In this paper we give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems. The focus of this paper is on the modeling of various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research.

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Modeling Industrial Lot Sizing Problems: A Review

The current paper presents a structured overview over the literature on dynamic simultaneous lotsizing and scheduling problems. We introduce a classification scheme, review the historical development of research in this area and identify recent developments. The main contribution of the present review is the discussion of the historical development of the body of knowledge in the field of simultaneous lotsizing and scheduling and the identification of recent trends. This helps to reveal research opportunities, but it can also be helpful in the selection of appropriate models for industrial applications.

Simultaneous lotsizing and scheduling problems: a classification and review of models

In production planning in the glass container industry, machine-dependent setup times and costs are incurred for switch overs from one product to another. The resulting multi-item capacitated lot-sizing problem has sequence-dependent setup times and costs. We present two novel linear mixed-integer programming formulations for this problem, incorporating all the necessary features of setup carryovers. The compact formulation has polynomially many constraints, whereas the stronger formulation uses an exponential number of constraints that can be separated in polynomial time. We also present a five-step heuristic that is effective both in finding a feasible solution (even for tightly capacitated instances) and in producing good solutions to these problems. We report computational experiments.

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Single machine multi-product capacitated lot sizing with sequence-dependent setups

Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs

This paper introduces an evolutionary algorithm as a procedure to solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem (SITLSP). This problem can be found in some industrial settings, mainly soft drink companies, where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. The challenge is to simultaneously determine the lot-sizing and scheduling of raw materials in tanks and soft drinks in bottling lines, where setup costs and times depend on the previous items stored and bottled. A multi-population genetic algorithm approach with a novel representation of solutions for individuals and a hierarchical ternary tree structure for populations is proposed. Computational tests include comparisons with an exact approach for small-to-moderate-sized instances and with real-world production plans provided by a manufacturer.

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Multi-population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem

The challenging problem of efficient lot sizing on parallel machines with sequence-dependent set-up times is modelled using a new mixed integer programming (MIP) formulation that permits multiple set-ups per planning period. The resulting model is generally too large to solve optimally and, given that it will be used on a rolling horizon basis with imperfect demand forecasts, approximate models that only generate exact schedules for the immediate periods are developed. Both static and rolling horizon snapshot tests are carried out. The approximate models are tested and found to be practical rolling horizon proxies for the exact model, reducing the dimensionality of the problem and allowing for faster solution by MIP and metaheuristic methods. However, for large problems the approximate models can also consume an impractical amount of computing time and so a rapid solution approach is presented to generate schedules by solving a succession of fast MIP models. Tests show that this approach is able to produc...

Simon J. Clark

Papers

Rolling-horizon lot-sizing when set-up times are sequence-dependent