Tabu search-based algorithm for the TOC product mix decision

The theory of constraints (TOC) is a management philosophy that maximizes profits in a manufacturing plant with a demonstrated bottleneck. The product mix decision is one application of TOC that involves determination of the quantity and the identification of each product to produce. However, the original TOC heuristic is considered to produce unrealizable solution when a manufacturing plant has multiple resource constraints. This paper presents a tabu search-based TOC product mix heuristic to identify optimal or near optimal product mix for small problem instances under conditions where the original TOC heuristic failed. The tabu search-based TOC product mix heuristic is further used to solve large problem instances typical of practical manufacturing scenario. The experimental results for small to medium size problem show that the tabu search-based TOC heuristic compares favourably with those of optimal methods. Large size problems for which optimal methods have not been established in terms of feasibility in computation times were also solved in reasonable times with good quality solutions, thus confirming that the proposed approach is appropriate for adoption by production planners for the product mix problem in the manufacturing industry.     

Multiple machine JIT scheduling: a tabu search approach

This paper presents an approach to solving the multiple machine, non-preemptive, earliness-tardiness scheduling problem with unequal due dates in a flow shop with machine tiers (FMT). In this variant of the flow shop problem, machines are arranged in tiers or groups, and the jobs must visit one machine in each tier. The processing times, machine assignments, and due dates are deterministic and known in advance. The objective is to find a permutation schedule that minimizes the total deviation of each job from its due date. A tabu search (TS) meta-heuristic combined with an LP evaluation function is applied to solve this problem and results are compared to optimal permutation solutions for small problems and the earliest due date schedule for large problems. Several neighborhood generation methods and two diversification strategies are examined to determine their effect on solution quality. Results show that the TS method works well for this problem. TS found the optimal solution in all but one of the small problem instances and improved the earliest due date solutions for larger instances where no optimal solutions could be found.     

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.     

Comparison of multi-objective evolutionary approaches for task scheduling in distributed computing systems

Parallel and distributed systems play an important part in the improvement of high performance computing. In these type of systems task scheduling is a key issue in achieving high performance of the system. In general, task scheduling problems have been shown to be NP-hard. As deterministic techniques consume much time in solving the problem, several heuristic methods are attempted in obtaining optimal solutions. This paper presents an application of Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and a Non-dominated Sorting Particle Swarm Optimization Algorithm (NSPSO) to schedule independent tasks in a distributed system comprising of heterogeneous processors. The problem is formulated as a multi-objective optimization problem, aiming to obtain schedules achieving minimum makespan and flowtime. The applied algorithms generate Pareto set of global optimal solutions for the considered multi-objective scheduling problem. The algorithms are validated against a set of benchmark instances and the performance of the algorithms evaluated using standard metrics. Experimental results and performance measures infer that NSGA-II produces quality schedules compared to NSPSO.     

Job shop scheduling with the option of jobs outsourcing

Incorporating outsourcing in scheduling is addressed by several researchers recently. However, this scope is not investigated thoroughly, particularly in the job shop environment. In this paper, a new job shop scheduling problem is studied with the option of jobs outsourcing. The problem objective is to minimise a weighted sum of makespan and total outsourcing cost. With the aim of solving this problem optimally, two solution approaches of combinatorial optimisation problems, i.e. mathematical programming and constraint programming are examined. Furthermore, two problem relaxation approaches are developed to obtain strong lower bounds for some large scale problems for which the optimality is not proven by the applied solution techniques. Using extensive numerical experiments, the performance of the solution approaches is evaluated. Moreover, the effect the objectives's weights in the objective function on the performance of the solution approaches is also investigated. It is concluded that constraint programming outperforms mathematical programming significantly in proving solution optimality, as it can solve small and medium size problems optimally. Moreover, by solving the relaxed problems, one can obtain good lower bounds for optimal solutions even in some large scale problems.     

Coordination of set-ups between two stages of a supply chain using multi-objective genetic algorithms

A multi-objective genetic algorithm (MOGA) solution approach for a sequencing problem to coordinate set-ups between two successive stages of a supply chain is presented in this paper. The production batches are processed according to the same sequence in both stages. Each production batch has two distinct attributes and a set-up occurs in the upstream stage every time the first attribute of the new batch is different from the previous one. In the downstream stage, there is a set-up when the second attribute of the new batch is different from that of the previous one. Two objectives need to be considered in sequencing the production batches including minimizing total set-ups and minimizing the maximum number of set-ups between the two stages. Both problems are NP-hard so attainment of an optimal solution for large problems is prohibited. The solution approach starts with an initialization stage followed by evolution of the initial solution set over generations. The MOGA makes use of non-dominated sorting and a niche mechanism to rank individuals in the population. Selected individuals taken from a given population form the succeeding generation using four genetic operators as: reproduction, crossover, mutation and inversion. Experiments in a number of test problems show that the MOGA is capable of finding Pareto-optimal solutions for small problems and near Pareto-optimal solutions for large instances in a short CPU time.     

A robust cell formation approach for varying product demands

In cellular manufacturing environments, manufacturing cells are generally formed based on deterministic product demands. In this paper, we consider a system configuration problem with product demands expressed in a number of probabilistic scenarios. An optimization model integrating cell formation and part allocation is developed to generate a robust system configuration to minimize machine cost and expected inter-cell material handling cost. A two-stage Tabu search based heuristic algorithm is developed to find the optimal or near optimal solutions to the NP-hard problem. Numerical examples show that this model leads to an appropriate compromise between system configuration costs and expected material handling costs to meet the varying product demands. These example problems also show that the proposed algorithm is effective and computationally efficient for small or medium size problems.     

Integrated multi-factory production and distribution scheduling applying vehicle routing approach

This paper introduces a new integrated multi-factory production and distribution scheduling problem in supply chain management. This supply chain consists of a number of factories joined together in a network configuration. The factories produce intermediate or finished products and supply them to other factories or to end customers that are distributed in various geographical zones. The problem consists of finding a production schedule together with a vehicle routing solution simultaneously to minimise the sum of tardiness cost and transportation cost. A mixed-integer programming model is developed to tackle the small-sized problems using CPLEX, optimally. Due to the NP-hardness, to deal with medium- and large-sized instances, this paper develops a novel Improved Imperialist Competitive Algorithm (IICA) employing a local search based on simulated annealing algorithm. Performance of the proposed IICA is compared with the optimal solution and also with four variants of population-based metaheuristics: Imperialist Competitive Algorithm, Genetic Algorithm, Particle Swarm Optimisation (PSO), and Improved PSO. Based on the computational results, it is statistically shown that quality of the IICA’s solutions is the same as optimal ones solving small problems. It also outperforms other algorithms in finding near-optimal solutions dealing with medium and large instances in a reasonably short running time.     

Multi-objective optimization for the multi-mode finance-based project scheduling problem

The finance-based scheduling problem (FBSP) is about scheduling project activities without exceeding a credit line financing limit. The FBSP is extended to consider different execution modes that result in the multi-mode FBSP (MMFBSP). Unfortunately, researchers have abandoned the development of exact models to solve the FBSP and its extensions. Instead, researchers have heavily relied on the use of heuristics and meta-heuristics, which do not guarantee solution optimality. No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP. CPLEX, which is an exact solver, has witnessed a significant decrease in its computation time. Moreover, its current version, CPLEX 12.9, solves multi-objective optimization problems. This study presents a mixed-integer linear programming model for the multi-objective MMFBSP. Using CPLEX 12.9, we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP. We test our model by solving several problems from the literature. We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases. The small increase in computation time compared with possible cost savings make exact models a must for practitioners. Moreover, the linear programming-relaxation of the model, which takes seconds, can provide an excellent lower bound.     

An improved multi-objective genetic algorithm for heterogeneous coverage RFID network planning

Recent research has demonstrated the potential benefits of radio frequency identification (RFID) technology in the supply chain and production management via its item-level visibility. However, the RFID coverage performance is largely impacted by the surrounding environment and potential collisions between the RFID devices. Thus, through RFID network planning (RNP) to achieve the desired coverage within the budget becomes a key factor for success. In this study, we establish a novel and generic multi-objective RNP model by simultaneously optimising two conflicted objectives with satisfying the heterogeneous coverage requirements. Then, we design an improved multi-objective genetic algorithm (IMOGA) integrating a divide-and-conquer greedy heuristic algorithm to solve the model. We further construct a number of computational cases abstracted from an automobile mixed-model assembly line to illustrate how the proposed model and algorithm are applied in a real RNP application. The results show that the proposed IMOGA achieves highly competitive solutions compared with Pareto optimal solutions and the solutions given by four recently developed well-known multi-objective evolutionary and swarm-based optimisers (SPEA2, NSGA-II, MOPSO and MOPS²O) in terms of solution quality and computational robustness.     

Bi-objective partial flexible job shop scheduling problem: NSGA-II,NRGA, MOGA and PAES approaches

This paper deals with a problem of partial flexible job shop with the objective of minimising makespan and minimising total operation costs. This problem is a kind of flexible job shop problem that is known to be NP-hard. Hence four multi-objective, Pareto-based, meta-heuristic optimisation methods, namely non-dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), multi-objective genetic algorithm (MOGA) and Pareto archive evolutionary strategy (PAES) are proposed to solve the problem with the aim of finding approximations of optimal Pareto front. A new solution representation is introduced with the aim of solving the addressed problem. For the purpose of performance evaluation of our proposed algorithms, we generate some instances and use some benchmarks which have been applied in the literature. Also a comprehensive computational and statistical analysis is conducted in order to analyse the performance of the applied algorithms in five metrics including non-dominated solution, diversification, mean ideal distance, quality metric and data envelopment analysis are presented. Data envelopment analysis is a well-known method for efficiently evaluating the effectiveness of multi-criteria decision making. In this study we proposed this method of assessment of the non-dominated solutions. The results indicate that in general NRGA and PAES have had a better performance in comparison with the other two algorithms.     

Combining mutual information and stable matching strategy for dynamic evolutionary multi-objective optimization

It is reasonable to assume that the changing of the optimization environment is smooth when considering a dynamic multi-objective optimization problem. Learning techniques are widely used to explore the dependence structure to facilitate population re-initialization in evolutionary search paradigms. The aim of the learning techniques is to discover knowledge from history information, thereby to track the movement of the optimal front quickly through good initialization when a change occurs. In this article, a new learning strategy is proposed, where the main ideas are (1) to use mutual information to identify the relationship between previously found approximated solutions; (2) to use a stable matching mechanism strategy to associate previously found optimal solutions bijectively; and (3) to re-initialize the new population based on a kinematics model. Controlled experiments were carried out systematically on some widely used test problems. Comparison against several state-of-the-art dynamic multi-objective evolutionary algorithms showed comparable performance in favour of the developed algorithm.     

Scheduling on uniform parallel machines with periodic unavailability constraints

Scheduling problems under unavailability constraints has become a popular research topic in the last few years. Despite it’s important application in the real world, the uniform parallel machine scheduling problem was the least studied due to its complexity. In this paper, we investigated the uniform parallel machine scheduling problem under deterministic availability constraints. Each machine is subject to one unavailability period. Different versions of the problem regarding the type of jobs (identical and non-identical) and the performance measures (the total completion times and the makespan) were studied. For the case of identical jobs and for both performance measures, we developed linear programming models and optimal algorithms to provide a solution to the problem. For the case of non-identical jobs, we proved that the problem is NP-hard and propose a quadratic program. Because, this later cannot solve problems with very large number of jobs and machines, a heuristic was developed to find near optimal solutions to the problem especially with very large number of jobs and machines. The computational results showed that the heuristic’s performance is very high regardless the dimensions of problem instances.     

An improved imperialist competitive algorithm for multi-objective optimization

This article proposes an improved imperialistic competitive algorithm to solve multi-objective optimization problems. The proposed multi-objective imperialistic competitive algorithm (MOICA) uses the elitist strategy, based on the mutation and crossover as in genetic algorithms, and the Pareto concept to store simultaneously optimal solutions of multiple conflicting functions. Three performance metrics are used to evaluate the performance of the new algorithm: convergence to the true Pareto-optimal set, solution diversity and robustness, characterized by the variance over 10 runs. To validate the efficiency of the proposed algorithm, several multi-objective standard test functions with true solutions are used. The obtained results show that the MOICA outperforms most of the methods available in the literature. The proposed algorithm can also handle multi-objective engineering design problems with high dimensions.     

A heuristic based on Vogel's approximation method for sequencing mixed-model assembly lines

Sequencing mixed-model assembly lines is a well researched topic in the literature. However, many methods that have been developed to solve this problem fail to cope with either the large size or the specific characteristics of real-life problems. In this paper, a heuristic is proposed that is derived from Vogel's approximation method for transportation planning. The heuristic is able to handle large and supposedly difficult problem instances. Sophisticated test scenarios considering real-life aspects were generated to evaluate the performance of the heuristic for realistic problem instances. It is shown that the proposed heuristic significantly outperforms priority rule-based methods and requires only reasonable computational effort.     

Minimizing production flow time in a process and assembly job shop

Scheduling is one of the most important issues in the planning and operation of production systems, but in medium to large shops, the generation of consistently good schedules has proven to be extremely difficult. The problem is that optimal scheduling solutions involve costly and impractical enumeration procedures. In the literature, most scheduling problems only address jobs with serial or sequential operations. Rarely do they consider jobs in which machining and assembly operations are simultaneously involved. This lack of attention to scheduling problems that involve both machining and assembly goes against what one would normally find in most job shops. In this paper, the problem of scheduling a set of N final products on M machines in a job shop environment that involve both machining and assembly operations is addressed. The objective pursued is the minimization of production flow time (makespan). A mathematical model is developed in an effort to obtain optimal solutions. Because this type of model grows exponentially as the size of the problems increases, an heuristic solution approach is developed to solve the problems more efficiently. The models are tested and compared on several test problems.     

Optimal feeding profile in fed-batch bioreactors using a genetic algorithm

An optimal feeding profile for a fed-batch process was designed based on an evolutionary algorithm. Usually the presence of multiple objectives in a problem leads to a set of optimal solutions, commonly known as Pareto-optimal solutions. Evolutionary algorithms are well suited for deriving multi-objective optimisation since they evolve a set of non-dominated solutions distributed along the Pareto front. Several evolutionary multi-objective optimisation algorithms have been developed, among which the Non-dominated Sorting Genetic Algorithm NSGA-II is recognised to be very effective in overcoming a variety of problems. To demonstrate the applicability of this technique, an optimal control problem from the literature was solved using several methods considering the single-objective dynamic optimisation problem.     

A three-phase heuristic algorithm for fixed-charge capacitated material flow network design with input/output points location

In this paper, we consider the material flow network design problem in which locations of input and output points of departments and flow paths are determined concurrently on a given block layout. The objective of the problem is to minimize the sum of transportation cost, flow paths construction cost and penalty cost for non-smooth material flows, i.e., flows with turns. A mixed integer programming model is given for the problem and a three-phase heuristic algorithm is developed to solve the problem. In the suggested algorithm, we generate an initial flow network by determining locations of input/output points and flow paths sequentially in the first and second phases, respectively, and then improve it by changing locations of input/output points and flow paths iteratively in the third phase. To evaluate the performance of the suggested algorithms, a series of computational experiments are performed on well-known problem instances as well as randomly generated test problems. Results of computational experiments show that the suggested algorithm gives good solutions in a short computation time.     

A new relaxed flexible bay structure representation and particle swarm optimization for the unequal area facility layout problem

The facility layout problem (FLP) with unequal area departments is a very hard problem to be optimally solved. In this article, a hybrid particle swarm optimization (PSO) and local search approach is proposed to solve the FLP with unequal area departments. The flexible bay structure (FBS), which is a very common layout in manufacturing and retail facilities, is used. Furthermore, the FBS is relaxed by allowing empty spaces in bays, which results in more flexibility while assigning departments in bays. The proposed PSO approach is used to solve the FLP instances from the literature with varying sizes. The comparative results show that the PSO approach is very promising and able to find the previously known-optimal solutions in very short CPU times. In addition, new best solutions have been found for some test problems. Improvements have been achieved by allowing partially filled bays.