Abstract: This paper considers a project scheduling environment in which the activities of the project network are partitioned among a set of agents. Activity durations are controllable, i.e., every agent is allowed to shorten the duration of its activities, incurring a crashing cost. If the project makespan is reduced with respect to its normal value, a reward is offered to the agents and each agent receives a given ratio of the total reward. Agents want to maximize their profit. Assuming a complete knowledge of the agents’ parameters and of the activity network, this problem is modeled as a non-cooperative game and Nash equilibria are analyzed. We characterize Nash equilibria in terms of the existence of certain types of cuts on the project network. We show that finding one Nash equilibrium is easy, while finding a Nash strategy that minimizes the project makespan is NP-hard in the strong sense. The particular case where each activity belongs to a different agent is also studied and some polynomial-time algorithms are proposed for this case. PubDate: 2015-02-01

Abstract: There are many situations when, due to unexpected delays, the supplier may not be able to deliver some orders by the promised due dates. We present a model for quoting attainable delivery times to minimize tardiness penalties and delivery costs, when deliveries take place in batches. We show that the general problem is strongly
\({\mathcal {NP}}\)
-hard, but when all orders have the same per-unit due-date-assignment cost, it is
\({\mathcal {NP}}\)
-hard only in the ordinary sense. For the latter case, we present a pseudo-polynomial algorithm, which is converted into a fully polynomial-time approximation scheme. If the tardiness penalties are also identical, we show that the problem can be solved in polynomial time. PubDate: 2015-02-01

Abstract: In this paper, we initiate the study of minimizing power consumption in the broadcast scheduling model. In this setting, there is a wireless transmitter. Over time requests arrive at the transmitter for pages of information. Multiple requests may be for the same page. When a page is transmitted, all requests for that page receive the transmission simultaneously. The speed the transmitter sends data at can be dynamically scaled to conserve energy. We consider the problem of minimizing flow time plus energy, the most popular scheduling metric considered in the standard online scheduling model when the scheduler is energy aware. We will assume that the power consumed is modeled by an arbitrary convex function. For this problem, there is an
\(\Omega (n)\)
lower bound on the competitive ratio. Due to the lower bound, we consider using resource augmentation and give a scalable algorithm. PubDate: 2015-02-01

Abstract: This paper introduces a shift rostering problem that surprisingly has not been studied in the literature: the weekend shift rostering problem. It is motivated by our experience that employees’ shift preferences predominantly focus on the weekends, since many social activities happen during weekends. The weekend rostering problem (WRP) addresses the rostering of weekend shifts, for which we design a problem-specific heuristic. We consider the WRP as the first phase of the shift rostering problem. To complete the shift roster, the second phase assigns the weekday shifts. This decomposition reflects how shift rosters are often created manually in practice, which makes the decomposition method proposed in this paper a more intuitive approach for business users compared to approaches without this decomposition. We believe that such approaches enable business users to effectively analyze and steer the outcomes of algorithms for shift rostering especially on criteria that are relevant to them such as those concerning weekends. We analyze and discuss effects of this two-phase approach both on the weekend shift roster and on the roster as a whole. We demonstrate that our first-phase weekend rostering heuristic is effective both on generated instances and real-life instances. For situations where the weekend shift roster is one of the key determinants of the quality of the complete roster, our two-phase approach is shown to be effective. PubDate: 2015-02-01

Abstract: We study a set of scheduling problems on a uniform machine setting. We focus on the case of equal processing time jobs with the additional feature of job rejection. Jobs can either be processed on a predefined set of machines or rejected. Rejected jobs incur a rejection penalty and have no effect on the scheduling criterion under consideration. A solution to our problems consists of partitioning the jobs into two subsets,
\(A\)
and
\(\overline{A}\)
, which are the set of accepted and the set of rejected jobs, respectively. In addition, jobs in set
\(A\)
have to be scheduled on the
\(m\)
machines. We evaluate the quality of a solution by two criteria. The first,
\(F_{1}\)
, can be any regular scheduling criterion, while the latter,
\(F_{2}\)
, is the total rejection cost. We consider two possible types of regular scheduling criteria; the former is a maximization criterion, while the latter is a summation criterion. For each criterion type we consider four different problem variations. We prove that all four variations are solvable in polynomial time for
\(any\)
maximization type of a regular scheduling criterion. When the scheduling criterion is of summation type, we show that only one of the four problem variations is solvable in polynomial time. We provide a pseudo-polynomial time algorithms to solve interesting variants of the
\(\mathcal {NP}\)
-hard problems, as well as a polynomial time algorithm that solves various other special cases. PubDate: 2015-02-01

Abstract: In this paper, we consider a single-machine scheduling problem (P) inspired from manufacturing instances. A release date, a deadline, and a regular (i.e., non-decreasing) cost function are associated with each job. The problem takes into account sequence-dependent setup times and setup costs between jobs of different families. Moreover, the company has the possibility to reject some jobs/orders, in which case a penalty (abandon cost) is incurred. Therefore, the problem at hand can be viewed as an order acceptance and scheduling problem. Order acceptance problems have gained interest among the research community over the last decades, particularly in a make-to-order environment. We propose and compare a constructive heuristic, local search methods, and population-based algorithms. Tests are performed on realistic instances and show that the developed metaheuristics significantly outperform the currently available resolution methods for the same problem. PubDate: 2015-02-01

Abstract: We study mechanism design for a single-server setting where jobs require compensation for waiting, while waiting cost is private information to the jobs. With given priors on the private information of jobs, we aim to find a Bayes–Nash incentive compatible mechanism that minimizes the total expected payments to the jobs. Following earlier work in the auction literature, we show that this problem is solved, in polynomial time, by a version of Smith’s rule. When both waiting cost and processing times are private, we show that optimal mechanisms generally do not satisfy an independence condition known as IIA, and conclude that a closed form for optimal mechanisms is generally not conceivable. PubDate: 2015-02-01

Abstract: We address a novel integrated maintenance and production scheduling problem in a multi-machine and multi-period production system, considering maintenance as a long-term decision. Deterioration of machines over time decreases production capacity. Since maintenance activities not only improve machine conditions, increasing production capacity, but also take time that cannot be used for production, the challenge is to assign maintenance to periods and to schedule maintenance and production activities within each period to minimize the combined cost of maintenance and lost production over the planning horizon. Motivated by logic-based Benders decomposition, we design an integrated two-stage algorithm to solve the problem. The first stage assigns maintenance to machines and time periods, abstracting the scheduling problem, while the second stage creates a schedule for the current time period. The first stage is then re-solved using feedback from the schedule. This iteration between maintenance planning and scheduling continues until the solution costs in two stages converge. The integrated approach models the interdependencies between maintenance and scheduling decisions in highly coupled processes such as wafer fabrication in the semiconductor manufacturing. Our results demonstrate that the benefit of integrated decision making increases when maintenance is less expensive relative to lost production cost and that a longer horizon for maintenance planning is beneficial when maintenance cost increases. PubDate: 2015-01-20

Abstract: In a scenario characterized by a continuous growth of air transportation demand, the runways of large airports serve hundreds of aircraft every day. Aircraft sequencing is a challenging problem that aims to increase runway capacity in order to reduce delays as well as the workload of air traffic controllers. In many cases, the air traffic controllers solve the problem using the simple “first-come-first-serve” (FCFS) rule. In this paper, we present a rolling horizon approach which partitions a sequence of aircraft into chunks and solves the aircraft sequencing problem (ASP) individually for each of these chunks. Some rules for deciding how to partition a given aircraft sequence are proposed and their effects on solution quality investigated. Moreover, two mixed integer linear programming models for the ASP are reviewed in order to formalize the problem, and a tabu search heuristic is proposed for finding solutions to the ASP in a short computation time. Finally, we develop an IRHA which, using different chunking rules, is able to find solutions significantly improving on the FCFS rule for real-world air traffic instances from Milano Linate Airport. PubDate: 2015-01-20

Abstract: In this paper, we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. Each agent decides on a fixed order to submit its tasks to an external coordination subject, who sequences them according to a known priority rule. We consider the problem from different perspectives. First, we characterize the set of Pareto-optimal schedules in terms of size and computational complexity. We then address the problem from the single-agent point-of-view, that is, we consider the problem of deciding how to submit one agent’s tasks only taking into account its own objective function against the other agent, the opponent. In this regard, we consider two different settings depending on the information available to the agents: In one setting, the considered agent knows in advance all information about the submission sequence of the opponent; and in the second setting (as in minimax strategies in game theory), the agent has no information on the opponent strategy and wants to devise a strategy that minimizes its solution cost in the worst possible case. Finally, we assess the performance of some classical single-agent sequencing rules in the two-agent setting. PubDate: 2015-01-06

Abstract: The well-known
\(O(n^2)\)
minmax cost algorithm of Lawler (MANAGE SCI 19(5):544–546, 1973) was developed to minimize the maximum cost of jobs processed by a single machine under precedence constraints. We propose two results related to Lawler’s algorithm. Lawler’s algorithm delivers one specific optimal schedule while there can exist other optimal schedules. We present necessary and sufficient conditions for the optimality of a schedule for the problem with strictly increasing cost functions. The second result concerns the same scheduling problem under uncertainty. The cost function for each job is of a special decomposable form and depends on the job completion time and on an additional numerical parameter, for which only an interval of possible values is known. For this problem we derive an
\(O(n^2)\)
algorithm for constructing a schedule that minimizes the maximum regret criterion . To obtain this schedule, we use Lawler’s algorithm as a part of our technique. PubDate: 2015-01-04

Abstract: Consider the following scheduling problem. We are given a set of jobs, each having a release time, a due date, a processing time, and demand for machine capacity. The goal is to schedule all jobs non-preemptively in their release-time deadline windows on machines that can process multiple jobs simultaneously, subject to machine capacity constraints, with the objective to minimize the total busy time of the machines. Our problem naturally arises in power-aware scheduling, optical network design, and customer service systems, among others. The problem is APX-hard by a simple reduction from the subset sum problem. A main result of this paper is a 5-approximation algorithm for general instances. While the algorithm is simple, its analysis involves a non-trivial charging scheme which bounds the total busy time in terms of work and span lower bounds on the optimum. This improves and extends the results of Flammini et al. (Theor Comput Sci 411(40–42):3553–3562, 2010). We extend this approximation to the case of moldable jobs, where the algorithm also needs to choose, for each job, one of several processing-time versus demand configurations. Better bounds and exact algorithms are derived for several special cases, including proper interval graphs, intervals forming a clique and laminar families of intervals. PubDate: 2014-12-19

Abstract: We study a scheduling problem, in which jobs of two agents are performed in agent specific batches on the same serial unbounded batching machine. On this machine, jobs of the same batch complete simultaneously, and the batch processing time is equal to the total processing time of its jobs plus a setup time. Each agent aims at minimizing a function which depends only on the completion times of its jobs. The problem is to find a schedule that minimizes the objective function of one agent, subject to the objective function of the other agent does not exceed a given threshold. The problem appears in optimizing product consolidation operations of a cross-docking distribution center. Polynomial and pseudo-polynomial dynamic programming algorithms are derived for settings with various combinations of the objective functions. PubDate: 2014-12-18

Abstract: Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby, the XHSTT format serves as a common ground for researchers within this area. This paper describes the first exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a mixed-integer linear programming (MIP) model, which is solved in two steps with a commercial general-purpose MIP solver. Computational results show that our approach is able to find previously unknown optimal solutions for 2 instances of XHSTT and proves optimality of 4 known solutions. For the instances not solved to optimality, new non-trivial lower bounds were found in 11 cases, and new best known solutions were found in 9 cases. Furthermore, the approach is compared with the finalists of Round 2 of the International Timetabling Competition 2011 and is shown to be competitive with one of the finalists. PubDate: 2014-12-09

Abstract: In this paper, we study online algorithms that schedule malleable jobs, i.e., jobs that can be parallelized on any subset of the available
\(m\)
identical machines. We study a model that accounts for the tradeoff between multiprocessor speedup and overhead time, namely, if job
\(j\)
has processing requirement
\(p_j\)
and is assigned to run on
\(k_j\)
machines, then
\(j\)
’s execution time becomes
\(p_j/k_j + (k_j -1)c\)
, where
\(c\)
is a constant parameter to the problem. For
\(m=2\)
, we present an online algorithm OCS that has a strong competitive ratio of 3/2, matching a previously established lower bound. We also present an online algorithm ASYM2 that is asymptotically
\(((4-\epsilon )/(3-\epsilon ))\)
-competitive when
\(m=2\)
, where
\(0 < \epsilon \le 2\)
is a parameter to the algorithm, improving upon an existing asymptotically (3/2)-competitive algorithm. Finally, we present an online algorithm OTO that is strongly
\(2\)
-competitive when
\(m = 3\)
, improving upon the previous best upper bound of
\(9/4\)
. PubDate: 2014-12-09

Abstract: This paper addresses a scheduling problem with continuous resources and energy constraints. Given a set of non-preemptive activities, each activity requires a continuously divisible resource whose instantaneous usage is limited in maximum and minimum, its processing satisfying a time window and a total energy (time
\(\times \)
resource-usage) requirement. The goal consists of getting a schedule satisfying all the constraints. The problem, which we refer to as the Energy-Constrained Scheduling Problem with Continuous Resources (CECSP), is a generalization of the well-known cumulative scheduling problem for which the “energetic reasoning” or “left-shift/right-shift” necessary feasibility condition yielded a popular polynomially computable satisfiability test. The paper presents a generalization of the energetic reasoning for the CECSP, defining precisely the activity minimum consumptions and exhibiting a polynomial number of relevant time intervals on which it is sufficient to apply the satisfiability tests. A strongly polynomial energetic reasoning satisfiability test can be derived for the considered generalization, which also yields a short proof for the complexity of the original algorithm. Some limits of the approach, as well as an approximation framework for more general resource consumption functions, are also addressed. PubDate: 2014-12-03

Abstract: Westside High School (WHS) of Omaha, Nebraska utilizes a sophisticated scheduling environment called “modular scheduling.” Modular scheduling empowers teachers with the ability to design the structure of their classes by adjusting the frequency, duration, and location of each of their lessons. This paper presents a novel heuristic methodology, implemented as a computer program called the sequential modular algorithmic routines for timetabling (SMART) Scheduler, which creates cohesive modular class schedules using effective techniques such as ejection trees and student sectioning. In experimentation, the SMART Scheduler is able to schedule over 2,800 distinct lessons in less than 4 s using data provided by WHS. This paper describes algorithms within the SMART Scheduler as well as computational results of its implementation. PubDate: 2014-12-02

Abstract: The present paper introduces a learning-based optimization approach to the resource-constrained multi-project scheduling problem. Multiple projects, each with their own set of activities, need to be scheduled. The objectives dealt with here include minimization of the average project delay and total makespan. The availability of local and global resources, precedence relations between activities, and non-equal project start times have to be considered. The proposed approach relies on a simple sequence learning game played by a group of project managers. The project managers each learn their activity list locally using reinforcement learning, more specifically learning automata. Meanwhile, they learn how to choose a suitable place in the overall sequence of all activity lists. All the projects need to arrive at a unique place in this sequence. A mediator, who usually has to solve a complex optimization problem, now manages a simple dispersion game. Through the mediator, a sequence of feasible activity lists is eventually scheduled by using a serial schedule generation scheme, which is adopted from single project scheduling. It is shown that the sequence learning approach has a large positive effect on minimizing the average project delay. In fact, the combination of local reinforcement learning, the sequence learning game and a forward-backward implementation of the serial scheduler significantly improves the best known results for all the MPSPLIB datasets. In addition, several new best results were obtained for both considered objectives: minimizing the average project delay and minimizing the total makespan. PubDate: 2014-11-04