On PERT Networks with Alternatives

Management of projects often requires decisions concerning the choice of alternative activities. Then, the completion time of the whole project (i.e. the makerpan) is computed. In this paper, we aim at selecting the required activities simultaneously with the computation of the makespan. This problem is referred to as PERT Problem with Alternatives (PPA). The corresponding model is similar to a conventional PERT graph, except that two types of nodes are involved to represent either the choice between activities, or the fact that a set of activities should be completed before starting another set of activities. A formalization of the problem and some important properties concerning the optimal solution are given. Several well- solvable cases of the problem and a powerful decomposition algorithm running in polynomial time are presented. This decomposition is applicable for solving many real-life problems

On-line Part Scheduling in a Surface Treatment System

A real-time scheduling algorithm which guarantees an optimal makespan to each part which arrives in a line of chemical baths for surface treatment purpose is proposed. We first consider the case when the treatment preriods are much greater than the transportation times, which allows us to neglect these times. We then extend our approach to the case when transportation times cannot be neglected. Some numerical examples are provided to illustrate this approach

Single-machine sceduling with fuzzy precedence constraints

リサーチレポート（北陸先端科学技術大学院大学情報科学研究科）本文は図書館に配架されています。 / This material is stored in the JAIST library

Entropy-Based Algorithm for Supply-Chain Complexity Assessment

This paper considers a graph model of hierarchical supply chains. The goal is to measure the complexity of links between different components of the chain, for instance, between the principal equipment manufacturer (a root node) and its suppliers (preceding supply nodes). The information entropy is used to serve as a measure of knowledge about the complexity of shortages and pitfalls in relationship between the supply chain components under uncertainty. The concept of conditional (relative) entropy is introduced which is a generalization of the conventional (non-relative) entropy. An entropy-based algorithm providing efficient assessment of the supply chain complexity as a function of the SC size is developed

A parametric critical path problem and an application for cyclic scheduling

AbstractThe paper addresses a problem of finding critical paths in PERT networks (digraphs) with variable arc lengths depending on a parameter. By equipping the Bellman-Ford label-correcting algorithm with variable vectorial labels depending on the parameter, we derive its version that solves the problem in O(mn2) time, for all possible parameter values (where m stands for the number of arcs, and n is the number of nodes in the digraph). An application related to cyclic scheduling of tasks in a robotic cell is considered

Maximizing the Average Environmental Benefit of a Fleet of Drones under a Periodic Schedule of Tasks

Unmanned aerial vehicles (UAVs, drones) are not just a technological achievement based on modern ideas of artificial intelligence; they also provide a sustainable solution for green technologies in logistics, transport, and material handling. In particular, using battery-powered UAVs to transport products can significantly decrease energy and fuel expenses, reduce environmental pollution, and improve the efficiency of clean technologies through improved energy-saving efficiency. We consider the problem of maximizing the average environmental benefit of a fleet of drones given a periodic schedule of tasks performed by the fleet of vehicles. To solve the problem efficiently, we formulate it as an optimization problem on an infinite periodic graph and reduce it to a special type of parametric assignment problem. We exactly solve the problem under consideration in O(n3) time, where n is the number of flights performed by UAVs

An improved approximation scheme for scheduling a maintenance and proportional deteriorating jobs

International audienceIn this paper, we re-visit the problem of scheduling a set of proportional deteriorating non-resumable jobs on a single machine subject to maintenance. The maintenance has to be started prior to a given deadline. The jobs as well as the maintenance are to be scheduled so that to minimize the total completion time. For this problem we propose a new dynamic programming algorithm and a faster fully polynomial time approximation scheme improving a recent result by Luo and Chen [JIMO (2012), 8:2, 271-283]

Improving the solution complexity of the scheduling problem with deadlines: A general technique

The aim of this paper is to develop improved polynomial-time approximation algorithms belonging to the family of the fully polynomial time approximation schemes (FPTAS) for a group of scheduling problems. In particular, the new technique provides a positive answer to a question posed more than three decades ago by Gens and Levner [G.V. Gens and E.V. Levner, Discrete Appl. Math. 3 (1981) 313–318]: “Can an epsilon-approximation algorithm be found for the minimization version of the job-sequencing-with-deadlines problem running with the same complexity as the algorithms for the maximization form of the problem?