https://sci2s.ugr.es/sites/default/files/files/Teaching/GraduatesCourses/Metaheuristicas/Bibliography/VNS.pdf

Variable neighborhood search

Variable Neighborhood Search.

Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.

/pdf/the-capacitated-lot-sizing-problem-a-review-of-models-and-4w6zf77n9a.pdf

The capacitated lot sizing problem: a review of models and algorithms

Integrated production/distribution planning in supply chains: An invited review

Mixed-model assembly lines are used to produce many different products without carrying large inventories. The effective utilization of these lines requires that a schedule for assembling the different products be determined. For Just-In-Time JIT production systems, which require producing only the necessary products in the necessary quantities at the necessary times, the objective is to keep a constant rate of usage of all parts used by the line. This is called levelling or balancing the schedule. This paper develops a theoretical basis for scheduling these systems, and presents new scheduling algorithms and heuristics.

Level schedules for mixed-model assembly lines in just-in-time production systems

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...

https://www.jstor.org/stable/pdfplus/2631977.pdf

Capacitated lot sizing with setup times

This paper investigates a multi-item, multi-level production scheduling problem with linear costs and production and inventory constraints at one key facility. Two multi-item problems-one in which the constraint was on shipping capability and one in which there was a final stage bottleneck machine-motivated the paper. A multi-item facilities-in-series problem is formulated, in standard fashion, as a linear program. Then we show that in certain important cases the 3-period problem is a network problem. This 3-period result is used as the basis for a rolling heuristic for T-period problems. The conditions under which this heuristic fails to find optimal solutions are discussed and computational comparisons to standard linear programming are given. Finally, we discuss ways of dealing with two constrained facilities and with setup costs.

William W. Trigeiro

Papers

Capacitated lot sizing with setup times

Network Programming Models for Production Scheduling in Multi-Stage, Multi-Item Capacitated Systems