Multi-level Lot Sizing Research Articles

Multilevel Lot Sizing with a Genetic Algorithm Under Fixed and Rolling Horizons

Multilevel Lot Sizing with a Genetic Algorithm Under Fixed and Rolling Horizons

A genetic algorithm to solve the general multi-level lot-sizing problem with time-varying costs

The multi-level lot-sizing (MLLS) problem in material requirements planning (MRP) systems belongs to those problems that industry manufacturers daily face in organizing their overall production plans. However, this combinatorial optimization problem can be solved optimally in a reasonable CPU only when very small instances are considered. This legitimates the search for heuristic techniques that achieve a satisfactory balance between computational demands and cost effectiveness. In this paper, we propose a solution method that exploits the virtues and relative simplicity of genetic algorithms to address combinatorial problems. The MLLS problem that is examined here is the most general version in which the possibility of time-varying costs is allowed. We develop a binary encoding genetic algorithm and design five specific genetic operators to ensure that exploration takes place within the set of feasible solutions. An experimental framework is set up to test the efficiency of the proposed method, which turns out to rate high both in terms of cost effectiveness and execution speed.

A multi-class multi-level capacitated lot sizing model

When demand loading is higher than available capacity, it takes a great deal of effort for a traditional MRP system to obtain a capacity-feasible production plan. Also, the separation of lot sizing decisions and capacity requirement planning makes the setup decisions more difficult. In a practical application, a production planning system should prioritize demands when allocating manufacturing resources. This study proposes a planning model that integrates all MRP computation modules. The model not only includes multi-level capacitated lot sizing problems but also considers multiple demand classes. Each demand class corresponds to a mixed integer programming (MIP) problem. By sequentially solving the MIP problems according to their demand class priorities, this proposed approach allocates finite manufacturing resources and generates feasible production plans. In this paper we experiment with three heuristic search algorithms: (1) tabu search; (2) simulated annealing, and (3) genetic algorithm, to solve the MIP problems. Experimental designs and statistical methods are used to evaluate and analyse the performance of these three algorithms. The results show that tabu search and simulated annealing perform best in the confirmed order demand class and forecast demand class, respectively.

Multi-level lotsizing and scheduling by batch sequencing

Multi-level lotsizing and scheduling by batch sequencing

Multi-level lotsizing and scheduling by batch sequencing

We consider a single-machine scheduling problem with a multi-level product structure. Setups are required if the machine changes production from one product type to another, and the scheduling decision must satisfy dynamic demand. We propose a lotsizing as well as a scheduling model, and we compare solution procedures for both models on a very restricted set of instances. As a result the multi-level structure complicates the inventory balance constraints in the lotsizing model. In the scheduling model, however, the multi-level structure translates into precedence constraints between jobs (leading to a smaller search space) which allows it to solve the scheduling model to optimality.

Multi-Level Lotsizing and Scheduling by Batch Sequencing

Multi-Level Lotsizing and Scheduling by Batch Sequencing

Feasible sequential decisions and a flexible Lagrangean-based heuristic for dynamic multi-level lot sizing

We propose an extended model for dynamic multi-level lot sizing with general acyclic product structure and unconstrained resources (MLUR), including additional constraints on lot sizes and cumulative production. These allow for interactive decisions and flexible planning sequences. For three types of decisions we examine the space of feasible decisions, the main part being dedicated to single-product decisions. In order to be able to solve the single-product problems with the algorithm by Chen et al. ( Journal of Global Optimization, 4(4),397–413). We focus on the case where the decision space can be given by upper and lower bound constraints on lot sizes and cumulative production. We establish a characterization of this case as well as sufficient conditions of wide applicability and give algorithms to compute the bounds. As an application, we formulate a Lagrangean-based heuristic using a primal procedure with flexible planning sequence. Extensive testing on classical MLUR problems shows consistent improvement in solution quality compared with other heuristics.

Demand shuffle?A method for multilevel proportional lot sizing and scheduling

This contribution acquaints the reader with a model for multilevel single-machine proportional lot sizing and scheduling problems (PLSPs) that appear in the scope of short-term production planning. It is one of the first articles that deals with dynamic capacitated multilevel lot sizing and scheduling, which is of great practical importance. The PLSP model refines well-known mixed-integer programming formulations for dynamic capacitated lot sizing and scheduling as, for instance, the DLSP or the CSLP. A special emphasis is given on a new method called demand shuffle to solve multilevel PLSP instances efficiently but suboptimally. Although the basic idea is very simple, it becomes clear that in the presence of precedence and capacity constraints many nontrivial details are to be concerned. Computational studies show that the presented approach decidedly improves recent results.

Lot sizing and scheduling — Survey and extensions

This contribution summarizes recent work in the field of lot sizing and scheduling. The objective is not to give a comprehensive literature survey, but to explain differences of formal models and to provide some first readings recommendations. Our focus is on capacitated, dynamic, and deterministic cases. To underscore the importance of the research efforts, current practice is described and its shortcomings are exposed. Mathematical programming models where the planning horizon is subdivided into several discrete periods are given for both approaches that are well-established and approaches which may represent tomorrow's state of the art. Two research directions are discussed in more detail: continuous time models and multi-level lot sizing and scheduling. The paper concludes with some advice for future research activities.

A capacity-oriented hierarchical approach to single-item and small-batch production planning using project-scheduling methods

Most production planning and control (PPC) systems used in practice have an essential weakness in that they do not support hierarchical planning with feedback and do not observe resource constraints at all production levels. Also, PPC systems often do not deal with particular types of production, for example, low-volume production. We propose a capacity-oriented hierarchical approach to single-item and small-batch-production planning for make-to-order production. In particular, the planning stages of capacitated master production scheduling, multi-level lot sizing, temporal and capacity planning, and shop floor scheduling are discussed, where the degree of aggregation of products and resources decreases from stage to stage. It turns out that the optimization problems arising at most stages can be modelled as resourceconstrained project scheduling problems.

Demand shuffle—A method for multilevel proportional lot sizing and scheduling

This contribution acquaints the reader with a model for multilevel single-machine proportional lot sizing and scheduling problems (PLSPs) that appear in the scope of short-term production planning. It is one of the first articles that deals with dynamic capacitated multilevel lot sizing and scheduling, which is of great practical importance. The PLSP model refines well-known mixed-integer programming formulations for dynamic capacitated lot sizing and scheduling as, for instance, the DLSP or the CSLP. A special emphasis is given on a new method called demand shuffle to solve multilevel PLSP instances efficiently but suboptimally. Although the basic idea is very simple, it becomes clear that in the presence of precedence and capacity constraints many nontrivial details are to be concerned. Computational studies show that the presented approach decidedly improves recent results. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 319–340, 1997

Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing

Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing

Resource-constrained materials requirements planning- MRP rc

Computerized MRP systems used in industrial practice have been criticized by researchers as well as industrial users with respect to their limited ability to generate feasible production schedules. In this paper the lot size planning stage of a typical MRP system is considered. Several modelling alternatives for multi-level lot sizing are discussed with the help of a small example. A resourceconstrained approach to lot sizing- called MRP rc- is presented that cooperates with standard production planning and control systems. In this approach the item-by-item lot size planning is substituted by the heuristic solution of a multi-level multi-item dynamic capacitated lot sizing problem with setup times for general product structures.

Competitive methods for multi-level lot sizing and scheduling: tabu search and randomized regrets

This contribution presents two heuristic approaches for multi-level, single-machine lot sizing and scheduling. The first one is a variant of a so-called randomized regret based heuristic which is assumed to be the fastest available method for this particular class of problems. The second approach is a tabu search technique that is competitive with respect to both the run-time performance and the average deviation from the optimum objective function values.

Setups and effective capacity: the impact of lot sizing techniques in an MRP environment

Abstract This study investigates how lot sizing techniques influence the profit performance, inventory level, and order lardiness of an assembly job shop controlled by MRP. Four single-level lot sizing techniques are compared by simulation analysis under two levels of master schedule instability and two levels of end item demand. A second analysis investigates the influence of a multilevel lot sizing technique, the generalized constrained-K (GCK) cost modification, on the four single-level techniques at low demand and low nervousness. The analyses reveal a previously unreported phenomenon. Given the same inventory costs, the single-level lot sizing techniques generate substantially different average batch sizes. The lot sizing techniques maintain the following order of increasing average batch size (and decreasing total setup time): economic order quantity (EOQ) period order quantity (POQ) least total cost (LTC) Silver-Meal heuristic (SML) The causes for different average batch sizes among the lot sizing ...

A simple procedure for solving single level lot sizing problems

We introduce a short procedure for solving single level lot sizing problems. It does not require extensive training to understand the procedure, and is so simple that it can be done on the “back of an envelope”. Even under “hard” test conditions it results in inventory costs that average only 0.70% higher than optimal. The procedure can also be used as a conceptual “building block” for explaining multi-level lot sizing problems.

LINEAR PROGRAMMING, SIMULATED ANNEALING AND TABU SEARCH HEURISTICS FOR LOTSIZING IN BOTTLENECK ASSEMBLY SYSTEMS

Multilevel lotsizing is one of the most challenging subjects in production planning, especially in the presence of capacity constraints. In this paper we investigate lotsizing heuristics for assembly production systems with a bottleneck. More specifically, we discuss heuristics based on Linear Programming (LP), and compare the performance of these heuristics with the performance of approaches based on simulated annealing and tabu search techniques.A comparison of the three heuristics on a set of test problems shows that simulated annealing and tabu search perform well compared to pure LP-based heuristics, but the effectiveness of the latter heuristics can be improved by combining them with elements from simulated annealing and tabu search.

An Improved Heuristic for Multilevel Lot Sizing in Material Requirements Planning

Improvement on existing techniques for multilevel lot sizing in material requirements planning was sought by developing a theoretical and mathematical basis for the problem. Such a foundation was employed to design a heuristic which was superior in both cost performance and computational efficiency, and provided consistent results regardless of designated environmental factors. This represents a significant advantage over other algorithms tested here and within the literature, in that their performances are dependent upon various lot‐sizing environmental factors.The heuristic is based on the technique for order placement and sizing (TOPS), a single‐item technique, and utilizes a mechanism for linking interdependent lot‐sizing decisions. The inputs are applied in a sequential manner to constitute sequential TOPS with incremental look‐down (STIL). A two‐phase experimental design was employed to evaluate the performance of STIL against optimality and other heuristics. Results from the initial phase of simplified problems revealed practical indifference from optimality for the new algorithm. Phase 2 emphasized the relative strength and consistency of the proposed heuristic versus all other rules tested over more difficult examples. The final stage also indentified environments in which STIL performed particularly well. These were more descriptive of common industrial settings than were cases in which existing methods have been shown to be effective.

Combining items for lot sizing in multi-level assembly systems

Abstract Multi-level lot sizing problems are difficult to solve optimally when the product structure contains more than a few items. This paper identifies conditions on the cost parameters which, when applicable, allow items to be combined for purpose of optimization, thereby reducing the size of the problem.

Note—On MRP Lot Sizing

In this Note we present an alternative formulation to the MRP lot sizing model of Steinberg and Napier (SN) (Steinberg, E., H. A. Napier. 1980. Optimal multi-level lot sizing for requirements planning systems. Management Sci. 26 (2) 1258–1271.). The alternative is more parsimonious and the notation less cumbersome. We also point out several errors in the formulation of the SN model which are significant for future research.