Single machine scheduling with job-dependent machine deterioration

We consider the single machine scheduling problem with job-dependent machine deterioration. In the problem, we are given a single machine with an initial non-negative maintenance level, and a set of jobs each with a non-preemptive processing time and a machine deterioration. Such a machine deterioration quantifies the decrement in the machine maintenance level after processing the job. To avoid machine breakdown, one should guarantee a non-negative maintenance level at any time point; and whenever necessary, a maintenance activity must be allocated for restoring the machine maintenance level. The goal of the problem is to schedule the jobs and the maintenance activities such that the total completion time of jobs is minimized. There are two variants of maintenance activities: in the partial maintenance case each activity can be allocated to increase the machine maintenance level to any level not exceeding the maximum; in the full maintenance case every activity must be allocated to increase the machine maintenance level to the maximum. In a recent work, the problem in the full maintenance case has been proven NP-hard; several special cases of the problem in the partial maintenance case were shown solvable in polynomial time, but the complexity of the general problem is left open. In this paper we first prove that the problem in the partial maintenance case is NP-hard, thus settling the open problem; we then design a $2$-approximation algorithm.Comment: 15 page

Genetic and memetic algorithms for scheduling railway maintenance activities

Nowadays railway companies are confronted with high infrastructure maintenance costs. Therefore good strategies are needed to carry out these maintenance activities in a most cost effective way. In this paper we solve the preventive maintenance scheduling problem (PMSP) using genetic algorithms, memetic algorithms and a two-phase heuristic based on opportunities. The aim of the PMSP is to schedule the (short) routine activities and (long) unique projects for one link in the rail network for a certain planning period such that the overall cost is minimized. To reduce costs and inconvenience for the travellers and operators, these maintenance works are clustered as much as possible in the same time period. The performance of the algorithms presented in this paper are compared with the performance of the methods from an earlier work, Budai et al. (2006), using some randomly generated instances.genetic algorithm;heuristics;opportunities;maintenance optimization;memetic algorithm

Decentralized Greedy-Based Algorithm for Smart Energy Management in Plug-in Electric Vehicle Energy Distribution Systems

Variations in electricity tariffs arising due to stochastic demand loads on the power grids have stimulated research in finding optimal charging/discharging scheduling solutions for electric vehicles (EVs). Most of the current EV scheduling solutions are either centralized, which suffer from low reliability and high complexity, while existing decentralized solutions do not facilitate the efficient scheduling of on-move EVs in large-scale networks considering a smart energy distribution system. Motivated by smart cities applications, we consider in this paper the optimal scheduling of EVs in a geographically large-scale smart energy distribution system where EVs have the flexibility of charging/discharging at spatially-deployed smart charging stations (CSs) operated by individual aggregators. In such a scenario, we define the social welfare maximization problem as the total profit of both supply and demand sides in the form of a mixed integer non-linear programming (MINLP) model. Due to the intractability, we then propose an online decentralized algorithm with low complexity which utilizes effective heuristics to forward each EV to the most profitable CS in a smart manner. Results of simulations on the IEEE 37 bus distribution network verify that the proposed algorithm improves the social welfare by about 30% on average with respect to an alternative scheduling strategy under the equal participation of EVs in charging and discharging operations. Considering the best-case performance where only EV profit maximization is concerned, our solution also achieves upto 20% improvement in flatting the final electricity load. Furthermore, the results reveal the existence of an optimal number of CSs and an optimal vehicle-to-grid penetration threshold for which the overall profit can be maximized. Our findings serve as guidelines for V2G system designers in smart city scenarios to plan a cost-effective strategy for large-scale EVs distributed energy management

Joint scheduling of jobs and preventive maintenance operations in the flowshop sequencing problem: A resolution with sequential and integrated strategies.

International audienceUsually, scheduling of maintenance operations and production sequencing are dealt with separately in the literature and, therefore, also in the industry. Given that maintenance affects available production time and elapsed production time affects the probability of machine failure, this interdependency seems to be overlooked in the literature. This paper presents a comparative study on joint production and preventive maintenance scheduling strategies regarding flowshop problems. The sequential strategy which consists of two steps: first scheduling the production jobs then inserting maintenance operations, taking the production schedule as a strong constraint. The integrated one which consists of simultaneously scheduling both maintenance and production activities based on a common representation of these two activities. For each strategy, a constructive heuristic and two meta-heuristics are proposed: NEH heuristic, Genetic algorithm and Taboo search. The goal is to optimize an objective function which takes into account both production and maintenance criteria. The proposed heuristics have been applied to non-standard test problems which represent joint production and maintenance benchmark flowshop scheduling problems taken from Benbouzid et al. (2003). A comparison of the solutions yielded by the heuristics developed in this paper with the heuristic solutions given by Taillard (1993) is undertaken with respect to the minimization of performance loss after maintenance insertion. The comparison shows that the proposed integrated GAs are clearly superior to all the analyzed algorithms

Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Overcommitment in Cloud Services -- Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

Single machine scheduling with periodic machine availability

In this paper we address the problem of scheduling jobs on a single machine with cyclical machine availability periods. In this problem, the scheduling horizon is composed of periods where the machine is available followed by other periods where no operation can be performed. In the literature, the problem is denoted as scheduling with periodic maintenance, as it is usually assumed that these unavailability periods are employed to perform maintenance activities. Another situation is the one inspiring our research, i.e. the need of completing manufacturing operations within a shift. More specifically, we focus the single machine scheduling problem with makespan objective subject to periodic machine availability. There are several contributions proposing approximate procedures due to the NP-hardness shown for the problem. However, we are not aware of a computational evaluation among these procedures. Furthermore, the problem is similar to the classical bin packing problem, so it is of interest to explore the relation between both problems. In this paper, we address these two issues, and propose new approximate solution procedures for the problem.Ministerio de Ciencia e Innovación DPI2016-80750-

Scheduling commercial advertisements for television

The problem of scheduling the commercial advertisements in the television industry is investigated. Each advertiser client demands that the multiple airings of the same brand advertisement should be as spaced as possible over a given time period. Moreover, audience rating requests have to be taken into account in the scheduling. This is the first time this hard decision problem is dealt with in the literature. We design two mixed integer linear programming (MILP) models. Two constructive heuristics, local search procedures and simulated annealing (SA) approaches are also proposed. Extensive computational experiments, using several instances of various sizes, are performed. The results show that the proposed MILP model which represents the problem as a network flow obtains a larger number of optimal solutions and the best non-exact procedure is the one that uses SA