An improved approximation algorithm for single machine scheduling with job delivery

An improved on-line algorithm for single parallel-batch machine scheduling with delivery times

We consider a single machine scheduling problem with multiple maintenance activities, where the maintenance duration function is of the linear form f(t) = a+bt with a ≥ 0 and b > 1. We propose an approximation algorithm named FFD-LS2I with a worst-case bound of 2 for problem. We also show that there is no polynomial time approximation algorithm with a worst-case bound less than 2 for the problem with b ≥ 0 unless P = NP, which implies that the FFD-LS2I algorithm is the best possible algorithm for the case b > 1 and that the FFD-LS algorithm, which is proposed in the literature, is the best possible algorithm for the case b ≤ 1 both from the worst-case bound point of view.

The single-machine scheduling problem with truncated sum-of-processing-times-based learning effect and past-sequence-dependent job delivery times is considered. Each job's delivery time depends on ...

In this paper, a discrete state transition algorithm is introduced to solve a multiobjective single machine job shop scheduling problem. In the proposed approach, a non-dominated sort technique is used to select the best from a candidate state set, and a Pareto archived strategy is adopted to keep all the non-dominated solutions. Compared with the enumeration and other heuristics, experimental results have demonstrated the effectiveness of the multiobjective state transition algorithm.

This paper establishes a robust optimization model and proposes constraint generation algorithm to solve a robust single machine scheduling problem with random release times. The performance criterion of interest is the maximum waiting time (MWT) over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our robust optimization model needs only the information of release time intervals. We formulate this uncertain optimization problem as a 0–1 linear programming model with a large number of constraints. To solve the model efficiently, a constraint generation algorithm (CGA) is proposed which generate constraint iteratively to obtain the optimal solution. The robustness of the optimal sequence under various probability distributions of release times is verified by simulation. Extensive computational experiments are implemented to demonstrate the effectiveness and efficiency of the proposed solution method.

The warehouse of a hospital is responsible for wrapping medical materials into packages by a baler and dispatching packages to the departments of the hospital periodically to guarantee the requirements of patients. The manager of the warehouse wants to efficiently utilize the wrapping machine and reduce the times of distributions to decrease logistics cost. If we regard the baler as a single machine and medical materials as jobs, the problem can be summarized as a supply chain scheduling problem integrated with production and delivery. Owing to periodic working time of workers, the machine can be viewed as having periodic maintenance. Because the wrapping interruption of medical materials is not allowed in the hospital, processing of any job is nonresumable. All wrapped packages are dispatched before workers are off duty. This means that each delivery batch is delivered just before each maintenance. Our goal is to minimize sum of the total delivery time and the total delivery cost. We show that the problem is strongly NP-hard and provide a $$2$$2-approximation algorithm. Moreover, we propose a branch-and-bound algorithm. Finally we present computational results for some instances generated randomly. Numerical simulation results show that the approximation algorithm performs efficiently.

This paper presents a discrete artificial bee colony algorithm for a single machine earliness–tardiness scheduling problem. The objective of single machine earliness–tardiness scheduling problems is to find a job sequence that minimises the total sum of earliness–tardiness penalties. Artificial bee colony (ABC) algorithm is a swarm-based meta-heuristic, which mimics the foraging behaviour of honey bee swarms. In this study, several modifications to the original ABC algorithm are proposed for adapting the algorithm to efficiently solve combinatorial optimisation problems like single machine scheduling. In proposed study, instead of using a single search operator to generate neighbour solutions, random selection from an operator pool is employed. Moreover, novel crossover operators are presented and employed with several parent sets with different characteristics to enhance both exploration and exploitation behaviour of the proposed algorithm. The performance of the presented meta-heuristic is evaluated on several benchmark problems in detail and compared with the state-of-the-art algorithms. Computational results indicate that the algorithm can produce better solutions in terms of solution quality, robustness and computational time when compared to other algorithms.

A branch-and-bound algorithm for single-machine scheduling with batch delivery minimizing flow times and delivery costs

In this paper, we investigate a single machine scheduling problem with a proportional job deterioration. Under release times (dates) of jobs, the objective is to minimize the total weighted completion time. For the general condition, some dominance properties, a lower bound and an upper bound are given, then a branch-and-bound algorithm is proposed. In addition, some meta-heuristic algorithms (including the tabu search (TS), simulated annealing (SA) and heuristic (NEH) algorithms) are proposed. Finally, experimental results are provided to compare the branch-and-bound algorithm and another three algorithms, which indicate that the branch-and-bound algorithm can solve instances of 40 jobs within a reasonable time and that the NEH and SA are more accurate than the TS.

This study focuses on developing a scheduling model for sequencing a set of jobs with different release times in a single machine to meet non-similar due dates as well as to reduce total sequence-dependent setup time. A constraint programming (CP) model is proposed to solve the scheduling problem by minimizing makespan under multiple constraints, namely release times, sequence-dependent setup time, and due dates. The proposed constraint programming model is tested and compared with the baseline method derived from as-is scheduling of alloy wheels manufactures. The computational experiments show the proposed constraint programming model outperforms the baseline method in the average improvement in makespan and total setup time. For small-size problems, the proposed scheduling model were optimally solved in a short time, achieving the best average improvement in makespan of 4.8826% and the best average improvement in total setup time of 45.7924%. Despite increasing problem sizes, the proposed scheduling model's computational time deteriorates but continues to provide the best solutions, achieving the best average improvement in makespan of 7.4891% and the best average improvement in total setup time of 55.4033%.

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

This paper considers the single batch-processing machine scheduling problem with aging effect and multi-maintenance activity concept. Real processing time of jobs increases due to machine’s aging effect. Maintenance time is constant and the machine returns to its initial condition after each maintenance activity and the aging effect starts anew. Our scheduling problem is under assumptions: non identical job sizes and dynamic job arrivals. We have to determine jointly (1) the maintenance frequencies, (2) the position of the maintenance activities on the machine, (3) the grouping of the jobs into the batches, and (4) the sequence of the batches on the machine, to minimize makespan. At first, we formulate the problem as a mathematical model. Since this problem has been proved to be NP-hard; therefore, a heuristic and two meta-heuristic algorithms are offered for the real-sized problems. The performance of the proposed algorithms is analyzed on the various test problems based on the considered measures.

This paper analyzes a supply chain, which consists of a manufacturer, a retailer and several suppliers in which the retailer orders jobs to the manufacturer and the suppliers provide the requiring parts. The manufacturer schedules and processes the orders and dispatches them to the retailer either individually or collectively in batches. The manufacturer incurs a penalty cost for each tardy job and a transportation cost for every delivered batch and therefore, searches for a schedule that yields minimum number of tardy jobs and batches. Moreover, the manufacturer tries to optimize its supplying cost through locating the suppliers that offer appropriate release times and costs for manufacturing parts. Since the release times of parts directly affect scheduling of orders, in this research, we develop an integrated mathematical model for the manufacturer that incorporates suppliers' selection issue into the scheduling and batching decisions. Furthermore, we present a heuristic algorithm (greedy algorithm) and also a local search to quickly determine the optimal or near-optimal solutions. The computational analysis shows the importance of the integrated model and also the superiority and effectiveness of the heuristic algorithms.

In this paper, we address a model for supply chain coordination. There are m manufacturers modelled as single machines, each of which processes a specific set of jobs (products). After processing is completed, jobs are batched, and batches are shipped to a customer by means of vehicles. The problem consists in concurrently finding a production schedule of the jobs, a partition of jobs into delivery batches and an assignment of delivery batches to vehicles, so that jobs are delivered within their deadlines and total costs are minimised. We focus on a scenario characterised by fixed departure times and inventory holding costs. For each departure time there is a given number of vehicles, possibly having limited capacity. Each job incurs a cost proportional to the time from job completion to delivery departure. In this paper, we show that the problem is NP-hard even for a very restricted case, and report various polynomiality results for two scenarios, namely: (i) when the production sequence of each manufacturer is fixed in advance, and (ii) when there is a single manufacturer and processing times are all equal to 1. We also point out several open problems.

Unbounded parallel-batch scheduling with family jobs and delivery coordination