Self-adaptive randomized constructive heuristics for the multi-item capacitated lot-sizing problem

Capacitated lot-sizing problems (CLSPs) are important and challenging optimization problems in production planning. Amongst the many approaches developed for CLSPs, constructive heuristics are known to be the most intuitive and fastest method for finding good feasible solutions for the CLSPs, and therefore are often used as a subroutine in building more sophisticated exact and metaheuristic approaches. Classical constructive heuristics, such as the period-by-period heuristics and lot elimination heuristics, are first introduced in the 1990s, and thereafter widely used in solving the CLSPs. This paper evaluates the performance of period-by-period and lot elimination heuristics, and improves the heuristics using perturbation techniques and self-adaptive methods. We have also proposed a procedure for automatically adjusting the parameters of the proposed heuristics so that the values of the parameters can be chosen based on features of individual instances. Experimental results show that the proposed self-adaptive randomized period-by-period constructive heuristics are efficient and can find better solutions with less computational time than the tabu search and lot elimination heuristics. When the proposed constructive heuristic is used in a basic tabu search framework, high-quality solutions with 0.88% average optimality gap can be obtained on benchmark instances of 12 periods and 12 items, and optimality gap within 1.2% for the instances with 24 periods and 24 items

Locating emergency services with priority rules: The priority queuing covering location problem

One of the assumptions of the Capacitated Facility Location Problem (CFLP) is that demand is known and fixed. Most often, this is not the case when managers take some strategic decisions such as locating facilities and assigning demand points to those facilities. In this paper we consider demand as stochastic and we model each of the facilities as an independent queue. Stochastic models of manufacturing systems and deterministic location models are put together in order to obtain a formula for the backlogging probability at a potential facility location. Several solution techniques have been proposed to solve the CFLP. One of the most recently proposed heuristics, a Reactive Greedy Adaptive Search Procedure, is implemented in order to solve the model formulated. We present some computational experiments in order to evaluate the heuristics’ performance and to illustrate the use of this new formulation for the CFLP. The paper finishes with a simple simulation exercise.Location, queuing, greedy heuristics, simulation

An Integrated Strategy for a Production Planning and Warehouse Layout Problem: Modeling and Solution Approaches

We study a real-world production warehousing case, where the company always faces the challenge to find available space for their products and to manage the items in the warehouse. To resolve the problem, an integrated strategy that combines warehouse layout with the capacitated lot-sizing problem is presented, which have been traditionally treated separately in the existing literature. We develop a mixed integer linear programming model to formulate the integrated optimization problem with the objective of minimizing the total cost of production and warehouse operations. The problem with real data is a large-scale instance that is beyond the capability of optimization solvers. A novel Lagrangian relax-and-fix heuristic approach and its variants are proposed to solve the large-scale problem. The preliminary numerical results from the heuristic approaches are reported

Integrated production-distribution systems : Trends and perspectives

During the last two decades, integrated production-distribution problems have attracted a great deal of attention in the operations research literature. Within a short period, a large number of papers have been published and the field has expanded dramatically. The purpose of this paper is to provide a comprehensive review of the existing literature by classifying the existing models into several different categories based on multiple characteristics. The paper also discusses some trends and list promising avenues for future research

A Multi-level Capacitated Lot-sizing Problem with Safety Stock Deficit and Production Manners: A Revised Simulated Annealing

[1] Corresponding author e-mail: [email protected]   [1] Corresponding author e-mail: [email protected]   Lot-sizing problems (LSPs) belong to the class of production planning problems in which the availability quantities of the production plan are always considered as a decision variable. This paper aims at developing a new mathematical model for the multi-level capacitated LSP with setup times, safety stock deficit, shortage, and different production manners. Since the proposed linear mixed integer programming model is NP-hard, a new version of simulated annealing algorithm (SA) is developed to solve the model named revised SA algorithm (RSA). Since the performance of the meta-heuristics severely depends on their parameters, Taguchi approach is applied to tune the parameters of both SA and RSA. In order to justify the proposed mathematical model, we utilize an exact approach to compare the results. To demonstrate the efficiency of the proposed RSA, first, some test problems are generated; then, the results are statistically and graphically compared with the traditional SA algorithm

Integrating Capacitated Lot-Sizing and Lot Streaming in Flowshop Schedules with Time Varying Demand

Any reasonable production planning contains three important decisions on lot size, lead time, and capacity. The common approach in the literature is to divide the planning problem into lot sizing, lot sequencing, and lot splitting sub-problems. Very few studies, to the best of our knowledge, have been conducted on the interdependencies and three- way interaction of lead-time, lot size, and actual capacity usage. A particular lot size calculated by the sub-problem method, however, will likely yield an infeasible solution or at least result in schedule instability (nervousness). This is just because in most capacitated lot sizing models, the capacity constraints in the model only take into consideration the available time on each work station, ignoring the sequencing of lots, sublot sizes, and their effect on makespan and lead times. In this thesis we bridge the gap between lot sizing and scheduling in flowshops, and examine the use of the lot splitting and sequencing techniques to reduce schedule instability. A mixed integer programming formulation is presented, which enables us to simultaneously find the optimal lot sizes as well as the corresponding sublot sizes and sequence of jobs. With this model, small size problems can be solved within a reasonable time. The computational results confirm that this model can be advantageous in dampening the scheduling nervousness. For larger size instances, a Genetic algorithm is proposed

A General Large Neighborhood Search Framework for Solving Integer Programs

This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi

The evolution of cell formation problem methodologies based on recent studies (1997-2008): review and directions for future research

This paper presents a literature review of the cell formation (CF) problem concentrating on formulations proposed in the last decade. It refers to a number of solution approaches that have been employed for CF such as mathematical programming, heuristic and metaheuristic methodologies and artificial intelligence strategies. A comparison and evaluation of all methodologies is attempted and some shortcomings are highlighted. Finally, suggestions for future research are proposed useful for CF researchers

Fix-and-Optimize and Variable Neighborhood Search Approaches for Stochastic Multi-Item Capacitated Lot-Sizing Problems

We discuss stochastic multi-item capacitated lot-sizing problems with and without setup carryovers (also known as link lot size), S-MICLSP and S-MICLSP-L. The two models are motivated from a real-world steel enterprise. To overcome the nonlinearity of the models, a piecewise linear approximation method is proposed. We develop a new fix-and-optimize (FO) approach to solve the approximated models. Compared with the existing FO approach(es), our FO is based on the concept of “k-degree-connection” for decomposing the problems. Furthermore, we also propose an integrative approach combining our FO and variable neighborhood search (FO-VNS), which can improve the solution quality of our FO approach by diversifying the search space. Numerical experiments are performed on the instances following the nature of realistic steel products. Our approximation method is shown to be efficient. The results also show that the proposed FO and FO-VNS approaches significantly outperform the recent FO approaches, and the FO-VNS approaches can be more outstanding on the solution quality with moderate computational effort