A search heuristic for the sequence-dependent economic lot scheduling problem

Almost all of the research on the economic lot scheduling problem (ELSP) has assumed that setup times are sequence-independent even though sequence-dependent problems are common in practice. Furthermore, most of the solution approaches that have been developed solve for a single optimal schedule when in practice it is more important to provide managers with a range of schedules of different length and complexity. In this paper, we develop a heuristic procedure to solve the ELSP problem with sequence-dependent setups. The heuristic provides a range of solutions from which a manager can choose, which should prove useful in an actual stochastic production environment. We show that our heuristic can outperform Dobson's heuristic when the utilization is high and the sequence-dependent setup times and costs are significant.     

Perturbation resilience for the facility location problem

We analyze a simple local search heuristic for the facility location problem using the notion of perturbation resilience: an instance is $\gamma$-perturbation resilient if all costs can be perturbed by a factor of $\gamma$ without changing the optimal solution.We prove that local search for FLP succeeds in finding the optimal solution for $\gamma$-perturbation resilient instances for $\gamma \ge 3$, and we show that this is tight.     

考虑货架存放期的经济批量排产问题的求解

在化工、造纸、制药、钢铁等工业生产中，一台设备或一条生产线可以生产多种产品的情况很常见。在生产中，如何安排各类产品的生产顺序以及生产数量显得十分重要。这类问题通常称作经济批量排产问题，这类问题是生产库存中的经典问题。本文研究的经济批量排产问题考虑了产品货架存放期因素，针对以往研究的不足，本文提出用批量变动方法求解该类问题，由计算结果显示，按照这种排产方法花费的成本要低于其他两种经济批量排产问题常用的方法。     

Homogeneously non-idling schedules of unit-time jobs on identical parallel machines

In this paper, we study the basic homogeneous $m$-machine scheduling problem where weakly dependent unit-time jobs have to be scheduled within the time windows between their release dates and due dates so that, for any subset of machines, the set of the time units at which at least one machine is busy, is in interval. We first introduce the notions of pyramidal structure, $k$-hole, $m$-matching, preschedule, $k$-schedule and schedule for this problem. Then we provide a feasibility criteria for a preschedule. The key result of the paper is then to provide a structural necessary and sufficient condition for an instance of the problem to be feasible. We conclude by giving the directions of ongoing works and by bringing open questions related to different variants of the basic non-idling $m$-machine scheduling problem.     

Simple and efficient heuristic approach for the multiple-depot vehicle scheduling problem

In this paper, a fast heuristic approach is proposed for solving the multiple depot vehicle scheduling problem (MDVSP), a well-known NP-hard problem. The heuristic is based on a two stage procedure. The first one applies two state space reduction procedures towards reducing the problem complexity. One procedure is based on the solutions of the single-depot vehicle scheduling for each depot, while the other uses the solution of a relaxed formulation of the MDVSP, in which a vehicle can finish its task sequence in a different depot from where it started. Next, the reduced problem is solved by employing a truncated column generation approach. The heuristic approach has been implemented in several variants, through different combinations of the reduction procedures, and tested on a series of benchmark problems provided by Pepin et al. (J Sched 12:17–30, 2009). The heuristic variants found solutions with very narrow gaps (below 0.7 %, on average) to best-known solutions (Pepin et al., J Sched 12:17–30, 2009), decreasing the required CPU time by an overall average factor of 17 in comparison with reported results in the literature (Otsuki and Aihara, J Heuristics 1–19, 2014).     

A note on “scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan”

In a recent paper, Chen [J.S. Chen, Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan, European Journal of Operational Research 190 (2008) 90–102] proposes a heuristic algorithm to deal with the problem Scheduling of Nonresumable Jobs and Flexible Maintenance Activities on A Single Machine to Minimize Makespan  . Chen also provides computational results to demonstrate its effectiveness. In this note, we first show that the worst-case performance bound of this heuristic algorithm is 2. Then we show that there is no polynomial time approximation algorithm with a worst-case performance bound less than 2 unless P=NP$P=\mathit{NP}$, which implies that Chen’s heuristic algorithm is the best possible polynomial time approximation algorithm for the considered scheduling problem.     

The Systems Approach to Hospitals

By exploiting the relationship between scheduling and sorting, this paper describes a functional heuristic algorithm for seeking a quick and approximate solution to the n-job, M-machine flowshop scheduling problem under the assumption that all jobs are processed on all machines in the same order and no passing of jobs is permitted. The proposed functional heuristic algorithm can be executed by hand for reasonably large size problems and yields solutions which are closer to optimal solutions than those obtained by Palmer's slope index algorithm.     

Computing minimum multiway cuts in hypergraphs

The hypergraph $k$-cut problem is the problem of finding a minimum capacity set of hyperedges whose removal divides a given hypergraph into at least $k$ connected components. We present an algorithm for this problem, that runs in strongly polynomial time if both $k$ and the maximum size of the hyperedges are constants. Our algorithm extends the algorithm proposed by Thorup (2008) for computing minimum $k$-cuts of graphs from greedy packings of spanning trees.     

Constraint Propagation and Problem Decomposition: A Preprocessing Procedure for the Job Shop Problem

In recent years, constraint propagation techniques have been shown to be highly effective for solving difficult scheduling problems. In this paper, we present an algorithm which combines constraint propagation with a problem decomposition approach in order to simplify the solution of the job shop scheduling problem. This is mainly guided by the observation that constraint propagation is more effective for small problem instances. Roughly speaking, the algorithm consists of deducing operation sequences that are likely to occur in an optimal solution of the job shop scheduling problem (JSP).The algorithm for which the name edge-guessing procedure has been chosen – since with respect to the job shop scheduling problem (JSP) the deduction of machine sequences is mainly equivalent to orienting edges in a disjunctive graph – can be applied in a preprocessing step, reducing the solution space, thus speeding up the overall solution process. In spite of the heuristic nature of edge-guessing, it still leads to near-optimal solutions. If combined with a heuristic algorithm, we will demonstrate that given the same amount of computation time, the additional application of edge-guessing leads to better solutions. This has been tested on a set of well-known JSP benchmark problem instances.