Minimizing total tardiness and earliness on unrelated parallel machines with controllable processing times

Minimizing total tardiness on a single machine with controllable processing times

Scheduling with controllable release dates and processing times: Total completion time minimization

Identical parallel machine scheduling problem with controllable processing times is investigated in this research. In such an area, our focus is mostly motivated by the adoption of just-in-time (JIT) philosophy with the objective of minimizing total weighted tardiness and earliness as well as job compressions/expansion cost simultaneously. Also the optimal set amounts of job compressions/expansion plus the job sequence are determined on each machine. It is assumed that the jobs processing times can vary within a given interval, i.e., it is permitted to compress or expand in return for compression/expansion cost. A mixed integer linear programming (MILP) model for the considered problem is firstly proposed and thereafter the optimal jobs set amounts of compression and expansion processing times in a known sequence are determined via parallel net benefit compression–net benefit expansion called PNBC–NBE heuristic. An intelligent water drop (IWD) algorithm, as a new swarm-based nature-inspired optimization one, is also adopted to solve this multi-criteria problem. A heuristic method besides three meta-heuristic algorithms is then employed to solve small- and medium- to large-size sample-generated instances. Computational results reveal that the proposed IWDNN outperforms the other techniques and is a trustable one which can solve such complicated problems with satisfactory consequences.

We study the problem of maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times. Unlike the vast majority of the literature, we do not restrict ourselves to a specific model of processing time function. Rather, we assume that the processing time function can be of any functional structure that is according to one of the following two cases. The first is the case where the job processing times are under a learning effect, i.e., each job processing time is a non-increasing function of its position in the sequence. In the second case, an aging effect is assumed, i.e., each job processing time is a non-decreasing function of its position in the sequence. We prove that the problem is strongly $$\mathcal{N }\mathcal{P }$$ N P -hard under a learning effect, even if all the weights are identical. When there is an aging effect, we introduce a dynamic programming (DP) procedure that solves the problem with arbitrary weights in $$O(n^{3})$$ O ( n 3 ) time (where $$n$$ n is the number of jobs). For identical weights, a faster optimization algorithm that runs in $$O(n\log n)$$ O ( n log n ) time is presented. We also extend the analysis to the case of scheduling on a set of $$m$$ m parallel unrelated machines and provide a DP procedure that solves the problem in polynomial time, given that $$m$$ m is fixed and that the jobs are under an aging effect.

Production scheduling and reliability of machinery are prominent issues in flexible manufacturing systems that are led to decreasing of production costs and increasing of system efficiency. In this paper, multiobjective optimization of stochastic failure‐prone job shop scheduling problem is sought wherein that job processing time seems to be controllable. It endeavours to determine the best sequence of jobs, optimal production rate, and optimum preventive maintenance period for simultaneous optimization of three criteria of sum of earliness and tardiness, system reliability, and energy consumption. First, a new mixed integer programming model is proposed to formulate the problem. Then, by combining of simulation and NSGA‐II algorithm, a new algorithm is put forward for solving the problem. A set of Pareto optimal solutions is achieved through this algorithm. The stochastic failure‐prone job shop with controllable processing times has not been investigated in the earlier research, and for the first time, a new hedging point policy is presented. The computational results reveal that the proposed metaheuristic algorithm converges into optimal or near‐optimal solution. To end, results and managerial insights for the problem are presented.

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.21

Unrelated parallel machine scheduling problem with special controllable processing times and setups

Efficient scheduling of a stochastic no-wait job shop with controllable processing times

Single machine scheduling with common due date and controllable processing times

This chapter considers a dynamic multi-objective machine scheduling problem in response to continuous arrival of new jobs with deterioration effect, under the assumption that jobs can be rejected and job processing time is controllable by allocating extra resources. By deterioration effect, we mean that each job’s processing time may be subject to change due to the capability deterioration with machine’s usage, i.e., the actual processing time of a job becomes longer if the job starts processing later. The operational cost and the disruption cost need to be optimized simultaneously. To solve these dynamic scheduling problems, a directed search strategy (DSS) is introduced into the elitist non-dominated sorting genetic algorithm (NSGA-II) to enhance its capability of tracking changing optimums while maintaining fast convergence. The DSS consists of a population re-initialization mechanism (PRM) to be adopted upon the arrival of new jobs and an offspring generation mechanism (OGM) during evolutionary optimization. PRM re-initializes the population by repairing the non-dominated solutions obtained before the disturbances occur, modifying randomly generated solutions according to the structural properties, as well as randomly generating solutions. OGM generates offspring individuals by fine-tuning a few randomly selected individuals in the parent population, employing intermediate crossover in combination with Gaussian mutations to generate offspring, and using intermediate crossover together with differential evolution based mutation operator. Both PRM and OGM aim to strike a good balance between exploration and exploitation in solving the dynamic multi-objective scheduling problem. Comparative studies are performed on a variety of problem instances of different sizes and with different changing dynamics. Experimental results demonstrate that the proposed DSS is effective in handling the dynamic scheduling problems under investigation.

This paper deals with the capacitated single-stage production lot sizing and scheduling problem with multiple items, setup time, stochastic demand and unrelated parallel machines. A stochastic mixed-integer linear programming model is proposed to formulate the problem. Based on the uncertain constraints, the chance constrained programming approach is used to transform them into equivalent deterministic constraints and then obtain an optimal solution by deterministic mixed-integer linear programming model. Due to the complexity of problem, the mixed-integer programming (MIP) of the equivalence deterministic model of the capacitated single-stage production lot sizing problem with multiple items, setup time, stochastic demand and unrelated parallel machines is reformulated as a shortest path reformulation problem. The proposed algorithm is evaluated through a numerical example. Computational results show that the proposed method gives optimal or near optimal solution and have good-quality result for the test problem.

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Single machine scheduling with controllable processing times: a parametric study

Two-machine open shop problem with controllable processing times

The hybrid flow shop scheduling problem (HFSP), as a realistic extension of the classical flow shop scheduling problem, widely exists in real-world industrial production systems. In practice, the fact that machines are unrelated is important and cannot be neglected. This study focuses on the HFSP with unrelated parallel machines (HFSP-UPM) to minimize the makespan. To address this problem, a hybrid representation that combines single-sequence coding and full-sequence coding is developed to search for solution space that is not covered by common encoding methods. An initialization block integrating random heuristic strategies is proposed for improving the quality of the initial sparrow swarm. To improve the diversity of a sparrow swarm further, a perturbation block embedded with a set of historical best positions and an enhancement strategy are developed. A critical set based local search block is designed for high-intensity local exploitation of promising regions when necessary. Several benchmark cases from the literature as well as some randomly generated instances characterized by the distribution of real data from factory studies are employed to participate in the test. The test results reveal the effectiveness of the proposed perturbation block and local search block. Compared to state-of-the-art metaheuristic algorithms, the enhanced sparrow search algorithm (ESSA) demonstrates higher convergence accuracy when handling instances. The value of the gap between a solution found by the ESSA and a feasible solution found by the mixed-integer programming (MIP) model can reach 0.6%.