A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

A review of discrete-time optimization models for tactical production planning

Abstract: This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively...

Parallel machine, capacitated lot-sizing and scheduling for the pipe-insulation industry

Abstract: We develop a solution procedure for a production problem that involves the optimal lot-sizing and scheduling of multiple products on parallel machines over a long planning horizon. The objective is...

An analysis of formulations for the capacitated lot sizing problem with setup crossover

Abstract: The lot sizing problem with capacity constraints and setup crossover was studied.We compare the two formulations proposed in the literature.We propose new constraints to break the symmetry in the formulations from the literature.We analyze the impact of the proposed adaptations of the formulations.We analyze the factors that have an impact on the benefits of allowing a setup crossover. The lot sizing problem with setup crossover is an extension of the standard big bucket capacitated lot sizing problem (CLSP). The general idea is that the first setup operation of each planning period can already start in the previous period, if not all the capacity is used in that previous period. This provides more flexibility in the planning and increases the possibility of finding feasible and better solutions compared to the standard assumption. Two different formulations have been presented in the literature to model a setup crossover. Since these formulations have not been compared directly to each other, we present a computational study to determine which is the best formulation. Furthermore, we explore ideas indicating that in one of the formulations from the literature it is not necessary to impose binary conditions on the crossover variables and we propose symmetry breaking constraints for both formulations from the literature. Finally, we quantify the value of this type of flexibility in a computational experiment and analyze which factors influence this value.

The capacitated lot-sizing problem with linked lot-sizes

Abstract: In this paper a new mixed integer programming (MIP) model formulation and its incorporation into a time-oriented decomposition heuristic for the capacitated lot-sizing problem with linked lot sizes (CLSPL) is proposed. The solution approach is based on an extended model formulation and valid inequalities to yield a tight formulation. Extensive computational tests prove the capability of this approach and show a superior solution quality with respect to other solution algorithms published so far.

Capacitated lot-sizing problem with production carry-over and set-up splitting: mathematical models

Abstract: This work proposes mathematical models (MMs) for the capacitated lot-sizing problem with production carry-over and set-up splitting, which can handle two scenarios, namely (1) situation/scenario where the set-up costs and holding costs are product dependent and time independent, and with no backorders or lost sales, and (2) situation where the set-up costs and holding costs are product dependent and time dependent, and with no backorders or lost sales. Previously, in an existing study the authors had developed a MM for the same problem and situation where the set-up costs and holding costs are product dependent and time independent, i.e. our Scenario 1. We compare our proposed models with the model in the existing study that appears to be incorrect.

A review of scheduling research involving setup considerations

Abstract: The majority of scheduling research assumes setup as negligible or part of the processing time. While this assumption simplifies the analysis and/or reflects certain applications, it adversely affects the solution quality for many applications which require explicit treatment of setup. Such applications, coupled with the emergence of production concepts like time-based competition and group technology, have motivated increasing interest to include setup considerations in scheduling problems. This paper provides a comprehensive review of the literature on scheduling problems involving setup times (costs). It classifies scheduling problems into batch and non-batch, sequence-independent and sequence-dependent setup, and categorizes the literature according to the shop environments of single machine, parallel machines, flowshops, and job shops. The suggested classification scheme organizes the scheduling literature involving setup considerations, summarizes the current research results for different problem types, and finally provides guidelines for future research.

Capacitated lot sizing with setup times

Abstract: This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems. The Lagrangian dual costs are updated by subgradient optimization, and the single-item problems are solved by dynamic programming. A heuristic smoothing procedure constructs feasible solutions (production plans) which do not require overtime. The algorithm solves problems with setup time or setup cost. Problems with extremely tightly binding capacity constraints were much more difficult to solve than anticipated. Solutions without overtime could not always be found for them. The most significant results are that (1) the tightness of the capacity constraint is a good indicator of problem difficulty for problems with setup time; and (2) the algorithm solve...

Modeling Industrial Lot Sizing Problems: A Review

Abstract: 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.

Dynamic capacitated lot-sizing problems: a classification and review of solution approaches

Abstract: This paper presents a review of four decades of research on dynamic lot-sizing with capacity constraints. We discuss both different modeling approaches to the optimization problems and different algorithmic solution approaches. The focus is on research that separates the lot-sizing problem from the detailed sequencing and scheduling problem. Our conceptional point of reference is the multi-level capacitated lot-sizing problem (MLCLSP). We show how different streams of research emerged over time. One result is that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice. Our review also shows that currently mathematical programing and the use of metaheuristics are particularly popular among researchers in a vivid and flourishing field of research.

Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic

Abstract: This paper presents a new algorithm for the dynamic multi-level capacitated lot sizing problem with setup carry-overs (MLCLSP-L) The MLCLSP-L is a big-bucket model that allows the production of any number of products within a period, but it incorporates partial sequencing of the production orders in the sense that the first and the last products produced in a period are determined by the model We solve a model which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs Our algorithm solves a series of mixed-integer linear programs in an iterative so-called fix-and-optimize approach In each instance of these mixed-integer linear programs a large number of binary setup variables is fixed whereas only a small subset of these variables is optimized, together with the complete set of the inventory and lot size variables A numerical study shows that the algorithm provides high-quality results and that the computational effort is moderate