Minimizing value-at-risk in the single-machine total weighted tardiness problem

The vast majority of the machine scheduling literature focuses on deterministic problems, in which all data is known with certainty a priori. This may be a reasonable assumption when the variability in the problem parameters is low. However, as variability in the parameters increases incorporating this uncertainty explicitly into a scheduling model is essential to mitigate the resulting adverse effects. In this paper, we consider the celebrated single-machine total weighted tardiness (TWT) problem in the presence of uncertain problem parameters. We impose a probabilistic constraint on the random TWT and introduce a risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) measure on the random TWT at a specified confidence level. Furthermore, we develop a lower bound on the optimal VaR that may also benefit alternate solution approaches in the future. In this study, we implement a tabu-search heuristic to obtain reasonably good feasible solutions and present results to demonstrate the effect of the risk parameter and the value of the proposed model with respect to a corresponding risk-neutral approach

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

Resource-constrained project scheduling for timely project completion with stochastic activity durations.

We investigate resource-constrained project scheduling with stochastic activity durations. Various objective functions related to timely project completion are examined, as well as the correlation between these objectives. We develop a GRASP-heuristic to produce high-quality solutions, using so-called descriptive sampling. The algorithm outperforms other existing algorithms for expected-makespan minimization. The distribution of the possible makespan realizations for a given scheduling policy is studied, and problem difficulty is explored as a function of problem parameters.GRASP; Project scheduling; Uncertainty;

Scheduling reentrant jobs on parallel machines with a remote server

This paper explores a specific combinatorial problem relating to re-entrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem is inspired by the logistics of a semi-automated micro-biology laboratory. The testing programme in the laboratory corresponds roughly to a hybrid flowshop, whose bottleneck stage is the subject of study. We demonstrate the NP-hard nature of the problem, and provide various structural features. A heuristic is developed and tested on randomly generated benchmark data. Results indicate solutions reliably within 1.5% of optimum. We also provide a greedy 2-approximation algorithm. Test on real-life data from the microbiology laboratory indicate a 20% saving relative to current practice, which is more than can be achieved currently with 3 instead of 2 people staffing the primary machines

Collision-free Time Slot Reuse in Multi-hop Wireless Sensor Networks

To ensure a long-lived network of wireless communicating sensors, we are in need of a medium access control protocol that is able to prevent energy-wasting effects like idle listening, hidden terminal problem or collision of packets. Schedule-based medium access protocols are in general robust against these effects, but require a mechanism to establish a non-conflicting schedule. In this paper, we present such a mechanism which allows wireless sensors to choose a time interval for transmission, which is not interfering or causing collisions with other transmissions. In our solution, we do not assume any hierarchical organization in the network and all operation is localized. We empirically show that our localized algorithm is successful within a factor 2 of the minimum necessary time slots in random networks; well in range of the expected (worst case) factor 3-approximation of known first-fit algorithms. Our algorithm assures similar minimum distance between simultaneous transmissions as CSMA(/CD)-based approaches

Probabilistic alternatives for competitive analysis

In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: it sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.operations research and management science;

Common Due-Date Problem: Exact Polynomial Algorithms for a Given Job Sequence

This paper considers the problem of scheduling jobs on single and parallel machines where all the jobs possess different processing times but a common due date. There is a penalty involved with each job if it is processed earlier or later than the due date. The objective of the problem is to find the assignment of jobs to machines, the processing sequence of jobs and the time at which they are processed, which minimizes the total penalty incurred due to tardiness or earliness of the jobs. This work presents exact polynomial algorithms for optimizing a given job sequence or single and parallel machines with the run-time complexities of $O(n \log n)$ and $O(mn^2 \log n)$ respectively, where $n$ is the number of jobs and $m$ the number of machines. The algorithms take a sequence consisting of all the jobs $(J_i, i=1,2,\dots,n)$ as input and distribute the jobs to machines (for $m>1$) along with their best completion times so as to get the least possible total penalty for this sequence. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we present the results for the benchmark instances and compare with previous work for single and parallel machine cases, up to $200$ jobs.Comment: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computin

Restricted Mobility Improves Delay-Throughput Trade-offs in Mobile Ad-Hoc Networks

In this paper we revisit two classes of mobility models which are widely used to repre-sent users ’ mobility in wireless networks: Random Waypoint (RWP) and Random Direction (RD). For both models we obtain systems of partial differential equations which describe the evolution of the users ’ distribution. For the RD model, we show how the equations can be solved analytically both in the stationary and transient regime adopting standard mathematical techniques. Our main contributions are i) simple expressions which relate the transient dura-tion to the model parameters; ii) the definition of a generalized random direction model whose stationary distribution of mobiles in the physical space corresponds to an assigned distribution