Abstract: Abstract
We study practical scheduling problems with a major decision referring to the number of machines to be used. We focus on a two-stage flexible flowshop, where each job is processed on the first (critical) machine, and then continues to one of the second-stage parallel machines. Jobs are assumed to have identical processing times, and are processed in batches. A setup time is required when starting a new batch. We consider two objective functions: minimum makespan and minimum flowtime. In both cases, a closed form expression for the optimal number of machines to be used is introduced, and a unique and unusual sequence of decreasing batch sizes is shown to be optimal. PubDate: 2014-04-01

Abstract: Abstract
The multi-activity multi-task shift scheduling problem requires the assignment of interruptible activities and uninterruptible tasks to a set of employees in order to satisfy a demand function. In this paper, we consider the personalized variant of the problem where the employees have different qualifications, preferences, and availabilities. We present a branch-and-price algorithm to solve this problem. The pricing subproblems in column generation are formulated with context-free grammars that are able to model complex rules in the construction of feasible shifts for an employee. We present results for a large set of instances inspired by real cases and show that this approach is sufficiently flexible to handle different classes of problems. PubDate: 2014-04-01

Abstract: Abstract
Resource leveling problems arise whenever it is expedient to reduce the fluctuations in resource utilization over time, while maintaining a prescribed project completion deadline. Several resource leveling objective functions may be defined, consideration of which results in well-balanced resource profiles. In this paper, we concentrate on a special objective function that determines the costs arising from increasing or decreasing the resource utilizations. The resulting total adjustment cost problem occurs, for example, in the construction industry and can be formulated using mixed-integer linear programming models. Apart from a discrete time-based formulation, two polynomial formulations, namely an event-based model and a start-based model, which exploit structural properties of the problem are presented. In addition, a heuristic solution algorithm is proposed to generate start solutions for the problem. We use CPLEX 12.4 to solve medium-scale instances known from the literature. A computational performance analysis shows that the discrete time-based model and the start-based model are suitable for practical applications. PubDate: 2014-04-01

Abstract: Abstract
In the past two decades, scheduling with machine availability constraints has received considerable attention. Until recently most research has focused on the setting where all machine unavailability information is known at the beginning of the scheduling horizon. In reality, this is not practical in some cases. The machine may become unavailable to process jobs due to a machine breakdown or an occurrence of an emergent job that has to be processed immediately. In both cases, the start time of the unavailable interval is unknown beforehand, and the length of the interval may not be known until the end of the interval. In this article, we consider the situation in which the scheduler has to make scheduling decisions without any knowledge of the machine unavailable intervals. Of particular interest is the problem of minimizing total weighted completion time. When there are two or more unavailable intervals on a single machine, Fu et al. (2009) have shown that the problem is exponentially inapproximable even when jobs’ weights are equal to their processing times and one has full knowledge of unavailability. So in this paper we consider the scheduling problem on a single machine with a single unavailable period. And, we assume that every job has a weight proportional to its processing time. Based on whether the unavailable interval is due to a breakdown or an emergent job, we have the breakdown model and the emergent job model. First we show that no
$\tfrac{\sqrt{5}+1}{2}$
-competitive online algorithm exists for the breakdown model, and no
$\tfrac{11-\sqrt{2}}{7}$
-competitive online algorithm exists for the emergent job model. Next, we show that the simple LPT rule can give a 2- and a
$\tfrac{9}{5}$
-competitive ratio for the breakdown model and the emergent job model, respectively. Further, we show that the ratios are tight by examples. For the offline case, we show that the First Fit LPT (FF-LPT) rule can give a tight approximation ratio of 2 and 4/3 for the breakdown model and the emergent job model, respectively. Finally, our experimental results show that, in practice, both LPT and FF-LPT perform very well and the performance improves when the number of jobs
$n$
increases. In both models, when
$n \ge 50$
, the worst case error ratio is much better than the theoretical bounds. PubDate: 2014-04-01

Abstract: Abstract
We consider online preemptive scheduling problems where jobs have deadlines and the objective is to maximize the total weight of jobs completed before their deadlines. In the first problem, preemptions are not free but incur a penalty. In the second problem, a job has to be accepted or rejected immediately upon arrival, and may need to be immediately allocated a fixed scheduling interval as well; if these accepted jobs are not eventually completed, the job is lost, and a penalty is incurred. We give an algorithm with the optimal competitive ratio for the first problem, and new and improved algorithms for the second problem, under different models of preemptions and job weights. PubDate: 2014-04-01

Abstract: Abstract
In this paper we discuss exact and approximation algorithms for scheduling a single machine with additional non-renewable resource constraints. Given the initial stock levels of some non-renewable resources (e.g., raw materials, fuel, money), and time points along with replenishment quantities, a set of resource consuming jobs has to be scheduled on the machine such that there are enough resources for starting each job, and the makespan is minimized. We show that the problem admits a pseudo-polynomial time algorithm when the number of replenishments is not part of the input, and also present an FPTAS when there is only a single resource, and it is replenished only once. We also describe a PTAS for the problem with a constant number of replenishments. PubDate: 2014-04-01

Abstract: Abstract
This paper presents a new model and solution methodology for the problem faced by companies that provide rehabilitative services to clinic and home-bound patients. Given a set of multi-skilled therapists and a group of geographically dispersed patients, the objective is to construct weekly tours for the therapists that minimize the travel, treatment, and administrative costs while ensuring that all patients are seen within their time windows and that a host of labor laws and contractual agreements are observed. The problem is complicated by three factors that prevent a daily decomposition: (i) overtime rates kick in only after 40 regular hours are worked during the week, (ii) new patients must be seen by a licensed therapist on their first visit, and (iii) for some patients only the frequency and not the actual days on which they are to be seen is specified. The problem is formulated as a mixed-integer linear program but after repeated attempts to solve small instances with commercial software failed, we developed an adaptive sequential greedy randomized adaptive search procedure. The phase I logic of the procedure builds one daily schedule at a time for each therapist until all patients are routed. In phase II, several neighborhoods are explored to arrive at a local optimum. Extensive testing with both real data provided by a U.S. rehab company and datasets derived from them demonstrated the value of the purposed procedure with respect to current practice. The results indicated that cost reductions averaging over 18.09 % are possible. PubDate: 2014-04-01

Abstract: Abstract
We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job part is processed. During setup, a machine cannot process or set up any other job. We concentrate on the basic case in which setup times are job-, machine- and sequence-independent. Problems of this kind were encountered when modelling practical problems in planning disaster relief operations. Our main algorithmic result is a polynomial-time algorithm for minimising total completion time on two parallel identical machines. We argue, why the same problem with three machines is not an easy extension of the two-machine case, leaving the complexity of this case as a tantalising open problem. We give a constant-factor approximation algorithm for the general case with any number of machines and a polynomial-time approximation scheme for a fixed number of machines. For the version with the objective to minimise total weighted completion time, we prove NP-hardness. Finally, we conclude with an overview of the state of the art for other split scheduling problems with job-, machine- and sequence-independent setup times. PubDate: 2014-02-18

Abstract: Abstract
This paper addresses the flow shop batching and scheduling problem where sequence-dependent family setup times are present and the objective is to minimize makespan. We consider violating the group technology assumption by dividing product families into batches. In order to reduce setup times, inconsistent batches are formed on different machines, which lead to non-permutation schedules. To the best of our knowledge, this is the first time that the splitting of job families into inconsistent batches has been considered in a flow shop system. A tabu search algorithm is developed which contains several neighbourhood functions, double tabu lists and a multilevel diversification structure. Compared to the state-of-the-art meta-heuristics for this problem, the proposed tabu search algorithm achieves further improvement when the group scheduling assumption is dropped. Also, various experiments conducted on the benchmark problem instances confirm the benefits of batching. Therefore, it will be prudent for the practitioners to consider adopting inconsistent batches and non-permutation schedules to improve their operational efficiency within a reasonable amount of computational effort. PubDate: 2014-02-07

Abstract: Abstract
In this paper, we consider two problems about the preemptive scheduling of a set of jobs with release times on a single machine. In the first problem, each job has a deadline. The objective is to find a feasible schedule which minimizes the total completion time of the jobs. In the second problem (called two-agent scheduling problem), the set of jobs is partitioned into two subsets
$\mathcal{J}^{(1)}$
and
$\mathcal{J}^{(2)}$
. Each job in
$\mathcal{J}^{(2)}$
has a deadline. The objective is to find a feasible schedule which minimizes the total completion time of the jobs in
$\mathcal{J}^{(1)}$
. For the first problem, Du and Leung (Journal of Algorithms 14:45–68, 1993) showed that the problem is NP-hard. We show in this paper that there is a flaw in their NP-hardness proof. For the second problem, Leung et al. (Operations Research 58:458–469, 2010) showed that the problem can be solved in polynomial time. Yuan et al. (Private Communication) showed that their polynomial-time algorithm is invalid so the complexity of the second problem is still open. In this paper, by a modification of Du and Leung’s NP-hardness proof, we show that the first problem is NP-hard even when the jobs have only two distinct deadlines. Using the same reduction, we also show that the second problem is NP-hard even when the jobs in
$\mathcal{J}^{(2)}$
has a common deadline
$D>0$
and a common release time 0. PubDate: 2014-02-04

Abstract: Abstract
In this paper, we explore problems and algorithms related to the optimisation of locks, as used in inland shipping. We define several optimisation problems associated with inland shipping. We prove that the problem of scheduling a lock is NP-hard if one allows multiple ships to go through in the same lock operation. The single-ship lock optimization problem can, however, be solved in polynomial time and a novel deterministic scheduling algorithm for solving this problem is presented in this paper. PubDate: 2014-02-01

Abstract: Abstract
We consider the two-machine flow-shop serial-batching scheduling problem where the machines have a limited capacity in terms of the number of jobs. Two criteria are considered here. The first criterion is the number of batches to be minimized. This criterion reflects situations where processing of any batch induces a fixed cost, which leads to a total cost proportional to the number of batches. The second criterion is the makespan. This model is relevant in different production contexts, especially when considering joint production and inbound delivery scheduling. We study the complexity of the problem and propose two polynomial-time approximation algorithms with a guaranteed performance. The effectiveness of these algorithms is evaluated using numerical experiments. Exact polynomial-time algorithms are also provided for some particular cases. PubDate: 2014-02-01

Abstract: Abstract
This paper considers a cutting and scheduling problem of minimizing scrap motivated by float glass manufacturing and introduces the float glass scheduling problem. We relate it to classical problems in the scheduling literature such as no-wait hybrid flow shops and cyclic scheduling. We show that the problem is NP-hard, and identify when each of the problem’s components are polynomially solvable and when they induce hardness. In addition, we propose a simple heuristic algorithm, provide its worst-case performance bounds, and demonstrate that the bounds are tight. When the number of machines is two, the worst-case performance is 5/3. PubDate: 2014-02-01

Abstract: Abstract
We consider preemptive online and semi-online scheduling of unit jobs on two uniformly related machines. Jobs are presented one by one to an algorithm, and each job has a rejection penalty associated with it. A new job can either be rejected, in which case the algorithm pays its rejection penalty, or it can be scheduled preemptively on the machines, in which case it may increase the maximum completion time of any machine in the schedule, also known as the makespan of the constructed schedule. The objective is to minimize the sum of the makespan of the schedule of all accepted jobs and the total penalty of all rejected jobs. We study two versions of the problem. The first one is the online problem where the jobs arrive unsorted, and the second variant is the semi-online case, where the jobs arrive sorted by a non-increasing order of penalties. We also show that the variant where the jobs arrive sorted by a non-decreasing order of penalties is equivalent to the unsorted one. We design optimal online algorithms for both cases. These algorithms have smaller competitive ratios than the optimal competitive ratio for the more general problem with arbitrary processing times (except for the case of identical machines), but larger competitive ratios than the optimal competitive ratio for preemptive scheduling of unit jobs without rejection. PubDate: 2014-02-01

Abstract: Abstract
Periodic scheduling has many attractions for wireless telecommunications. It offers energy saving where equipment can be turned off between transmissions, and high-quality reception through the elimination of jitter, caused by irregularity of reception. However, perfect periodic schedules, in which each (of
$n$
) client is serviced at regular, prespecified intervals, are notoriously difficult to construct. The problem is known to be NP-hard even when service times are identical. This paper focuses on cases of up to three distinct periodicities, with unit service times. Our contribution is to derive a
$O(n^4)$
test for the existence of a feasible schedule, and a method of constructing a feasible schedule if one exists, for the given combination of client periodicities. We also indicate why schedules with a higher number of periodicities are unlikely to be useful in practice. This methodology can be used to support perfect periodic scheduling in a wide range in real world settings, including machine maintenance service, wireless mesh networks and various other telecommunication networks transmitting packet size data. PubDate: 2014-02-01

Abstract: Abstract
In this paper, we model a research-and-development project as consisting of several modules, with each module containing one or more activities. We examine how to schedule the activities of such a project in order to maximize the expected profit when the activities have a probability of failure and when an activity’s failure can cause its module and thereby the overall project to fail. A module succeeds when at least one of its constituent activities is successfully executed. All activities are scheduled on a scarce resource that is modeled as a single machine. We describe various policy classes, establish the relations among them, develop exact algorithms to optimize over two different classes (one dynamic program and one branch-and-bound algorithm), and examine the computational performance of the algorithms on two randomly generated instance sets. PubDate: 2014-02-01

Abstract: Abstract
This article focuses on the aircraft landing problem that is to assign landing times to aircraft approaching the airport under consideration. Each aircraft’s landing time must be in a time interval encompassing a target landing time. If the actual landing time deviates from the target landing time additional costs occur which depend on the amount of earliness and lateness, respectively. The objective is to minimize overall cost. We consider the set of aircraft being partitioned into aircraft classes such that two aircraft of the same class are equal with respect to wake turbulence. We develop algorithms to solve the corresponding problem. Analyzing the worst case run-time behavior, we show that our algorithms run in polynomial time for fairly general cases of the problem. Moreover, we present integer programming models. We show by means of a computational study how optimality properties can be used to increase efficiency of standard solvers. PubDate: 2014-02-01

Abstract: Abstract
This paper introduces the use of conditional-value-at-risk (CVaR) as a criterion for stochastic scheduling problems. This criterion has the tendency of simultaneously reducing both the expectation and variance of a performance measure, while retaining linearity whenever the expectation can be represented by a linear expression. In this regard, it offers an added advantage over traditional nonlinear expectation-variance-based approaches. We begin by formulating a scenario-based mixed-integer program formulation for minimizing CVaR for general scheduling problems. We then demonstrate its application for the single machine total weighted tardiness problem, for which we present both a specialized l-shaped algorithm and a dynamic programming-based heuristic procedure. Our numerical experimental results reveal the benefits and effectiveness of using the CVaR criterion. Likewise, we also exhibit the use and effectiveness of minimizing CVaR in the context of the parallel machine total weighted tardiness problem. We believe that minimizing CVaR is an effective approach and holds great promise for achieving risk-averse solutions for stochastic scheduling problems that arise in diverse practical applications. PubDate: 2014-02-01