Sequence-dependent Setup Costs Research Articles

Relax-and-Fix Heuristics Applied to a Real-World Lot Sizing and Scheduling Problem in the Personal Care Consumer Goods Industry

This paper addresses an integrated lot sizing and scheduling problem in the industry of consumer goods for personal care, a very competitive market in which good customer service and cost management are crucial in the competition for clients. In this research, a complex operational environment composed of unrelated parallel machines with limited production capacity and sequence-dependent setup times and costs is studied. There is also a limitation in the total storage capacity for finished goods, a characteristic not found in the literature. Backordering is allowed, but it is extremely undesirable. The problem is described through a mixed integer linear programming formulation. Since the problem is NP-hard, relax-and-fix heuristics with hybrid partitioning strategies are investigated. Computational experiments with randomly generated and real-world instances are presented. The results show the efficacy and efficiency of the proposed approaches. Compared to the current solutions used by the company, the best proposed strategies yield results with substantially lower costs, primarily from the reduction in inventory levels and better allocation of production batches on the machines.

Scheduling mobile dental clinics: A heuristic approach considering fairness among school districts.

Mobile dental clinics (MDCs) are suitable solutions for servicing people living in rural and urban areas that require dental healthcare. MDCs can provide dental care to the most vulnerable high-school students. However, scheduling MDCs to visit patients is critical to developing efficient dental programs. Here, we study a mobile dental clinic scheduling problem that arises from the real-life logistics management challenge faced by a school-based mobile dental care program in Southern Chile. This problem involves scheduling MDCs to treat high-school students at public schools while considering a fairness constraint among districts. Schools are circumscribed into districts, and by program regulations, at least 50% of the students in each district must receive dental care during the first semester. Fairness prevents some districts from waiting more time to receive dental care than others. We model the problem as a parallel machine scheduling problem with sequence-dependent setup costs and batch due dates and propose a mathematical model and a genetic algorithm-based solution to solve the problem. Our computational results demonstrate the effectiveness of our approaches in obtaining near-optimal solutions. Finally, dental program managers can use the methodologies presented in this work to schedule mobile dental clinics and improve their operations.

The capacitated lot-sizing and energy efficient single machine scheduling problem with sequence dependent setup times and costs in a closed-loop supply chain network

The capacitated lot-sizing and energy efficient single machine scheduling problem with sequence dependent setup times and costs in a closed-loop supply chain network

Coordinating lot sizing and integrated production and distribution scheduling with batch delivery and holding cost

PurposeThe aim of this paper is to present a method for finding the optimum balance between sequence-dependent setup costs, holding costs, delivery costs and delay penalties in an integrated production–distribution system with lot sizing decisions.Design/methodology/approachTwo mixed integer linear programming models and an optimality property are proposed for the problem. Since the problem is NP-hard, a genetic algorithm reinforced with a heuristic is developed for solving the model in large-scale settings. The algorithm parameters are tuned using the Taguchi method.FindingsThe results obtained on randomly generated instances reveal a performance advantage for the proposed algorithm; it is shown that lot sizing can reduce the average cost of the supply chain up to 11.8%. Furthermore, the effects of different parameters and factors of the proposed model on supply chain costs are examined through a sensitivity analysis.Originality/valueAlthough integrated production and distribution scheduling in make-to-order industries has received a great deal of attention from researchers, most researchers in this area have treated each order as a job processed in an uninterrupted time interval, and no temporary holding costs are assumed. Even among the few studies where temporary holding costs are taken into consideration, none has examined the effect of splitting an order at the production stage (lot sizing) and the possibility of reducing costs through splitting. The present study is the first to take holding costs into consideration while incorporating lot sizing decisions in the operational production and distribution problem.

Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources

The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one.

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.

Scheduling the Capacitated Identical Parallel Machines Problem: A New Formulation with Sequence-Dependent Setup Costs and Different Due Dates

This paper schedules capacitated parallel machines of a real production system by considering different quantities of production and processing times required to complete customer orders. A new mixed linear programming model is developed according to the concept of constrained vehicle routing problems to have a complete schedule for machines by determining the sequence of both jobs and idle times for each machine. The optimisation model minimises the total cost of the production system, including tardiness, earliness and sequence-dependent setup costs. A constraint programming (CP) model and a meta-heuristic hybrid algorithm are also developed to compare their results with the mixed linear programming model. The numerical findings show that the total cost estimated by the mixed integer programming model is 10%-13% better (lower) than the ones estimated by the CP model and the meta-heuristic algorithm when small instances of the scheduling problem are solved. By increasing the size of the scheduling problem, the meta-heuristic algorithm shows the best computational performance estimating 11% better (lower) total cost compared with the CP model. [Received: 14 April 2020; Accepted: 26 October 2020]

Scheduling the capacitated identical parallel machines problem: a new formulation with sequence-dependent setup costs and different due dates

Scheduling the capacitated identical parallel machines problem: a new formulation with sequence-dependent setup costs and different due dates

DECOMPOSITION BASED HEURISTICS FOR A LOT SIZING AND SCHEDULING PROBLEM ON MULTIPLE HETEROGENEOUS PRODUCTION LINES WITH PERISHABLE PRODUCTS

In this paper, we propose a novel MIP-based heuristic method to deal with a lot sizing and scheduling problem with multiple heterogeneous production lines in a production setting with perishable items. The problem is inspired by the production processes adopted by some Brazilian food industries and it considers that several production lines share the same scarce production resources. Therefore, only a subset of those lines can simultaneously operate in each production period. Moreover, the production environment is characterized by the existence of sequence-dependent setup times and costs, and by the production of perishable items which can be stocked for a short period only. Firstly, we propose a facility location reformulation for a model previously proposed in the literature. Secondly, we propose a heuristic composed of two phases. The first phase has an elaborated approach to building feasible solutions solving initially an aggregated lot sizing problem to decide which production lines to assemble, followed by the resolution of the various single line lot sizing and scheduling problems. The second phase applies improvement heuristics exploring principles of fix-and-optimize and local branching procedures. Computational results carried out using a data set proposed in the literature are presented in order to study the efficiency of the proposed approach. The results demonstrate that our heuristics provide superior results when benchmarked with a heuristic from the literature specifically developed to solve the problem under consideration, and with a commercial MIP solver.

Single machine campaign planning under sequence dependent family setups and co-production

We investigate tactical level production planning problem in process industries, with float glass manufacturing being the specific application domain. In the presence of high sequence dependent family setup costs, the need for planning production in batches, or campaigns as named in the float glass industry, arises. Moreover, the float glass manufacturing has some unique properties such as partially controllable co-production and uninterruptible production. The motivation of our work is a real life problem encountered at a major float glass manufacturing company in Turkey. We develop two mixed integer programming formulations and investigate some variants to solve the problem. Our formulations are capable of handling different resolutions in input data such as demand forecast expressed in discrete time and setup durations expressed in continuous time. We compare formulations both theoretically and by running computational experiments. Furthermore, we conduct additional experiments to gain insights about characteristics of the generated campaign plans from a business perspective.

A linearisation approach to the stochastic dynamic capacitated lotsizing problem with sequence-dependent changeovers

We present a mixed-integer linear programming formulation that simultaneously optimises lot sizes and production sequences on a capacity constrained machine with sequence-dependent changeovers subject to stochastic dynamic demand while at the same time satisfying a fill rate constraint. To tackle the non-linearity of the exact formulation, we introduce a piecewise linearisation technique both for the expected inventory on hand and for the backorder functions that uses the target service level and the parameters of the demand distribution to assign breakpoints to the most promising intervals of the linearisation domain. We show that our strategy leads to lower cost and to more conservative production plans, in comparison to techniques recommended by earlier research. In addition, we discuss why any breakpoint selection strategy that does not exclude the concave region for , is prone to be outperformed by the approach we present. Finally, we propose a Relax-and-Fix with Fix-and-Optimize heuristic, and show based on the broad set of instances from Haase, Knut, and Alf Kimms [2000. “Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities.” International Journal of Production Economics 66 (2): 159–169], that it is more effective than a state-of-the-art solver in terms of run time and solution quality.

Solution Approach for Solving Multi-Objective Single-Machine Problem with Sequence-Dependent Setup Times and Setup Costs

A single machine scheduling problem with sequence-dependent setup times and setup costs has a critical role in manufacturing and service sectors to minimize orders delays and costs. This study provides multiple objectives model to solve the single machine total weighted tardiness and setup costs scheduling problem associated with sequence-dependent setup times and sequence-dependent setup costs (MOSTWTSCSD). The objectives are to minimize the total weighted tardiness and the total setup costs for all jobs without any certain relationship between the setup time and the setup cost, as happened in some machines. An alternative heuristic procedure based on discrete particle swarm optimization (DPSO) is suggested to find representative Pareto front (non-dominated) solutions. Many efficient methods have been used inside the DPSO to improve its performance. Results show that the ability of the suggested solution approach to provide a representative Pareto fronts in reasonable computational efforts compared with another heuristic.

MIP approaches for a lot sizing and scheduling problem on multiple production lines with scarce resources, temporary workstations, and perishable products

This paper addresses a lot sizing and scheduling problem inspired from a real-world production environment apparent in food industry. Due to the scarcity of resources, only a subset of production lines can operate simultaneously, and those lines need to be assembled in each production period. In addition, the products are perishable, and there are often significant sequence-dependent setup times and costs. We first propose a standard mixed integer programming model for the problem, and then a reformulation of the standard model in order to allow us to define a branching rule to accelerate the performance of the branch-and-bound algorithm. We also propose an efficient relax-and-fix procedure that can provide high-quality feasible solutions and competitive dual bounds for the problem. Computational experiments indicate that our approaches provide superior results when benchmarked with a commercial solver and an established relax-and-fix heuristic from the literature.

Sustainability in a lot-sizing and scheduling problem with delivery time window and sequence-dependent setup cost consideration

Sustainability in manufacturing operations scheduling is a necessary requirement for companies. Although this subject has attracted much attention, joint decisions of lot-sizing and scheduling with sustainability consideration have not been completely examined in the literature. In this regard, we aim to present a bi-objective model to solve a lot-sizing and scheduling problem simultaneously that would maximize the total profit and minimize CO2 emissions. Also, an augmented ε-constraint method is utilized to transform the model into a single-objective formulation. The proposed model considers Earliness/Tardiness penalties with the delivery time window and sequence-dependent setup costs. Moreover, the model is implemented in a case study of steel company and practical conclusions and managerial insights are reported. Results show that the proposed model is useful for production managers in order to schedule their operations.

An exact optimization approach for an integrated process configuration, lot-sizing, and scheduling problem

We study an integrated process configuration, lot-sizing, and scheduling problem, which appears in a real production environment in the packaging industry. Products are produced by alternative process configurations. The production quantities and capacity consumption depend on which process configurations are used, how long they are used for, and in which sequence. For the particular case studied here, configuration decisions are generated at the same time as lot-sizing and sequencing decisions, which involve sequence-dependent setup costs and times. Due to dependency of these decisions, the model is nonlinear. Even though a linearization technique can be applied, the problem is still difficult to solve by a mixed integer programming (MIP) solver due to its complexity. This paper aims to develop efficient solution methods to deal with this integrated production planning problem. An exact branch-and-check (B&Ch) algorithm based on a relaxed formulation and using logic-based Benders cuts is proposed to find optimal solutions. In addition, symmetry-breaking constraints are applied to strengthen the formulations. Results show that in general, the B&Ch outperforms the linearized models solved by an MIP solver. To efficiently solve large instances, an MIP-based heuristic is then proposed to find good quality solutions in shorter computing times. Although the problem studied here is based on the packaging industry, the logic of the B&Ch and the proposed heuristic can be adapted to other applications where lot-sizing must be determined simultaneously with process configuration decisions.

A hybrid binomial inverse hypergeometric probability distribution: Theory and applications

In this paper, we define a novel probability distribution triggered by a due date setting problem from a multi-item single level production system. As a result, we derive a recurrence relation for the underlying distribution function and, finally, we also infer the novel discrete distribution function. We underpin our analytical findings by numerical results when computing the distribution function, the expected value as well as the variance. In order to apply and translate our apparatus to other problems, we come up with an application when determining due dates for a production system with sequence-dependent setup costs.

A sample average approximation algorithm for selective disassembly sequencing with abnormal disassembly operations and random operation times

Selective disassembly sequencing is the problem of determining the sequence of disassembly operations to extract one or more target components of a product. This study addresses a stochastic version of the problem in which abnormal disassembly operations and random operation times are considered under the parallel disassembly environment, i.e., one or more components that can be disassembled further remain after a disassembly operation is done. Abnormal disassembly operations are defined as those in which fasteners can be removed by additional random destructive operations without damaging to target components. After representing all possible sequences using the extended process graph, a stochastic integer programming model is developed that minimizes the sum of disassembly and penalty costs, where the disassembly cost consists of sequence-dependent setup and operation costs, and the penalty cost is the expectation of the costs incurred when the total disassembly time exceeds a given threshold value. A sample average approximation algorithm is proposed that incorporates a branch and bound algorithm to solve the deterministic problem under a scenario for abnormal operations and operation times optimally. Finally, the algorithm is illustrated with a hand-light example and a larger instance.

Selective disassembly sequencing with random operation times in parallel disassembly environment

Selective disassembly sequencing is the problem of determining the sequence of disassembly operations to extract one or more target components of a product. This study considers the problem with random operation times in the parallel disassembly environment in which one or more components can be removed at the same time by a single disassembly operation. After representing all possible disassembly sequences using the extended process graph, a stochastic integer programming model is developed for the objective of minimising the sum of disassembly and penalty costs, where the disassembly costs consist of sequence-dependent set-up and operation costs and the penalty cost is the expectation of the costs incurred when the total disassembly time exceeds a threshold value. A sample average approximation-based solution algorithm is proposed that incorporates an optimal algorithm to solve the sample average approximating problem under a given set of scenarios for disassembly operation times. The algorithm is illustrated with a hand-light case and a large-sized random instance, and the results are reported.

A New Branching Rule to Solve the Capacitated Lot Sizing and Scheduling Problem with Sequence Dependent Setups

In this paper, we deal with the Capacitated Lot Sizing and Scheduling Problem with sequencedependent setup times and costs - CLSD model. More specifically, we propose a simple reformulation for the CLSD model that enables us to define a new branching rule to be used in Branch-and-Bound (or Branch-and-Cut) algorithms to solve this NP-hard problem. Our branching rule can be easily implemented in commercial solvers. Computational tests performed in 240 test instances from the literature show that our approach can significantly reduce the running time to solve this problem using a Branch-and-Cut algorithm of a commercial MIP solver.Therefore, our approach can also improve the performance of other approaches that need to solve partial sub problems of the CLSD model in each iteration, such as Lagrangian approaches and heuristics based on the mathematical formulation of the problem.

Simultaneous scheduling and lot-sizing with earliness/tardiness penalties

The problem investigated in this paper is one of the simultaneous lot-sizing and scheduling problems with earliness/tardiness penalties along with the sequence-dependent setup time and cost. Minimising earliness and tardiness is of interest both in just-in-time production systems and in make-to-order ones. A mathematical model is presented similar to the travelling salesman problem. The problem objective is to determine the production lot-size and their schedules. In spite of its wide applications, this problem has not yet been reported in the literature. To solve the problem, two meta-heuristic algorithms: tabu search and ant colony system are presented. The efficiencies of the algorithms are investigated for different sets of problems. The results show that each of the ant colony system and the tabu search obtained optimal solutions for 196 and 203 problems, respectively, out of among the 333 problem instances. Despite the differences between these two methods, neither can be statistically preferred.