Abstract: Abstract
We consider the classical scheduling problem on a single machine, on which we need to schedule sequentially n given jobs. Every job j has a processing time
\(p_j\)
and a priority weight
\(w_j\)
, and for a given schedule a completion time
\(C_j\)
. In this paper, we consider the problem of minimizing the objective value
\(\sum _j w_j C_j^\beta \)
for some fixed constant
\(\beta >0\)
. This non-linearity is motivated for example by the learning effect of a machine improving its efficiency over time, or by the speed scaling model. For
\(\beta =1\)
, the well-known Smith’s rule that orders job in the non-increasing order of
\(w_j/p_j\)
gives the optimum schedule. However, for
\(\beta \ne 1\)
, the complexity status of this problem is open. Among other things, a key issue here is that the ordering between a pair of jobs is not well defined, and might depend on where the jobs lie in the schedule and also on the jobs between them. We investigate this question systematically and substantially generalize the previously known results in this direction. These results lead to interesting new dominance properties among schedules which lead to huge speed up in exact algorithms for the problem. An experimental study evaluates the impact of these properties on the exact algorithm A*. PubDate: 2016-01-16

Abstract: Abstract
In 1976, Coffman and Sethi conjectured that a natural extension of LPT list scheduling to the bicriteria scheduling problem of minimizing makespan over flowtime-optimal schedules, called the LD algorithm, has a simple worst-case performance bound:
\(\frac{5m-2}{4m-1}\)
, where m is the number of machines. We study the structure of potential minimal counterexamples to this conjecture, provide some new tools and techniques for the analysis of such algorithms, and prove that to verify the conjecture, it suffices to analyze the following case: for every
\(m \ge 4\)
,
\(n \in \{4m, 5m\}\)
, where n is the number of jobs. PubDate: 2016-01-09

Abstract: Abstract
Modern computers allow software to adjust power management settings like speed and sleep modes to decrease the power consumption, possibly at the price of a decreased performance. The impact of these techniques mainly depends on the schedule of the tasks. In this article, a survey on underlying theoretical results on power management, as well as offline scheduling algorithms that aim at minimizing the energy consumption under real-time constraints, is given. PubDate: 2016-01-08

Abstract: Abstract
In the paper, we consider the problem of scheduling jobs on parallel identical machines with the late work criterion and a common due date, both offline and online cases. Since the late work criterion has not been studied in the online mode so far, the analysis of the online problem is preceded by the analysis of the offline problem, whose complexity status has not been formally stated in the literature yet. Namely, for the offline mode, we prove that the two-machine problem is binary NP-hard, and the general case is unary NP-hard. In the online mode we assume that jobs arrive in the system one by one, i.e., we consider the online over list model. We give an algorithm with a competitive ratio being a function of the number of machines, and we prove the optimality of this approach for two identical machines. PubDate: 2015-12-21

Abstract: Abstract
In this paper, we consider a large-scale evacuation problem after a major disaster. The evacuation is assumed to occur by means of a fleet of buses, thus leading to scheduling the evacuation operations by buses [(bus evacuation problem (BEP)]. We propose time-indexed formulations as well as heuristic algorithms such as greedy algorithms and a matheuristic. This matheuristic uses the former formulation to improve the best solution obtained by the greedy heuristics. In computational experiments, we analyze and evaluate the efficiency of the proposed solution algorithms. PubDate: 2015-12-01

Abstract: Abstract
The Joint Replenishment Problem (
\({\hbox {JRP}}\)
) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods from a supplier to retailers. Over time, in response to demands at the retailers, the supplier ships orders, via a warehouse, to the retailers. The objective is to schedule these orders to minimize the sum of ordering costs and retailers’ waiting costs. We study the approximability of
\({\hbox {JRP-D}}\)
, the version of
\({\hbox {JRP}}\)
with deadlines, where instead of waiting costs the retailers impose strict deadlines. We study the integrality gap of the standard linear-program (LP) relaxation, giving a lower bound of
\(1.207\)
, a stronger, computer-assisted lower bound of
\(1.245\)
, as well as an upper bound and approximation ratio of
\(1.574\)
. The best previous upper bound and approximation ratio was
\(1.667\)
; no lower bound was previously published. For the special case when all demand periods are of equal length, we give an upper bound of
\(1.5\)
, a lower bound of
\(1.2\)
, and show APX-hardness. PubDate: 2015-12-01

Abstract: Abstract
Coupled tasks are two-operation tasks, where the two operations are separated by a time interval of fixed duration. Coupled task scheduling problems refer then to the scheduling of a set of coupled tasks on a single machine. Applications of these problems, reported in the literature, arise in connection with radar systems, robotic cells, and in manufacturing. Most of the complexity issues for scheduling coupled tasks have been settled. However, the complexity status has been unknown for the identical coupled task problem, where multiple copies of a single coupled task are to be processed. The purpose of the article is to solve this open problem in the cyclic case, for which we prove the polynomial complexity. PubDate: 2015-12-01

Abstract: Abstract
The resource-constrained project scheduling problem with minimum and maximum time lags (RCPSP/max) is a general model for resource scheduling in many real-world problems (such as manufacturing and construction engineering). We consider RCPSP/max problems where the durations of activities are stochastic and resources can have unforeseen breakdowns. Given a level of allowable risk,
\(\alpha \)
, our mechanisms aim to compute the minimum robust makespan execution strategy. Robust makespan for an execution strategy is any makespan value that has a risk less than
\(\alpha \)
. The risk for a makespan value,
\(M\)
given an execution strategy, is the probability that a schedule instantiated from the execution strategy will not finish before
\(M\)
given the uncertainty over durations and resources. We make three key contributions: (a) firstly, we provide an analytical evaluation of resource breakdowns and repairs on executions of activities; (b) we then incorporate such information into a local search framework and generate execution strategies that can absorb resource and durational uncertainties; and (c) finally, to improve robustness of resulting strategies, we propose resource breakdown aware chaining procedure with three different metrics. This chaining procedure computes resource allocations by predicting the effect of breakdowns on robustness of generated strategies. Experiments show effectiveness of our proposed methods in providing more robust execution strategies under uncertainty. PubDate: 2015-12-01

Abstract: 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: 2015-12-01

Abstract: Abstract
We consider the problem of scheduling a set of jobs on a single machine subject to inventory constraints, i.e., conditions that jobs add or remove items to or from a centralized inventory, respectively. Jobs that remove items cannot be processed if the required number of items is not available. We focus on scheduling problems on a single machine where the objective is to minimize the total weighted completion time. In this paper, we design 2-approximation algorithms for special cases of the problem that run in polynomial time. PubDate: 2015-12-01

Abstract: Abstract
In this paper, we study a robust single-machine scheduling problem under four alternative optimization criteria: minimizing total completion time, minimizing total weighted completion time, minimizing maximum lateness, and minimizing the number of late jobs. We assume that job processing times are subject to uncertainty. Accordingly, we construct three alternative uncertainty sets, each of which defines job processing times that can simultaneously occur. The robust optimization framework assumes that, given a job schedule, a worst-case set of processing times will be realized from among those allowed by the uncertainty set under consideration. For each combination of objective function and uncertainty set, we first analyze the problem of identifying a set of worst-case processing times with respect to a fixed schedule, and then investigate the problem of selecting a schedule whose worst-case objective is minimal. PubDate: 2015-12-01

Abstract: Abstract
Many supply chains use returnable packaging such as plastic and metal containers, folding boxes, racks, and trays to transport components from suppliers to buyers. This study investigates the scheduling problem of a supplier that produces jobs for several buyers where the jobs for each buyer have to be delivered in that buyer’s returnable containers. Empty containers are provided by the buyers at certain release dates. The supplier can process a job when no adequate empty containers are available, but then incurs extra handling costs to pack the job into auxiliary packaging and repack it later. This study extends single machine scheduling with weighted earliness and tardiness penalties and batching by including returnable containers and repacking penalties. A mathematical programming formulation and a two-stage heuristic for this previously unstudied NP-hard scheduling problem are proposed and evaluated in a numerical study. PubDate: 2015-12-01

Abstract: Abstract
We consider a semi-online multiprocessor scheduling problem with a given a set of identical machines and a sequence of jobs, the sum of whose processing times is known in advance. The jobs are to be assigned online to one of the machines and the objective is to minimize the makespan. The best known algorithm for this problem achieves a competitive ratio 1.6 (Cheng et al. in Theor Comput Sci 337:134–146, 2005). The best known lower bound is approximately 1.585 (Albers and Hellwig in Theor Comput Sci 443:1–9, 2012) if the number of machines tends to infinity. We present an elementary algorithm with competitive ratio equal to this lower bound. Thus, the algorithm is best possible if the number of machines tends to infinity. PubDate: 2015-12-01

Abstract: Abstract
This paper addresses a recent open scheduling problem which aims to minimize the summation of total weighted completion time and the total machine time slot cost. Focusing on the case of non-increasing time slot cost with non-preemptive jobs, we show that the problem can be solved in polynomial-time when the time slot cost decreases with certain patterns, including linearly decreasing, decreasing concave, and decreasing convex cases. Different methodologies are used for three cases. For the linearly decreasing case, we can classify all the jobs into three categories and schedule the job sets one by one. For the decreasing concave case, we calculate each job’s worst starting time and try to make them far away from their worst starting times. For the decreasing concave case, we calculate each job’s best starting time and let them start close to their best starting times. Finally, we show that the problem is NP-hard in the strong sense when the time slot cost decreases in an arbitrary way. PubDate: 2015-11-26

Abstract: Abstract
This paper studies a multi-agent scheduling problem on two identical parallel machines. There are g agents, and each agent’s objective is to minimize its makespan. We present an approximation algorithm such that the performance ratio of the makespan achieved by our algorithm relative to the minimum makespan is no more than
\(i+\frac{1}{6}\)
for the ith
\((i=1,2,\ldots ,g)\)
completed agent. Moreover, we show that the performance ratio is tight. PubDate: 2015-11-13

Abstract: Abstract
Many real-world situations involve queueing systems in which customers may abandon if service does not start sufficiently quickly. We study a comprehensive model of multi-class queue scheduling accounting for customer abandonment, with the objective of minimizing the total discounted or time-average sum of linear waiting costs, completion rewards, and abandonment penalties of customers in the system. We assume the service times and abandoning times are exponentially distributed. We solve analytically the case in which there is one server and there are one or two customers in the system and obtain an optimal policy. For the general case, we use the framework of restless bandits to analytically design a novel simple index rule with a natural interpretation. We show that the proposed rule achieves near-optimal or asymptotically optimal performance both in single- and multi-server cases, both in overload and underload regimes, and both in idling and non-idling systems. PubDate: 2015-11-11

Abstract: Abstract
The semiconductor manufacturing industry is significantly expensive both in equipment and materials. Cluster tools, a type of automated manufacturing system integrating processing modules and transport modules, are commonly used in this industry. Nowadays, multi-cluster tools, which are composed of several cluster tools connected by joint buffer modules, are often used for wafer production. This paper deals with K-unit cycle scheduling problems in single-armed two-cluster tools for processing identical wafers in deterministic settings. In a K-unit cycle, K wafers are exactly inserted into the two-cluster tool, and K completed wafers leave the two-cluster tool, usually not the same K wafers. Residency constraints and general moving times by the robot are both considered. The objective is to obtain optimal K-unit cycle schedules, which minimize cycle times. To analyze this scheduling problem in detail, a mixed integer linear programming (MILP) model is formulated and solved. Numerical examples are used to explain how the solution can be obtained from the MILP model in a K-unit cycle. PubDate: 2015-11-06

Abstract: Abstract
The application of the Late Acceptance Hill-Climbing (LAHC) to solve the High School Timetabling Problem is the subject of this manuscript. The original algorithm and two variants proposed here are tested jointly with other state-of-art methods to solve the instances proposed in the Third International Timetabling Competition. Following the same rules of the competition, the LAHC-based algorithms noticeably outperformed the winning methods. These results, and reports from the literature, suggest that the LAHC is a reliable method that can compete with the most employed local search algorithms. PubDate: 2015-11-06

Abstract: Abstract
It is well known that in the twentieth century, mathematical programming (MP) modeling and particularly linear programming (LP) modeling, even though strongly applied to combinatorial optimization, were not too successful when directed to scheduling problems. The purpose of this paper is to show that the field of successful applications of LP/MP modeling is still growing and includes also scheduling topics. We first focus on single machine scheduling. We consider a single machine scheduling model where a quadratic programming (QP) formulation handled by means of a QP solver is shown to be competitive with the state of the art approaches. Also, we discuss a single machine bicriterion scheduling problem and show that a standard LP formulation based on positional completion times performs reasonably well when handled by means of a LP solver. Then, we show how LP can be used to tighten bounds for approximation results in sequencing problems. Finally, we show how to enhance the complexity bounds of branch-and-reduce exact exponential algorithms by means of the so-called measure-and-conquer paradigm requiring always the solution of a specific MP model. PubDate: 2015-11-03

Abstract: Abstract
The resource leveling problem (RLP) involves the determination of a project baseline schedule that specifies the planned activity starting times while satisfying both the precedence constraints and the project deadline constraint under the objective of minimizing the variation in the resource utilization. However, uncertainty is inevitable during project execution. The baseline schedule generated by the deterministic RLP model tends to fail to achieve the desired objective when durations are uncertain. We study the robust resource leveling problem in which the activity durations are stochastic and the objective is to obtain a robust baseline schedule that minimizes the expected positive deviation of both resource utilizations and activity starting times. We present a genetic algorithm for the robust RLP. In order to demonstrate the effectiveness of our genetic algorithm, we conduct extensive computational experiments on a large number of randomly generated test instances and investigate the impact of different factors (the marginal cost of resource usage deviations, the marginal cost of activity starting time deviations, the activity duration variability, the due date, the order strength, the resource factor and the resource constrainedness). PubDate: 2015-10-16