Two-stage hybrid flow shop batching and lot streaming with variable sublots and sequence-dependent setups

A paint manufacturing firm's customers typically place orders for two or more products simultaneously. Each product belongs to a family that denotes batching compatibility during manufacturing. Further, products can be split into several sublots to allow overlapping production in a two-stage hybrid flow shop wherein various identical, capacitated machines operate in parallel at each stage. We present a mixed-integer linear program (MILP) for this integrated batching and lot streaming problem with variable sublots, incompatible job families, and sequence-dependent setup times. The model determines the number and size of sublots for each product and the production sequencing for each sublot such that the total weighted completion time is minimised. To promote practical implementation, we develop and evaluate heuristics to efficiently solve this problem.     

An immune algorithm for scheduling a hybrid flow shop with sequence-dependent setup times and machines with random breakdowns

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems that have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real-life industries a machine can be unavailable for many reasons, such as unanticipated breakdowns (stochastic unavailability), or due to scheduled preventive maintenance where the periods of unavailability are known in advance (deterministic unavailability). This paper deals with hybrid flow shop scheduling problems in which there are sequence-dependent setup times (SDSTs), and machines suffer stochastic breakdowns, to optimise objectives based on the expected makespan. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. An immune algorithm (IA) can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. In this research, a computational method based on a clonal selection principle and an affinity maturation mechanism of the immune response is used. This paper describes how we can incorporate simulation into an immune algorithm for the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdowns. The results obtained are analysed using a Taguchi experimental design.     

Scheduling a permutation flow shop with family setups to minimise total tardiness

This paper presents several procedures for scheduling a permutation flow shop with family setups when the objective is to minimise total tardiness. These procedures are tested on several problem sets with varying numbers of families, jobs, and machines, three setup time distributions, and various levels of due date tightness and variability. The results show that variable greedy algorithms are effective when solving small problems, but a neighbourhood search procedure that includes searches with a neighbourhood defined by the sequence of batches of jobs belonging to the same setup family is more effective when solving large problems. Results are also presented, showing that significant reductions in total tardiness can be obtained if the time required to perform the family setups is reduced.     

Single machine multi-product capacitated lot sizing with sequence-dependent setups

In production planning in the glass container industry, machine-dependent setup times and costs are incurred for switch overs from one product to another. The resulting multi-item capacitated lot-sizing problem has sequence-dependent setup times and costs. We present two novel linear mixed-integer programming formulations for this problem, incorporating all the necessary features of setup carryovers. The compact formulation has polynomially many constraints, whereas the stronger formulation uses an exponential number of constraints that can be separated in polynomial time. We also present a five-step heuristic that is effective both in finding a feasible solution (even for tightly capacitated instances) and in producing good solutions to these problems. We report computational experiments.     

Scheduling of a no-wait two-machine flow shop with sequence-dependent setup times and probable rework using robust meta-heuristics

This paper investigates the scheduling of a no-wait two-machine flow shop considering anticipatory sequence-dependent setup time and a probable rework for both machines to minimise mean completion time (MCT). To tackle the problem, a robust meta-heuristic algorithm, namely the adapted imperialist competitive algorithm (AICA), has been proposed and is compared with two common and popular meta-heuristic algorithms (i.e. genetic algorithm (GA) and population-based simulated annealing (PBSA)). In this study, we have adapted a traditional imperialist competitive algorithm (ICA) with some considerable changes. First of all, a revolution procedure is added to the algorithm for imperialists similar to colonies. Furthermore, the revolution is only performed when the new solution is better than the previous solution, and chief among them for preservation of premature convergence, the concept of global war is applied. However, the performance of AICA is sensitive to the choice of the best parameter values. Thus, to obtain optimal performance, a comprehensive calibration methodology called response surface methodology is employed to obtain the best combination of parameter values. In order to evaluate the effectiveness and efficiency of proposed algorithms, several test problems are generated and the results obtained from algorithms are then compared in terms of relative percentage deviation. Computational experiments indicate that AICA outperforms GA and PBSA in the MCT performance measure, and GA outperforms the others in terms of computational time.     

Neighbourhood search meta-heuristics for capacitated lot-sizing with sequence-dependent setups

We address a problem that often arises in industry, the multi-item capacitated-lot-sizing and scheduling problem with sequence-dependent setup times and costs. Powerful commercial solvers fail to solve even medium-sized instances of this NP-hard problem, therefore we employ a tabu search and a variable neighbourhood search meta-heuristic to solve it and compare the performance of these meta-heuristics over time. In contrast to the majority of the literature on this topic, the solution representation explicitly considers production quantities and setup variables, which enables us to develop fast search heuristics. A comprehensive set of computational experiments shows the effectiveness and efficiency of the proposed approaches in solving medium- to large-sized problems.     

A hierarchical approach for the capacitated lot-sizing and scheduling problem with a special structure of sequence-dependent setups

This research deals with the single machine multi-product capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup times and setup costs. The CLSP determines the production quantities and the sequence to satisfy deterministic and dynamic demand during multiple periods. The objective is to minimise the total sum of the inventory holding costs and the sequence-dependent setup costs. We consider a special form of sequence-dependent setup times where the larger product we produce next, the more setup time we need. As a solution approach, we propose a two-level hierarchical method consisting of upper-level planning and the lower-level planning. In the upper-level planning, we solve the lot-sizing problem with estimated sequence-independent setup times utilising the characteristic of the special structure of setup times. Then we solve the scheduling problem in the lower-level planning. The proposed method is compared with the single-level optimal CLSP solution and an existing heuristic developed for the uniform structure of setup times.     

MIP-based fix-and-optimise algorithms for the parallel machine capacitated lot-sizing and scheduling problem

This paper examines the capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup times, time windows, machine eligibility and preference constraints. Such a problem frequently arises in the semiconductor manufacturing industry by which this paper is motivated. A mixed integer programming (MIP) model is constructed for the problem. Two MIP-based fix-and-optimise algorithms are proposed in which the binary decision variables associated with the assignment of machines are first fixed using the randomised least flexible machine (RLFM) rule and the rest of the decision variables are settled by an MIP solver. Extensive experiments show that the proposed algorithms outperform the state-of-the-art MIP-based fix-and-optimise algorithms in the literature, especially for instances with high machine flexibility and high demand variation.     

More MILP models for hybrid flow shop scheduling problem and its extended problems

With the rapid development of computer technology and related softwares for mathematical models, mathematical modelling of scheduling problems is receiving growing attention from researchers. In this work, the hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the objective aimed to minimise the makespan is studied. According to the characteristics of the HFSP-UPM, eight mixed integer linear programming (MILP) models are formulated in order to obtain optimal solutions based on different modelling ideas. Then, these models are extended to solve HFSP-UPM with sequence-dependent setup times (HFSP-UPM-SDST), no-wait HFSP-UPM (HFSP-UPM-NW) and HFSP-UPM with blocking (HFSP-UPM-B). All the proposed models and the existing model are detailedly compared and evaluated under three aspects namely modelling process, size complexity and computational complexity. Numerical experiments show that MILP models dependent on diverse modelling ideas perform very differently. The model developed based on stage precedence is the best one and should be given preference in future applications. In addition, the proposed models of HFSP-UPM-NW and HFSP-UPM-B improve several best known solutions for the test instances in the existing literature.     

An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time

With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has gained deep research, but the practical case that considers both setup and transportation times still has rare research. This paper addresses the energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time to minimise both makespan as economic objective and energy consumption as green objective. The mathematical model of the problem is formulated. To solve such a bi-objective problem effectively, an improved multi-objective evolutionary algorithm based on decomposition is proposed. With decomposition strategy, the problem is decomposed into several sub-problems. In each generation, a dynamic strategy is designed to mate the solutions corresponding to the sub-problems. After analysing the properties of the problem, two heuristics to generate new solutions with smaller total setup times are proposed for designing local intensification to improve exploitation ability. Computational tests are carried out by using the instances both from a real-world manufacturing enterprise and generated randomly with larger sizes. The comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.     

Rescheduling strategies for integrating rush orders with preventive maintenance in a two-machine flow shop

Preventive maintenance and rush orders are related. Although preventive maintenance is essential for maximising equipment reliability, it can substantially slow the manufacturing process. Rush order rescheduling involves similar conflicts. Scheduling maintains the robustness of the production schedule, but rush orders require rescheduling. Although preventive maintenance and rush orders are essential manufacturing processes, research on the integration of these functions is insufficient. Unlike recent work that analyses preventive maintenance or rush orders as separate functions, this study proposes an integrated model that analyses both preventive maintenance and rush orders in a two-machine flow shop. The model is then evaluated using two different rescheduling methods. Non-parametric analysis of the models revealed that these two rescheduling methods differ significantly under integrated maintenance and rush order situations.     

MIP-based constructive heuristics for the three-dimensional Bin Packing Problem with transportation constraints

This article is about seeking a good feasible solution in a reasonable amount of computation time to the three-dimensional Multiple Bin Size Bin Packing Problem (MBSBPP). The MBSBPP studied considers additional constraints encountered in real world air transportation situations, such as cargo stability and the particular shape of containers. This MBSBPP has already been formulated as a Mixed Integer linear Programming problem, but as yet only poor results have been achieved for even fairly small problem sizes. The goal of the work this paper describes is to develop heuristics that are able to quickly provide good initial feasible solutions for the MBSBPP. Three methodologies are considered, which are based on the decomposition of the original problem into easier subproblems: the matheuristics Relax-and-Fix, Insert-and-Fix and Fractional Relax-and-Fix. They have been parametrised on real data sets and then compared to each other. In particular, two of these techniques show promising results in reasonable computational times.     

A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems

In this article, the multi-objective flexible flow shop scheduling problem with limited intermediate buffers is addressed. The objectives considered in this problem consist of minimizing the completion time of jobs and minimizing the total tardiness time of jobs. A hybrid water flow algorithm for solving this problem is proposed. Landscape analysis is performed to determine the weights of objective functions, which guide the exploration of feasible regions and movement towards the optimal Pareto solution set. Local and global neighbourhood structures are integrated in the erosion process of the algorithm, while evaporation and precipitation processes are included to enhance the solution exploitation capability of the algorithm in unexplored neighbouring regions. An improvement process is used to reinforce the final Pareto solution set obtained. The performance of the proposed algorithm is tested with benchmark and randomly generated instances. The computational results and comparisons demonstrate the effectiveness and efficiency of the proposed algorithm.     

Multi-objective production scheduling with controllable processing times and sequence-dependent setups for deteriorating items

The production scheduling problem is to find simultaneously the lot sizes and their sequence over a finite set of planning periods. This paper studies a single-stage production scheduling problem subject to controllable process times and sequence-dependent setups for deteriorating items. The paper formulates the problem by minimising two objectives of total costs and total variations in production volumes simultaneously. The problem is modelled and analysed as a mixed integer nonlinear program. Since it is proved that the problem is NP-hard, a problem-specific heuristic is proposed to generate a set of Pareto-optimal solutions. The heuristic is investigated analytically and experimentally. Computational experiences of running the heuristic and non-dominated sorting genetic algorithm-I over a set of randomly generated test problems are reported. The heuristic possesses at least 56.5% (in the worst case) and at most 94.7% (in the best case) of total global Pareto-optimal solutions in ordinary-size instances.     

Improving the migrating birds optimization metaheuristic for the permutation flow shop with sequence-dependent set-up times

This paper addresses the problem of scheduling a set of independent jobs with set-up times on a set of machines in a permutation flow shop environment. A metaheuristic known as the Migrating Birds Optimization (MBO) is adapted for the minimization of the makespan. Two versions of the algorithm are presented. The first is a basic MBO and the second introduces additional features. An extensive computational study is conducted to analyse the efficiency of the two methods on a benchmark of instances that can be found in Sistemas de Optimizacion Aplicada (http://soa.iti.es/problem-instances). The second version outperforms by far the first one. Moreover, the results that are produced by the latter show that it is suitable for solving real-world scheduling problems.     

A hybrid electromagnetism-like algorithm for two-stage assembly flow shop scheduling problem

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation.     

Two-stage flow shop scheduling with dedicated machines

This study is concerned with the manufacturing model that has a common machine at stage one and two parallel dedicated machines at stage two. All jobs need to be processed on the stage-one common machine. After the stage-one processing, the jobs of type 1 (type 2) will route to the first (second) dedicated machine at stage two. We first elaborate several published works on makespan minimisation which are not known to other streams of recent works. While the minimisation of maximum lateness is strongly NP-hard, we develop a linear-time algorithm to solve the case where two sequences of the two job types are given a priori.     

New heuristics for no-wait flow shops with a linear combination of makespan and maximum lateness

In this work we study a flow shop scheduling problem in which jobs are not allowed to wait between machines, a situation commonly referred to as no-wait. The criterion is to minimise a weighted sum of makespan and maximum lateness. A dominance relation for the case of three machines is presented and evaluated using experimental designs. Several heuristics and local search methods are proposed for the general m-machine case. The local search methods are based on genetic algorithms and iterated greedy procedures. An extensive computational analysis is conducted where it is shown that the proposed methods outperform existing heuristics and metaheuristics in all tested scenarios by a considerable margin and under identical CPU times.     

A new complexity proof for the two-stage hybrid flow shop scheduling problem with dedicated machines

This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines at stage 2. The objective is to minimise the makespan. There is one machine at stage 1 and two machines at stage 2. Each job must be processed on the single machine at stage 1 and, depending upon the job type, the job is processed on either of the two machines at stage 2. We first introduce this special type of the two-stage hybrid flow shop scheduling problem and present some preliminary results. We then present a counter example to the known complexity proof of Riane et al. [Riane, F., Artiba, A. and Elmaghraby, S.E., 2002. Sequencing a hybrid two-stage flowshop with dedicated machines. International Journal of Production Research, 40, 4353–4380.] Finally, we re-establish the complexity of the problem.