Solving two production scheduling problems with sequence-dependent set-up times

In today�s competitive markets, the importance of good scheduling strategies in manufacturing companies lead to the need of developing efficient methods to solve complex scheduling problems. In this paper, we studied two production scheduling problems with sequence-dependent setups times. The setup times are one of the most common complications in scheduling problems, and are usually associated with cleaning operations and changing tools and shapes in machines. The first problem considered is a single-machine scheduling with release dates, sequence-dependent setup times and delivery times. The performance measure is the maximum lateness. The second problem is a job-shop scheduling problem with sequence-dependent setup times where the objective is to minimize the makespan. We present several priority dispatching rules for both problems, followed by a study of their performance. Finally, conclusions and directions of future research are presented.Production-scheduling, set-up times, priority dispatching rules

Parallel machine scheduling with release dates, due dates and family setup times

In manufacturing, there is a fundamental conflict between efficient production and delivery performance. Maximizing machine utilization by batching similar jobs may lead to poor delivery performance. Minimizing customers' dissatisfaction may lead to an inefficient use of the machines. In this paper, we consider the problem of scheduling n independent jobs with release dates, due dates, and family setup times on m parallel machines. The objective is to minimize the maximum lateness of any job. We present a branch-and-bound algorithm to solve this problem. This algorithm exploits the fact that an optimal schedule is contained in a specific subset of all feasible schedules. For lower bounding purposes, we see setup times as setup jobs with release dates, due dates and processing times. We present two lower bounds for the problem with setup jobs, one of which proceeds by allowing preemption

Stochastic scheduling on unrelated machines

Two important characteristics encountered in many real-world scheduling problems are heterogeneous machines/processors and a certain degree of uncertainty about the actual sizes of jobs. The first characteristic entails machine dependent processing times of jobs and is captured by the classical unrelated machine scheduling model.The second characteristic is adequately addressed by stochastic processing times of jobs as they are studied in classical stochastic scheduling models. While there is an extensive but separate literature for the two scheduling models, we study for the first time a combined model that takes both characteristics into account simultaneously. Here, the processing time of job $j$ on machine $i$ is governed by random variable $P_{ij}$, and its actual realization becomes known only upon job completion. With $w_j$ being the given weight of job $j$, we study the classical objective to minimize the expected total weighted completion time $E[\sum_j w_jC_j]$, where $C_j$ is the completion time of job $j$. By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee $(3+\Delta)/2+\epsilon$. Here, $\epsilon>0$ is arbitrarily small, and $\Delta$ is an upper bound on the squared coefficient of variation of the processing times. We show that the dependence of the performance guarantee on $\Delta$ is tight, as we obtain a $\Delta/2$ lower bound for the type of policies that we use. When jobs also have individual release dates $r_{ij}$, our bound is $(2+\Delta)+\epsilon$. Via $\Delta=0$, currently best known bounds for deterministic scheduling are contained as a special case

On the Fine-Grained Parameterized Complexity of Partial Scheduling to Minimize the Makespan

We study a natural variant of scheduling that we call partial scheduling: In this variant an instance of a scheduling problem along with an integer k is given and one seeks an optimal schedule where not all, but only k jobs, have to be processed. Specifically, we aim to determine the fine-grained parameterized complexity of partial scheduling problems parameterized by k for all variants of scheduling problems that minimize the makespan and involve unit/arbitrary processing times, identical/unrelated parallel machines, release/due dates, and precedence constraints. That is, we investigate whether algorithms with runtimes of the type f(k)n^?(1) or n^?(f(k)) exist for a function f that is as small as possible. Our contribution is two-fold: First, we categorize each variant to be either in ?, NP-complete and fixed-parameter tractable by k, or ?[1]-hard parameterized by k. Second, for many interesting cases we further investigate the run time on a finer scale and obtain run times that are (almost) optimal assuming the Exponential Time Hypothesis. As one of our main technical contributions, we give an ?(8^k k(|V|+|E|)) time algorithm to solve instances of partial scheduling problems minimizing the makespan with unit length jobs, precedence constraints and release dates, where G = (V,E) is the graph with precedence constraints

Approximate Methods For Solving Flowshop Problems

The flow shop scheduling problem is a classical combinatorial problem being studied for years. The focus of this research is to study two variants of the flow shop scheduling problem in order to minimize makespan by scheduling n jobs on m machines. A solution approach is developed for the modified flow shop problem with due dates and release times. This algorithm is an attempt to contribute to the limited literature for the problem. Another tabu search-based solution approach is developed to solve the classical flow shop scheduling problem. This meta-heuristic (called 3XTS) allows an efficient search of the neighboring solutions leading to a fast solution procedure. Several control parameters affecting the quality of the algorithm are experimentally tested, and certain rules are established for different problem instances. The 3XTS is compared to another tabu search method (that seems to be a champion) in terms of solution quality and computation time

Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work, and depend linearly on an upper bound on the squared coefficient of variation of the jobs' processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 7.216, respectively. As to the technical contribution, the paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.Comment: Preliminary version appeared in IPCO 201