Setup Carryover Research Articles

Capacitated multi-item multi-echelon lot sizing with setup carry-over under uncertain demand

This study focuses on the lot sizing problem with setup carry-over in multi-item multi-echelon capacitated production systems under uncertain customer demand for end items, as well as components. We investigate budget-uncertainty robust optimization and scenario-based stochastic programming, to address the uncertainty in customer demand. Three modeling strategies are proposed within the stochastic programming framework, exploring different decision stages for setup carry-over and production quantities. In our examination of the robust model, we explore different robustness parameters, specifically the uncertainty budget and the variation interval. Extensive numerical experiments are conducted to compare the average and worst case performance of the models on out-of-sample scenarios. We fit conditional inference trees to the evaluation results and predict the suitability of robust and stochastic approaches for the test instances based on their problem characteristics. The findings provide valuable insights, potentially enabling decision makers to estimate the most appropriate approach based on certain characteristics of the lot sizing problem that is addressed. Moreover they highlight the importance of choosing appropriate robustness parameters for robust optimization models and emphasize the value of flexibility in carry-over and quantity decisions.

A Modeling and Hybridized Decomposition Approach for the Multi-level Capacitated Lot-Sizing Problem with Setup Carryover, Backlogging, and Emission Control

A Modeling and Hybridized Decomposition Approach for the Multi-level Capacitated Lot-Sizing Problem with Setup Carryover, Backlogging, and Emission Control

Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)'s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin's[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)'s[1] developed model.© 2023 Society of Manufacturing Engineers (SME). Published by Elsevier Ltd. All rights reserved.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)Peer-review under responsibility of the Scientific Committee of the NAMRI/SME.

The Setup Carryover Assignment Problem

The Setup Carryover Assignment Problem

A two-stage cooperative evolutionary algorithm for energy-efficient distributed group blocking flow shop with setup carryover in precast systems

As the main link of the rapidly developing prefabricated construction industry, the production of precast components (PCs) has become a research hotspot. Therefore, the distributed group flow shop scheduling problem with blocking and carryover sequence-dependent setup time constraints (DPGFSP-BCT) in precast systems is considered. To address this problem, first, a mixed integer linear model is presented. Second, a two-stage cooperative coevolutionary algorithm (TS-CCEA) is proposed to minimize both the makespan and total energy consumption (TEC). In TS-CCEA, two acceleration rules are designed to reduce computational efforts. Third, to diversify the population, different initialization methods are established for different populations. Based on the problem-specific knowledge of solution classification, the individuals of the group population and job population execute two neighborhood search algorithms. Subsequently, considering the TEC, a critical path based speed mutation strategy is proposed to further improve the exploitation ability. Furthermore, a reinitialization heuristic is developed to avoid premature convergence. Last, the performance of the TS-CCEA is verified after calibrating the parameters. The experimental results demonstrate the stability and effectiveness of the algorithm.

A goal programming approach to lean production system implementation

Companies use different production policies to ensure customer demands are satisfied in time. To track the performance of production policies some important Key Performance Indicators related to production control and management are On-Time Delivery (OTD), machine or line productivity (OEE – Overall Equipment Efficiency), optimization of inventory levels between workstations (WIP), customer satisfaction i.e. prioritization of customer orders according to requirements of the customer, and backlog minimization. In this study, a real-life production management problem is described, modelled, and solved to improve customer delivery rate and, to plan manufacturing orders using lean production tools. Currently, the Make-to-Stock policy is used for semi-finished materials. The problems encountered are low customer service level, high level of WIP between operations and efficiency losses. Therefore, the goal of this study is to increase efficiency (OTD, OEE, and customer satisfaction) by minimizing setup time, decreasing WIP by minimizing earliness, backlog quantity level and improving service level by minimizing lateness of orders. Since these goals contradict each other, we propose a multi-objective mathematical formulation with a setup carryover strategy. Then we formulate a Goal Programming (GP) model and solve it by using different GP variants and the normalization method. Finally, we discuss numerical results and provide our final remarks and conclusions.

Hybrid matheuristics to solve the integrated lot sizing and scheduling problem on parallel machines with sequence-dependent and non-triangular setup

This paper approaches the integrated lot sizing and scheduling problem (ILSSP), in which non-identical machines work in parallel with non-triangular sequence-dependent setup costs and times, setup carry-over and capacity limitation. The aim of the studied ILSSP, here called ILSSP-NT on parallel machines, is to determine a production planning and tasks sequencing that meet period demands without delay and in such a way that the total costs of production, machine setup and inventory are minimized. The dearth of literature on the ILSSP-NT, despite the increasing amount of applications in the industrial sector, mainly in the food processing industry, motivated us to conduct this study. In this paper, we propose efficient methods to solve the ILSSP-NT on parallel machines. The methods virtually consist in the hybridization of the relax-and-fix and fix-and-optimize methods with the path-relinking and kernel search heuristics. To assess how well the heuristics solve the ILSSP-NT on parallel machines, we compared their results with those of the CPLEX solver with a fixed CPU time limit. The proposed matheuristics significantly outperformed CPLEX in most of the tested instances.

Data-driven branching and selection for lot-sizing and scheduling problems with sequence-dependent setups and setup carryover

The capacitated lot-sizing and machine scheduling problem with sequence-dependent setup time and setup carryover is a challenging problem with a wide application in industries. For the problem, two mixed integer programming models are proposed in order to explore their relative efficiencies in obtaining optimal solutions and linear programming relaxation lower bounds. Furthermore, due to the fact that the complicating constraints involve pairs of items (the sequence-dependent setups) and pairs of consecutive periods (the setup carryovers), making it difficult to decompose the problem per item or per period, we instead present a Dantzig-Wolfe decomposition reformulation per machine to improve lower bounds. We propose a branching and selection method to solve the problem, in which a collection of variables rather than individual variables are put into a data-driven process to generate useful information which is then adopted in the branching and selection process. Extensive numerical experiments show that the proposed algorithm can obtain numerically near-optimal solutions for small-scale problems and outperforms CPLEX and other heuristics in terms of both solution quality and runtime when the scale of instances increases. More experiments have been conducted to extract some insightful features related to the model and algorithm.

Capacitated Lot-Sizing Problem with Sequence-Dependent Setup, Setup Carryover and Setup Crossover

Since setup operations have significant impacts on production environments, the capacitated lot-sizing problem considering arbitrary length of setup times helps to develop flexible and efficient production plans. This study discusses a capacitated lot-sizing problem with sequence-dependent setup, setup carryover and setup crossover. A new mixed integer programming formulation is proposed. The formulation is based on three building blocks: the facility location extended formulation; the setup variables with indices for the starting and the completion time periods; and exponential number of generalized subtour elimination constraints (GSECs). A separation routine is adopted to generate the violated GSECs. Computational experiments show that the proposed formulation outperforms models from the literature.

Impact analysis of setup carryover and crossover on lot sizing problems

This paper presents a literature classification and a detailed computational study analysing the impact of considering the possibility of setup carryover and crossover when solving the lot sizing problem. This problem is an extension of the standard Capacitated Lot Sizing Problem. A setup carryover is defined as the possibility to begin a period with production (instead of setup) of the item that was being produced at the end of the previous period. A setup crossover allows the opportunity to start a setup operation in one period and continue it to the following one, i.e. the setup operation can span over two periods. We adapt and compare two formulations proposed in the literature that have not been compared each other. Furthermore, some formulations proposed in the literature for modelling the setup crossover with a reduced number of binary variables, are extended to the addressed problem. Finally, a relax-and-fix and fix-and-optimise (RF-FO) heuristic is also applied to solve some difficult instances. Computational results are presented based on random generated data.

Three stage dynamic heuristic for multiple plants capacitated lot sizing with sequence-dependent transient costs

Abstract In this paper we investigate the demand planning problem for a petrochemical industry four tiers supply chain that integrates lot-sizing, scheduling with sequence dependent transient costs, transportation and warehousing decisions between suppliers, plants, warehouses, and customers. The problem was modeled using Mixed-Integer Linear Programming (MILP) and featuring a setup carryover and sub-tours elimination constraints. The problem is NP-Hard; therefore, an iterative three stage heuristic was developed which provides quality solutions with a very acceptable computational time. The heuristic computational efficiency was tested on different problem instances of different sizes, and the reported results were within a range of 0.09–2.00% gap from optimality.

Matheuristics for the lot sizing problem with back-ordering, setup carry-overs, and non-identical machines

Abstract In this study, the capacitated lot-sizing problem (CLSP) with back-ordering, setup carry-overs between periods, and non-identical parallel machines (CLSP-BOPM) is considered. The problem is one of the most general extensions of the well-known economic lot scheduling problems (ELSPs). Three matheuristics are designed and implemented starting from the ideas of variable neighborhood local search, local branching, and feasibility pump (FP), adapted and improved by considering the specific characteristics of the problem. Algorithms are tested on a set of medium to large problem instances. The FP algorithm outperforms all other algorithms and two different mixed-integer programming solvers as it requires a shorter computational time. To test the robustness of the algorithm, tests on three particular cases of the general problem, belonging to the family of discrete ELSPs, have been performed. Results from the proposed solver and a known specific state-of-the-art algorithm demonstrate substantial improvements.

Fix-and-optimize heuristics for capacitated lot sizing with setup carryover and backordering

PurposeThe capacitated lot sizing problem (CLSP) is one of the most important production planning problems which has been widely studied in lot sizing literature. The CLSP is the extension of the Wagner-Whitin problem where there is one product and no capacity constraints. The CLSP involves determining lot sizes for multiple products on a single machine with limited capacity that may change for each planning period. Determining the right lot sizes has a critical importance on the productivity and success of organizations. The paper aims to discuss these issues.Design/methodology/approachThis study focuses on the CLSP with setup carryover and backordering. The literature focusing on this problem is rather limited. To fill this gap, a number of problem-specific heuristics have been integrated with fix-and-optimize (FOPT) heuristic in this study. The authors have compared the performances of the proposed approaches to that of the commercial solver and recent results in literature. The obtained results have stated that the proposed approaches are efficient in solving this problem.FindingsThe computational experiments have shown that the proposed approaches are efficient in solving this problem.Originality/valueTo address the solution of the CLSP with setup carryover and backordering, a number of heuristic approaches consisting of FOPT heuristic are proposed in this paper.

A kernel search to the multi-plant capacitated lot sizing problem with setup carry-over

Lot sizing is one of the most challenging problems in production planning. This paper focuses on the multi-plant capacitated lot sizing problem (MPCLSP) with setup carry-over (MPCLSP-SC). To the best of our knowledge, the MPCLSP-SC has been the subject of one single study, despite the fact that it can bring financial benefits, primarily by considering case studies under tight capacity. Moreover, in spite of the significant improvement in the performance of benchmark optimization solvers over the years, they are still very time and memory consuming for large MPCLSP instances. Therefore, heuristics stand out among the solution methods to tackle this type of problem. This paper introduces a novel matheuristic, a kernel search (KS) method, to solve the MPCLSP-SC. Through computational experiments, it was possible to show the outstanding performance of the proposed method for large instances with diverse characteristics. The experiments also demonstrate that the introduced KS outperformed state-of-the-art methods to solve the MPCLSP.

Study on column generation for the lot-sizing and scheduling problem with sequencedependent setup time

The capacitated lot-sizing and scheduling problem with sequence-dependent setup time and carryover setup state is a challenge problem in the semiconductor assembly and test manufacturing. For the problem, a new mixed integer programming model is proposed, followed by exploring its relative efficiency in obtaining optimal solutions and linearly relaxed optimal solutions. On account of the sequence-dependent setup time and the carryover of setup states, a per-machine Danzig Wolfe decomposition is proposed. We then build a statistical estimation model to describe correlation between the optimal solutions and two lower bounds including the linear relaxation solutions, and the pricing sub-problem solutions of Danzig Wolfe decomposition, which gives insight on the optimal values about information regarding whether or not the setup variables in the optimal solution take the value of 1, and the information is further used in the branch and select procedure. Numerical experiments are conducted to test the performance of the algorithm.

A comparison of mixed integer programming formulations of the capacitated lot-sizing problem

We propose a novel mixed integer programming formulation for the capacitated lot-sizing problem with set-up times and set-up carryover. We compare our formulation to two earlier formulations, the Classical and Modified formulations, and a more recent formulation due to Suerie and Stadtler. Extensive computational experiments show that our formulation consistently outperforms the Classical and Modified formulations in terms of CPU time and solution quality. It is competitive with the Suerie–Stadtler (S&S) formulation, but outperforms all other formulations on the most challenging instances, those with low-capacity slack and a dense jobs matrix. We show that some of the differences in the performance of these various formulations arise from their different use of binary variables to represent production or set-up states. We also show that the LP relaxation of our Novel formulation provides a tighter lower bound than that of the Modified formulation. Our experiments demonstrate that, while the S&S formulation provides a much tighter LP bound, the Novel formulation is better able to exploit the intelligence of the CPLEX solution engine.

Multi-stage multi-product multi-period production planning with sequence-dependent setups in closed-loop supply chain

A multi-stage lot sizing problem with remanufacturing is modelled.Sequence dependent setups and setup carry-over in a flow shop are considered.A mixed integer programming is introduced to formulate the problem.Rolling horizon heuristics and a SA algorithm are proposed to solve the model.For large size problems SA algorithm would have better solutions than heuristics. This paper studies multi-stage multi-product multi-period capacitated production planning problem with sequence dependent setups in closed-loop supply chain. In this problem, manufacturing and remanufacturing of each product is regarded consequently, and in addition to the setup for changing products, a setup while changing the processes is needed. To formulate the problem, a mixed-integer programming (MIP) model is presented. Four MIP-based heuristic named non-permutation and permutation heuristics, using rolling horizon are utilized to solve this model. Moreover, a simulated annealing algorithm using a heuristic to provide initial solution is developed to solve the problem. To calibrate the parameters of the proposed simulated annealing algorithm, Taguchi method is applied. The numerical results indicate the efficiency of the proposed meta-heuristic algorithm against MIP-based heuristic algorithms.

A novel flexible model for lot sizing and scheduling with non-triangular, period overlapping and carryover setups in different machine configurations

This paper develops and tests an efficient mixed integer programming model for capacitated lot sizing and scheduling with non-triangular and sequence-dependent setup times and costs incorporating all necessary features of setup carryover and overlapping on different machine configurations. The model’s formulation is based on the asymmetric travelling salesman problem and allows multiple lots of a product within a period. The model conserves the setup state when no product is being processed over successive periods, allows starting a setup in a period and ending it in the next period, permits ending a setup in a period and starting production in the next period(s), and enforces a minimum lot size over multiple periods. This new comprehensive model thus relaxes all limitations of physical separation between the periods. The model is first developed for a single machine and then extended to other machine configurations, including parallel machines and flexible flow lines. Computational tests demonstrate the flexibility and comprehensiveness of the proposed models.

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.

A comparative study of hybrid approaches for solving capacitated lot sizing problem with setup carryover and backordering

The classical capacitated lot sizing problem is shown to be NP-hard for even a single item problem. This study deals with an extended version of this problem with setup carryover and backordering. To solve this computationally difficult lot sizing problem, we propose a number of hybrid meta-heuristic approaches consisting of genetic algorithms and a mixed integer programming-based heuristic. This MIP-based heuristic is combined with two types of decomposition schemes (i.e., product and time decomposition) to generate subproblems. Computational experiments are carried out on various problem sizes. We found that hybrid approaches employing only time decomposition scheme or combination of both time and product decomposition schemes in different forms outperform the other hybrid approaches. Moreover, we investigated the sensitivity of the two best performing approaches to changes in problem-specific parameters including backorder costs, setup times, setup costs, capacity utilisation and demand variability. [Received 2 November 2015; Revised 25 March 2016; Accepted 7 April 2016]