated solutions with a significant smaller downside deviation from service-level agreements and only a minor increase of costs. Literature reviewAccording to Bookbinder and Tan (1988), three planning strategies exist for dealing with demand uncertainty in production planning systems: the static uncertainty strategy, the static-dynamic uncertainty strategy and the dynamic uncertainty strategy. In the static uncertainty strategy, all setup and lot-size decisions are made once at the beginning of the planning interval. All decisions in the planning interval are realized and cannot be revised later. In the static-dynamic uncertainty strategy, setup decisions are made at the beginning of the planning interval, while lot-size decisions are made at the beginning of each period, when the initial inventory is known. In the dynamic uncertainty strategy, only decisions concerning the current period are made considering the current period's information. This strategy provides far-from-optimum solutions, especially if the ratio between setup and inventoryholding costs is high (Bookbinder and Tan 1988).Rolling schedules are an alternative to better cope with data uncertainty and are widely used in APS-, ERP-or MRP II-driven production planning Fleischmann et al. 2015). In rolling schedules a plan is generated for a finite planning interval, but only decisions for periods in the frozen horizon are realized . Decisions for periods beyond the frozen horizon are preliminary and can be revised later. After the re-planning interval has elapsed, information is updated and a new plan is generated. The determination of the frozen horizon length can either be period, order or service-level based (Meistering and Stadtler 2017). Thus, there are at least three rolling schedule strategies: the period-based, the order-based and the stabilized-cycle strategy. In the period-based strategy the frozen horizon is set to a given number of periods (often one period), while the frozen horizon in the order-based strategy i...
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