Optimizing a bi-objective multi-product EPQ model with defective items,rework and limited orders: NSGA-II and MOPSO algorithms

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.     

The bi-objective covering tour problem

The paper discusses the definition and solution of a bi-objective routing problem, namely the bi-objective covering tour problem. The bi-objective CTP is a generalization of the covering tour problem, which means that the covering distance and the associated constraints have been replaced by a new objective. We propose a two-phase cooperative strategy that combines a multi-objective evolutionary algorithm with a branch-and-cut algorithm initially designed to solve a single-objective covering tour problem. Experiments were conducted using both randomly generated instances and real data. Optimal Pareto sets were determined using a bi-objective exact method based on an ε$\epsilon$-constraint approach with a branch-and-cut algorithm.     

On finding representative non-dominated points for bi-objective integer network flow problems

This paper proposes a new algorithm to find a representation of the set of all non-dominated points of the bi-objective integer network flow problem. The algorithm solves a sequence of ε-constraint problems with a branch-and-bound algorithm to find a subset of non-dominated points that represents the set of all non-dominated points well in the sense of coverage or uniformity. At each iteration of the algorithm, one non-dominated point, determined by solving one ε-constraint problem, is added to the representation until it is guaranteed that the representation has the desired quality. Computational experiments on different problem types show the efficacy of the algorithm.     

A bacteria foraging algorithm based cell formation considering operation time

The cellular manufacturing system (CMS) is considered as an efficient production strategy for batch type production. The CMS relies on the principle of grouping machines into machine cells and grouping machine parts into part families based on pertinent similarity measures. The bacteria foraging algorithm (BFA) is a new in development computation technique extracted from the social foraging behavior of Escherichia coli (E. coli) bacteria. Ever since Kevin M. Passino invented the BFA, one of the main challenges has been employment of the algorithm to problem areas other than those for which the algorithm was proposed. This research work inquires the first applications of this emerging novel optimization algorithm to the cell formation (CF) problem. In addition, a newly developed BFA-based optimization algorithm for CF is discussed. In this paper, an attempt is made to solve the cell formation problem meanwhile taking into consideration number of voids in cells and a number of exceptional elements based on operational time of the parts required for processing in the machines. The BFA is suggested to create machine cells and part families. The performance of the proposed algorithm is compared with a number of algorithms that are most commonly used and reported in the corresponding scientific literature such as similarity coefficients methods (SCM), rank order clustering (ROC), ZODIAC, GRAFICS, MST, GATSP, GP, K-harmonic clustering (KHM), K-means clustering, C-link clustering, modified ART1, GA (genetic algorithm), evolutionary algorithm (EA), and simulated annealing (SA) using defined performance measures known as modified grouping efficiency and grouping efficacy. The results lie in favor of better performance of the proposed algorithm.     

Development of bacteria foraging optimization algorithm for cell formation in cellular manufacturing system considering cell load variations

The cellular manufacturing system (CMS) is considered as an efficient production strategy for batch type production. The CMS relies on the principle of grouping machines into machine cells and grouping machine parts into part families on the basis of pertinent similarity measures. The bacteria foraging optimization (BFO) algorithm is a modern evolutionary computation technique derived from the social foraging behavior of Escherichia coli bacteria. Ever since Kevin M. Passino invented the BFO, one of the main challenges has been the employment of the algorithm to problem areas other than those of which the algorithm was proposed. This paper investigates the first applications of this emerging novel optimization algorithm to the cell formation (CF) problem. In addition, for this purpose matrix-based bacteria foraging optimization algorithm traced constraints handling (MBATCH) is developed. In this paper, an attempt is made to solve the cell formation problem while considering cell load variations and a number of exceptional elements. The BFO algorithm is used to create machine cells and part families. The performance of the proposed algorithm is compared with a number of algorithms that are most commonly used and reported in the corresponding scientific literature such as K-means clustering, the C-link clustering and genetic algorithm using a well-known performance measure that combined cell load variations and a number of exceptional elements. The results lie in favor of better performance of the proposed algorithm.     

A hybrid genetic-variable neighborhood search algorithm for the cell formation problem based on grouping efficacy

Cell formation problem attempts to group machines and part families in dedicated manufacturing cells such that the number of voids and exceptional elements in cells are minimized. In this paper, we presented a linear fractional programming model with the objective of maximizing the grouping efficacy while the number of cells is unknown. To show the effectiveness of the proposed model, two test problems were applied. Then, to solve the model for real-sized applications, a hybrid meta-heuristic algorithm in which genetic algorithm and variable neighborhood search are combined. Using the grouping efficacy measure, we have also compared the performance of the proposed algorithm on a set of 35 test problems from the literature. The results show that the proposed GA-VNS method outperforms the state-of-the-art algorithms.     

A novel hybrid meta-heuristic algorithm for solving multi objective flexible job shop scheduling

Finding feasible scheduling that optimize all objective functions for flexible job shop scheduling problem (FJSP) is considered by many researchers. In this paper, the novel hybrid genetic algorithm and simulated annealing (NHGASA) is introduced to solve FJSP. The NHGASA is a combination of genetic algorithm and simulated annealing to propose the algorithm that is more efficient than others. The three objective functions in this paper are: minimize the maximum completion time of all the operations (makespan), minimize the workload of the most loaded machine and minimize the total workload of all machines. Pareto optimal solution approach is used in NHGASA for solving FJSP. Contrary to the other methods that assign weights to all objective functions to reduce them to one objective function, in the NHGASA and during all steps, problems are solved by three objectives. Experimental results prove that the NHGASA that uses Pareto optimal solutions for solving multi-objective FJSP overcome previous methods for solving the same benchmarks in the shorter computational time and higher quality.     

Solving a bi-objective unrelated parallel batch processing machines scheduling problem: A comparison study

Nowadays in competitive markets, production organizations are looking to increase their efficiency and optimize manufacturing operations. In addition, batch processor machines (BPMs) are faster and cheaper to carry out operations; thus the performance of manufacturing systems is increased. This paper studies a production scheduling problem on unrelated parallel BPMs with considering the release time and ready time for jobs as well as batch capacity constraints. In unrelated parallel BPMs, modern machines are used in a production line side by side with older machines that have different purchasing costs; so this factor is introduced as a novel objective to calculate the optimum cost for purchasing various machines due to the budget. Thus, a new bi-objective mathematical model is presented to minimize the makespan (i.e., C_max), tardiness/earliness penalties and the purchasing cost of machines simultaneously. The presented model is first coded and solved by the ε-constraint‌ method. Because of the complexity of the NP-hard problem, exact methods are not able to optimally solve large-sized problems in a reasonable time. Therefore, we propose a multi-objective harmony search (MOHS) algorithm. the results are compared with the multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective ant colony optimization algorithm (MOACO). To tune their parameters, the Taguchi method is used. The results are compared by five metrics that show the effectiveness of the proposed MOHS algorithm compared with the MOPSO, NSGA-II and MOACO. At last, the sensitivity of the model is analyzed on new parameters and impacts of each parameter are illustrated on bi- objective functions.     

Single machine scheduling to minimize total weighted late work: a comparison of scheduling rules and search algorithms

In this research the problem of scheduling n jobs to minimize the Total Weighted Late Work (TWLW) is evaluated within the single machine context. As the problem complexity increases, so does the solution complexity, and often the objective is to identify a heuristic or algorithm that may return a near optimal solution. Various scheduling rules, heuristics and algorithms, including the weighted shortest processing rule, a variation of the modified due date rule, a genetic algorithm, neighborhood job search, and space smoothing with neighborhood job search, are empirically evaluated using different parameters to determine the utility of each approach.     

A preference ordered classification for a multi-objective max–min redundancy allocation problem

In this study, we consider a bi-objective redundancy allocation problem on a series–parallel system with component level redundancy strategy. Our aim is to maximize the minimum subsystem reliability, while minimizing the overall system cost. The Pareto solutions of this problem are found by the augmented ε-constraint approach for small and moderate sized instances. After finding the Pareto solutions, we apply a well known sorting procedure, UTADIS, to categorize the solutions into preference ordered classes, such as A, B, and C. In this procedure, consecutive classes are separated by thresholds determined according to the utility function constructed from reference sets of classes. In redundancy allocation problems, reference sets may contain a small number of solutions (even a single solution). We propose the τ-neighborhood approach to increase the number of references. We perform experiments on some reliability optimization test problems and general test problems.     

Robust Platelet Logistics Planning in Disaster Relief Operations Under Uncertainty: a Coordinated Approach

Resource sharing, as a coordination mechanism, can mitigate disruptions in supply and changes in demand. It is particularly crucial for platelets because they have a short lifespan and need to be transferred and allocated within a limited time to prevent waste or shortages. Thus, a coordinated model comprised of a mixed vertical-horizontal structure, for the logistics of platelets, is proposed for disaster relief operations in the response phase. The aim of this research is to reduce the wastage and shortage of platelets due to their critical role in wound healing. We present a bi-objective location-allocation robust possibilistic programming model for designing a two-layer coordinated organization strategy for multi-type blood-derived platelets under demand uncertainty. Computational results, derived using a heuristic ε-constraint algorithm, are reported and discussed to show the applicability of the proposed model. The experimental results indicate that surpluses and shortages in platelets remarkably declined following instigation of a coordinated disaster relief operation.     

Finding non-dominated solutions in bi-objective integer network flow problems

This paper deals with an algorithm for finding all the non-dominated solutions and corresponding efficient solutions for bi-objective integer network flow problems. The algorithm solves a sequence of ?$?$-constraint problems and computes all the non-dominated solutions by decreasing order of one of the objective functions. The optimal integer solutions for the ?$?$-constraint problems are determined by exploring a branch-and-bound tree. The algorithm makes use of the network structure to perform the computations, i.e., the network structure of the problem is not destroyed with the inclusion of an ?$?$-constraint. This paper presents the main features of the algorithm, the theoretical bases of the proposed approach and some computational issues. Experiments were done and the results are also reported in the paper.     

Integrating employee timetabling with scheduling of machines and transporters in a job-shop environment: A mathematical formulation and an Anarchic Society Optimization algorithm

This paper addresses a ternary-integration scheduling problem that incorporates employee timetabling into the scheduling of machines and transporters in a job-shop environment with a finite number of heterogeneous transporters where the objective is to minimize the completion time of all jobs. The problem is first formulated as a mixed-integer linear programming model. Then, an Anarchic Society Optimization (ASO) algorithm is developed to solve large-sized instances of the problem. The formulation is used to solve small-sized instances and to evaluate the quality of the solutions obtained for instances with larger sizes. A comprehensive numerical study is carried out to assess the performance of the proposed ASO algorithm. The algorithm is compared with three alternative metaheuristic algorithms. It is also compared with several algorithms developed in the literature for the integrated scheduling of machines and transporters. Moreover, the algorithms are tested on a set of adapted benchmark instances for an integrated problem of machine scheduling and employee timetabling. The numerical analysis suggests that the ASO algorithm is both effective and efficient in solving large-sized instances of the proposed integrated job-shop scheduling problem.     

Design of a genetic algorithm for bi-objective unrelated parallel machines scheduling with sequence-dependent setup times and precedence constraints

This paper presents a novel, two-level mixed-integer programming model of scheduling N jobs on M parallel machines that minimizes bi-objectives, namely the number of tardy jobs and the total completion time of all the jobs. The proposed model considers unrelated parallel machines. The jobs have non-identical due dates and ready times, and there are some precedence relations between them. Furthermore, sequence-dependent setup times, which are included in the proposed model, may be different for each machine depending on their characteristics. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time using traditional approaches or optimization tools is extremely difficult. This paper proposes an efficient genetic algorithm (GA) to solve the bi-objective parallel machine scheduling problem. The performance of the presented model and the proposed GA is verified by a number of numerical experiments. The related results show the effectiveness of the proposed model and GA for small and large-sized problems.     

A hybrid GA-AUGMECON method to solve a cubic cell formation problem considering different worker skills

Part quality and consequently customer satisfaction besides cost functions are two of the most important issues for any firm. Balancing between these two goals leads to full utilization from manufacturing resources. Formerly, in cubic cell formation problem, where a part on a machine can be processed by various workers, worker assignment was done just by minimizing inter-cell movement criterion; so, the workers assigned into the processing cell are mostly selected rather than outsider workers. But, it is rational for the ties to be broken by skills of different workers in performing a special part on the dedicated machine. In this paper, a bi-objective cubic cell formation is presented with two non-homogeneous objective functions in order to minimize the inter-cell movements and maximize a part quality index. Quality index for each part is represented through a cubic matrix containing integer values of 1–5 (representing very bad, bad, medium, well and very well), which qualifies the process of part on a specific machine by a specific worker. To solve the problem, a hybrid GA-augmented ε-constraint method (GA-AUGMEON) is developed to reduce time consuming difficulty of AUGMECON method. To validate the model and the GA-AUGMECON algorithm, some randomly generated examples in small and large size are solved.     

Hybrid NSGA-II for an imperfect production system considering product quality and returns under two warranty policies

This study presents a new bi-objective mathematical model for an imperfect production system (IPS) that accounts for product returns and quality levels under two different warranty policies. We considered uncertain customer demand as stochastic behavior and product price as a function of return compensation, product quality level, and warranty-period length. We simultaneously looked at the pro rata warranty and free replacement/repair warranty policies and assumed that customers can choose the desired policy. A return policy for an online distributor was also included and two objective functions were used to address the problem. The first objective function maximized the total expected revenue, and the second objective function maximized customer satisfaction. The non-dominated sorting genetic algorithm (NSGA-II) and two others, the basic bee metaheuristic and teaching-learning-based optimization algorithms, were used to generate the initial solution for use in the NSGA-II algorithm. The results from the hybrid algorithms revealed that the proposed method improves the performance of the NSGA-II algorithm. Finally, several specific sensitivity analyses were conducted to determine the effects of the problem parameters.     

Preemptive scheduling on uniformly related machines: minimizing the sum of the largest pair of job completion times

We revisit the classic problem of preemptive scheduling on m uniformly related machines. In this problem, jobs can be arbitrarily split into parts, under the constraint that every job is processed completely, and that the parts of a job are not assigned to run in parallel on different machines. We study a new objective which is motivated by fairness, where the goal is to minimize the sum of the two maximal job completion times. We design a polynomial time algorithm for computing an optimal solution. The algorithm can act on any set of machine speeds and any set of input jobs. The algorithm has several cases, many of which are very different from algorithms for makespan minimization (algorithms that minimize the maximum completion time of any job), and from algorithms that minimize the total completion time of all jobs.     

Scheduling problems with two competing agents to minimized weighted earliness–tardiness

We study scheduling problems with two competing agents, sharing the same machines. All the jobs of both agents have identical processing times and a common due date. Each agent needs to process a set of jobs, and has his own objective function. The objective of the first agent is total weighted earliness–tardiness, whereas the objective of the second agent is maximum weighted deviation from the common due date. Our goal is to minimize the objective of the first agent, subject to an upper bound on the objective value of the second agent. We consider a single machine, and parallel (both identical and uniform) machine settings. An optimal solution in all cases is shown to be obtained in polynomial time by solving a number of linear assignment problems. We show that the running times of the single and the parallel identical machine algorithms are O(n^m+3), where n is the number of jobs and m is the number of machines. The algorithm for solving the problem on parallel uniform machine requires O(n^m+3m³) time, and under very reasonable assumptions on the machine speeds, is reduced to O(n^m+3). Since the number of machines is given, these running times are polynomial in the number of jobs.     

A branch-and-bound procedure for a single-machine earliness scheduling problem with two agents

This paper addresses a two-agent scheduling problem on a single machine where the objective is to minimize the total weighted earliness cost of all jobs, while keeping the earliness cost of one agent below or at a fixed level Q. A mixed-integer programming (MIP) model is first formulated to find the optimal solution which is useful for small-size problem instances. To solve medium- to large-size problem instances, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is then provided to derive the optimal solution. A simulated annealing heuristic algorithm incorporating with a heuristic procedure is developed to derive the near-optimal solutions for the problem. A computational experiment is also conducted to evaluate the performance of the proposed algorithms.     

Solving a bi-objective flowshop scheduling problem by a Multi-objective Immune System and comparing with SPEA2+ and SPGA

This paper presents a bi-objective flowshop scheduling problem with sequence-dependent setup times. The objective functions are to minimize the total completion time and the total earliness/tardiness for all jobs. An integer programming model is developed for the given problem that belongs to an NP-hard class. Thus, an algorithm based on a Multi-objective Immune System (MOIS) is proposed to find a locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed MOIS, different test problems are solved. Based on some comparison metrics, the computational results of the proposed MOIS is compared with the results obtained using two well-established multi-objective genetic algorithms, namely SPEA2+ and SPGA. The related results show that the proposed MOIS outperforms genetic algorithms, especially for the large-sized problems.