A novel extension of the classical vehicle routing and scheduling problems is introduced that integrates aspects of machine scheduling into vehicle routing. Associated with each customer order is a release date that defines the earliest time that the order is available to leave the depot for delivery and a due date that indicates the time by which the order should ideally be delivered to the customer. The objective is to minimize a convex combination of the operational costs and customer service level, represented by the total distance traveled and the total weighted tardiness of delivery, respectively. A path-relinking algorithm (PRA) is proposed to address the problem, and a variety of benchmark instances are generated to evaluate its performance. The PRA exploits the efficiency and aggressive improvement of neighborhood search but relies on a new path-relinking procedure and advanced population management strategies to navigate the search space effectively. To provide a comparator algorithm to the PRA, we embed the neighborhood search into a standard iterated local search algorithm (ILS). Extensive computational experiments on the benchmark instances show that the newly defined features have a significant and varied impact on the problem, and the performance of the PRA dominates that of the ILS algorithm. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0756 .

This paper introduces a modified shifting bottleneck approach to solve train scheduling and rescheduling problems. The problem is formulated as a job shop scheduling model and a mixed integer linear programming model is also presented. The shifting bottleneck procedure is a well-established heuristic method for obtaining solutions to the job shop and other machine scheduling problems. We modify the classical shifting bottleneck approach to make it suitable for the types of job shop problem that arises in train scheduling. The method decomposes the problem into several single machine problems. Different variations of the method are considered with regard to solving the single machine problems. We compare and report the performance of the algorithms for a case study based on part of the UK railway network.

Aset of original jobs has been scheduled on a single machine, but not processed, when a set of new jobs arrives. The decision maker needs to insert the new jobs into the existing schedule without excessively changing it. The objective is minimization of the maximum lateness of the jobs, subject to a customer service requirement modeled by a limit on the maximum time change of the original jobs. Because the schedule of the original jobs can be arbitrary, this problem models multiple disruptions from repeated new job arrivals. We show that this scheduling problem is intractable, even if no new jobs arrive. We describe several approximation algorithms and analyze their worst-case performance. Next, we develop a branch and bound algorithm that uses a variable neighborhood descent algorithm to obtain an initial upper bound, several dominance properties that we establish, and a lower bounding scheme based on a preemptive relaxation of the problem. The branch and bound algorithm solves 99.9% of randomly generated instances with up to 1,000 jobs within 60 CPU seconds. Our work demonstrates for the first time that optimization of large scale, intractable rescheduling problems is possible. More generally, it refocuses the literature on scheduling problems towards rescheduling issues.

This paper introduces a new neighborhood search technique, called dynasearch, that uses dynamic programming to search an exponential size neighborhood in polynomial time. While traditional local search algorithms make a single move at each iteration, dynasearch allows a series of moves to be performed. The aim is for the lookahead capabilities of dynasearch to prevent the search from being attracted to poor local optima. We evaluate dynasearch by applying it to the problem of scheduling jobs on a single machine to minimize the total weighted tardiness of the jobs. Dynasearch is more effective than traditional first-improve or best-improve descent in our computational tests. Furthermore, this superiority is much greater for starting solutions close to previous local minima. Computational results also show that an iterated dynasearch algorithm in which descents are performed a few random moves away from previous local minima is superior to other known local search procedures for the total weighted tardiness scheduling problem.

In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only on the machine, is required before a batch is processed on a machine, and all jobs in a batch remain at the machine until the entire batch is processed. The aim is to make batching and sequencing decisions, which specify a partition of the jobs into batches on each machine, and a processing order of the batches on each machine, respectively, so that the makespan is minimized. The flow-shop problem is shown to be strongly NP-hard. We demonstrate that there is an optimal solution with the same batches on the two machines; we refer to these as consistent batches. A heuristic is developed that selects the best schedule among several with one, two, or three consistent batches, and is shown to have a worst-case performance ratio of 4/3. For the open-shop, we show that the problem is NP-hard in the ordinary sense. By proving the existence of an optimal solution with one, two or three consistent batches, a close relationship is established with the problem of scheduling two or three identical parallel machines to minimize the makespan. This allows a pseudo-polynomial algorithm to be derived, and various heuristic methods to be suggested.

This paper presents several local search heuristics for the problem of scheduling a single machine to minimize total weighted tardiness. We introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences. This binary encoding scheme is compared to the usual “natural” permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems. Computational results indicate that all of the heuristics which employ our binary encoding are very robust in that they consistently produce good quality solutions, especially when multistart implementations are used instead of a single long run. The binary encoding is also used in a new genetic algorithm which performs very well and requires comparatively little computation time. A comparison of neighborhood search methods which use the permutation and binary representations shows that the permutation-based methods have a higher likelihood of generating an optimal solution, but are less robust in that some poor solutions are obtained. Of the neighborhood search methods, tabu search clearly dominates the others. Multistart descent performs remarkably well relative to simulated annealing and threshold accepting.

In the problem of scheduling a single machine to minimize total weighted late work, there are n jobs to be processed for which each has an integer processing time, a weight and a due date. The objective is to minimize the total weighted late work, where the late work for a job is the amount of processing of this job which is performed after its due date. An O(n log n) algorithm is derived for the preemptive total weighted late work problem. For non-preemptive scheduling, efficient algorithms are derived for the special cases in which all processing times are equal and in which all due dates are equal. A pseudopolynomial algorithm is presented for the general non-preemptive total weighted late work problem. Also, a branch and bound algorithm in which lower bounds are obtained using the dynamic programming state-space relaxation method is proposed for this general problem. Computational results with the branch and bound algorithm for problems with up to 700 jobs are given. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.