DYNAMIC LOT-SIZING PROBLEMS: A Review on Model and Efficient Algorithm

Due to their importance in industry, dynamic demand lot-sizing problems are frequently studied.This study consider dynamic lot-sizing problems with recent advances in problem and modelformulation, and algorithms that enable large-scale problems to be effectively solved.Comprehensive review is given on model formulation of dynamic lot-sizing problems, especiallyon capacitated lot-sizing (CLS) problem and the coordinated lot-sizing problem. Bothapproaches have their intercorrelated, where CLS can be employed for single or multilevel/stage, item, and some restrictions. When a need for joint setup replenishment exists, thenthe coordinated lot-sizing is the choice. Furthermore, both algorithmics and heuristics solutionin the research of dynamic lot sizing are considered, followed by an illustration to provide anefficient algorithm

A heuristic approach for big bucket multi-level production planning problems

Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems

The development and testing of new, single and multiple echelon, dynamic, capacitated, lot sizing heuristics

Three new heuristics and two random problem generators are introduced and tested. These heuristics and problem generators are associated with single and multiple echelon, dynamic, capacitated lot sizing problems, with or without setup times. These types of problems often occur in an MRP environment;First, the Dixon and Silver (DS) lot sizing heuristic was extended. The new, single echelon heuristic offers improved cost performance at a small computational expense. It incorporates newly developed perturbation factors that allow for multiple iterations of the DS heuristic. At the conclusion of all iterations, the lowest cost production plan is recalled. The second, single echelon heuristic developed and tested, the MG heuristic, is capable of solving large-scale, dynamic, capacitated, lot sizing problems, with or without setup times. This heuristic has three main sections: (A) Wagner-Whitin algorithm and a feasibility seeking subroutine; (B) a DS heuristic modified to allow for setup times; and (C) newly developed improvement algorithms that seek lower costs while maintaining feasibility;Comparison testing of the MG heuristic against other leading heuristics used a random problem generator to produce realistic, large-scale, single echelon problems. For even the largest group of problems tested, 4000 items and 25 periods, its average CPU time (on a DECstation 5000) was 1.0 minute. And, for all 216 problems tested, the MG heuristic\u27s average solution costs were just 0.86% higher than the best heuristic against which it was tested, at 0.026 the computation time;The new, multiple echelon heuristic utilizes multiple iterations of a sequential top-down approach that combines single echelon approaches with a feasibility feedback mechanism to higher echelons. Additionally, the heuristic incorporates two cost modification procedures: (A) Blackburn and Millen\u27s KCC procedure; and (B) newly developed holding cost adjustment factors, one for each echelon. The holding cost adjustment factors are available for application to each item on a particular echelon and assist the heuristic in finding a feasible solution to capacitated problems. Then, the best combination of factors is explored with a simulated annealing procedure. In comparison to other heuristics, encouraging test results were obtained for assembly problems produced using a new random problem generator

Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling 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 lot sizing with product returns

We address the dynamic lot sizing problem for systems with product returns. The demand and return amounts are deterministic over the finite planning horizon. Demands can be satisfied by manufactured/procured new items, but also by remanufactured returned items. The objective is to determine those lot sizes for manufacturing and remanufacturing that minimize the total cost composed of holding cost for returns and serviceable products and set-ups costs. Two different set-up cost schemes are considered; there is either a joint set-up cost for manufacturing and remanufacturing (single production line) or separate set-up costs (dedicated production lines). For the joint set-up cost case, we present an exact, polynomial time dynamic programming algorithm. For both cases, we propose a number of heuristics and test them in an extensive numerical study

A lot-sizing problem in deliberated and controlled co-production systems

We consider an uncapacitated lot sizing problem in co-production systems, in which it is possible to produce multiple items simultaneously in a single production run. Each product has a deterministic demand to be satisfied on time. The decision is to choose which items to co-produce and the amount of production throughout a predetermined planning horizon. We show that the lot sizing problem with co-production is strongly NP-Hard. Then, we develop various mixed-integer linear programming (MILP) formulation of the problem and show that LP relaxations of all MILPs are equal. We develop a separation algorithm based on a set of valid inequalities, lower bounds based on a dynamic lot-sizing relaxation of our problem and a constructive heuristic that is used to obtain an initial solution for the solver, which form the basis of our proposed Branch & Cut algorithm for the problem. We test our models and algorithms on different data sets and provide the results.WOS:000754103800001Scopus - Affiliation ID: 60105072Science Citation Index ExpandedQ2-Q3Article; Early AccessUluslararası işbirliği ile yapılan - HAYIRŞubat2022YÖK - 2021-22Aralı