Constructive heuristics for the unrelated parallel machines scheduling problem with machine eligibility and setup times

This work considers a scheduling problem identified in a factory producing customised Heating, Ventilation and Air Conditioning (HVAC) equipment. More specifically, the metal folding section is modelled as unrelated parallel machines with machine eligibility and sequence-dependent setup times. The objective under consideration is the minimisation of the total tardiness. The problem is known to be NP-hard so approximate methods are needed to solve real-size instances. In order to embed the scheduling procedure into a decision support system providing high-quality solutions in nearly real time, the goal of this paper is to develop fast, efficient constructive heuristics for the problem. Due to the lack of methods for this specific problem, some existing heuristics and one metaheuristic are selected from related problems and adapted. In addition, a set of heuristics with novel repair and improvement phases are proposed. The performance of the methods adapted and the proposals are compared with the optimal/approximate solutions obtained by a solver for an MILP in two sets of instances with small and medium sizes. Additionally, big-size instances (representing more realistic cases for our company) have been solved using the proposed constructive heuristics, providing efficient solutions in negligible computational times. Even if the adaptation of heuristics performs reasonably well, these are outperformed by the new heuristic proposed in this paper. In addition, when the new heuristic is embedded in the metaheuristic adapted from a related the problem, the results obtained are excellent in terms of the quality of the solution, even if the computational effort is somewhat higher.Ministerio de Ciencia en Innovación. “PROMISE

AN ALGORITHM TO SOLVE THE ASSOCIATIVE PARALLEL MACHINE SCHEDULING PROBLEM

Effective production scheduling is essential for improved performance. Scheduling strategies for various shop configurations and performance criteria have been widely studied. Scheduling in parallel machines (PM) is one among the many scheduling problems that has received considerable attention in the literature. An even more complex scheduling problem arises when there are several PM families and jobs are capable of being processed in more than one such family. This research addresses such a situation, which is defined as an Associative Parallel Machine scheduling (APMS) problem. This research presents the SAPT-II algorithm that solves a highly constrained APMS problem with the objective to minimize average flow time. A case example from a make-to-order industrial product manufacturer is used to illustrate the complexity of the problem and evaluate the effectiveness of the scheduling algorithm

Total Tardiness Minimization in a Single-Machine with Periodical Resource Constraints

In this paper we introduce a variant of the single machine considering resource restriction per period. The objective function to be minimized is the total tardiness.  We proposed an integer linear programming modeling based on a bin packing formulation. In view of the NP-hardness of the introduced variant, heuristic algorithms are required to find high-quality solutions within an admissible computation times. In this sense, we present a new hybrid matheuristic called Relax-and-Fix with Variable Fixing Search (RFVFS).  This innovative solution approach combines the relax-and-fix algorithm and a strategy for the fixation of decision variables based on the concept of the variable neighborhood search metaheuristic. As statistical indicators to evaluate the solution procedures under comparison, we employ the Average Relative Deviation Index (ARDI) and the Success Rate (SR). We performed extensive computational experimentation with a testbed composed by 450 proposed test problems. Considering the results for the number of jobs, the RFVFS returned ARDI and SR values of 35.6% and 41.3%, respectively. Our proposal outperformed the best solution approach available for a closely-related problem with statistical significance

Review on unrelated parallel machine scheduling problem with additional resources

This study deals with an unrelated parallel machine scheduling problem with additional resources (UPMR). That is one of the important sub-problems in the scheduling. UPMR consists of scheduling a set of jobs on unrelated machines. In addition to that, a number of one or more additional resources are needed. UPMR is very important and its importance comes from the wealth of applications; they are applicable to engineering and scientific situations and manufacturing systems such as industrial robots, nurses, machine operators, bus drivers, tools, assembly plant machines, fixtures, pallets, electricity, mechanics, dies, automated guided vehicles, fuel, and more. The importance also comes from the concern about the limitation of resources that are dedicated for the production process. Therefore, researchers and decision makers are still working on UPMR problem to get an optimum schedule for all instances which have not been obtained to this day. The optimum schedule is able to increase the profits and decrease the costs whilst satisfying the customers’ needs. This research aims to review and discuss studies related to unrelated parallel machines and additional resources. Overall, the review demonstrates the criticality of resolving the UPMR problem. Metaheuristic techniques exhibit significant effectiveness in generating results and surpassing other algorithms. Nevertheless, continued improvement is essential to satisfy the evolving requirements of UPMR, which are subject to operational changes based on customer demand

Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimization. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component - vital to guarantee the non-violation of the problem's constraints - which optimally allocates resources with respect to tardiness minimization. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure is revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight deadlines, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights

Multiobjective Order Acceptance and Scheduling on Unrelated Parallel Machines with Machine Eligibility Constraints

This paper studies the order acceptance and scheduling problem on unrelated parallel machines with machine eligibility constraints. Two objectives are considered to maximize total net profit and minimize the makespan, and the mathematical model of this problem is formulated as multiobjective mixed integer linear programming. Some properties with respect to the objectives are analysed, and then a classic list scheduling (LS) rule named the first available machine rule is extended, and three new LS rules are presented, which focus on the maximization of the net profit, the minimization of the makespan, and the trade-off between the two objectives, respectively. Furthermore, a list-scheduling-based multiobjective parthenogenetic algorithm (LS-MPGA) is presented with parthenogenetic operators and Pareto-ranking and selection method. Computational experiments on randomly generated instances are carried out to assess the effectiveness and efficiency of the four LS rules under the framework of LS-MPGA and discuss their application environments. Results demonstrate that the performance of the LS-MPGA developed for trade-off is superior to the other three algorithms

Guided genetic algorithm for solving unrelated parallel machine scheduling problem with additional resources

This paper solved the unrelated parallel machine scheduling with additional resources (UPMR) problem. The processing time and the number of required resources for each job rely on the machine that does the processing. Each job j needed units of resources (rjm) during its time of processing on a machine m. These additional resources are limited, and this made the UPMR a difficult problem to solve. In this study, the maximum completion time of jobs makespan must be minimized. Here, we proposed genetic algorithm (GA) to solve the UPMR problem because of the robustness and the success of GA in solving many optimization problems. An enhancement of GA was also proposed in this work. Generally, the experiment involves tuning the parameters of GA. Additionally, an appropriate selection of GA operators was also experimented. The guide genetic algorithm (GGA) is not used to solve the unspecified dynamic UPMR. Besides, the utilization of parameters tuning and operators gave a balance between exploration and exploitation and thus help the search escape the local optimum. Results show that the GGA outperforms the simple genetic algorithm (SGA), but it still didn't match the results in the literature. On the other hand, GGA significantly outperforms all methods in terms of CPU time

Hybrid genetic algorithm based on bin packing strategy for the unrelated parallel workgroup scheduling problem

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In this paper we focus on an unrelated parallel workgroup scheduling problem where each workgroup is composed of a number of personnel with similar work skills which has eligibility and human resource constraints. The most difference from the general unrelated parallel machine scheduling with resource constraints is that one workgroup can process multiple jobs at a time as long as the resources are available, which means that a feasible scheduling scheme is impossible to get if we consider the processing sequence of jobs only in time dimension. We construct this problem as an integer programming model with the objective of minimizing makespan. As it is incapable to get the optimal solution in the acceptable time for the presented model by exact algorithm, meta-heuristic is considered to design. A pure genetic algorithm based on special coding design is proposed firstly. Then a hybrid genetic algorithm based on bin packing strategy is further developed by the consideration of transforming the single workgroup scheduling to a strip-packing problem. Finally, the proposed algorithms, together with exact approach, are tested at different size of instances. Results demonstrate that the proposed hybrid genetic algorithm shows the effective performance