Michael Forbes

An exact algorithm for multiple depot bus scheduling

Abstract In this paper we present an exact algorithm for solving the multiple depot bus scheduling problem. The algorithm uses two well known linear programming relaxations of the problem. The first, a pure network flow problem, is used to obtaine a dual feasible solution to the second relaxation, a multi-commodity network flow problem, which is solved using dual simplex. Branch and bound is then used to obtaine the optimal integer solution. This technique is then used to solve exactly problems much greater than any previously reported technique. Results are presented for problems with up to 600 trips and 3 depots.

Vehicle routing and crew scheduling for metropolitan mail distribution at Australia Post

This paper presents a new multi-depot combined vehicle and crew scheduling algorithm, and uses it, in conjunction with a heuristic vehicle routing algorithm, to solve the intra-city mail distribution problem faced by Australia Post. First we describe the Australia Post mail distribution problem and outline the heuristic vehicle routing algorithm used to find vehicle routes. We present a new multi-depot combined vehicle and crew scheduling algorithm based on set covering with column generation. The paper concludes with a computational investigation examining the affect of different types of vehicle routing solutions on the vehicle and crew scheduling solution, comparing the different levels of integration possible with the new vehicle and crew scheduling algorithm and comparing the results of sequential versus simultaneous vehicle and crew scheduling, using real life data for Australia Post distribution networks. � 2005 Elsevier B.V. All rights reserved.

Optimizing Network Designs for the World's Largest Broadband Project

The national broadband network NBN is the largest public infrastructure project undertaken in Australia, and NBN Co is the government-owned company responsible for building the network. By using operations research, NBN Co expects to avoid more than

Disaggregated Benders Decomposition for solving a Network Maintenance Scheduling Problem

AUD1.7 billion in unnecessary construction and design costs on this

Puzzle—The Fillomino Puzzle

AUD36 billion project. At the beginning of this 10-year project, NBN Co divided the country into more than 3,000 fiber-serving-area modules FSAMs, each covering approximately 2,500 premises, and will design and construct one FSAM each day. NBN Co contracted with Biarri Networks, an Australian commercial mathematics company, to optimize the design task. To accomplish this, Biarri created a fiber-optic network design FOND software product based on a network-flow mixed-integer programming engine. This engine minimizes the cost of materials and labor for each FSAM, subject to a variety of constraints, and provides a solution in less than five minutes. To date, more than 650 FSAM designs have been completed using FOND. This has saved NBN Co an estimated

Monte-Carlo Tree Search in Dragline Operation Planning

AUD325 million in avoided construction cost, and the planning time per FSAM has decreased from 145 to 16 days.

Disaggregated Benders decomposition and branch-and-cut for solving the budget-constrained dynamic uncapacitated facility location and network design problem

We consider a problem concerning a network and a set of maintenance requests to be undertaken. The aim is to schedule the maintenance in such a way as to minimise the impact on the total throughput of the network. We embed disaggregated Benders decomposition in a branch-and-cut framework to solve the problem to optimality, as well as explore the strengths and weaknesses of the technique. We prove that our Benders cuts are Pareto-optimal. Solutions to the linear programming relaxation also provide further valid inequalities to reduce total solving time. We implement these techniques on simulated data presented in previous papers and compare our solution technique to previous methods and a direct mixed-integer programming formulation. We prove optimality in many problem instances that have not previously been proven.

Planning dragline positioning sequence with A* search algorithm

Logic puzzles form an excellent set of problems for the teaching of advanced solution techniques in operations research. They are an opportunity for students to test their modelling skills on a different style of problem, and some puzzles even require advanced techniques to become tractable. Fillomino is a puzzle in which the player must enter integers into a grid to satisfy certain rules. This puzzle is a good exercise in using lazy constraints and composite variables to solve difficult problems.

Exact Solution of Locomotive Scheduling Problems

Draglines are one of the largest earthmoving machines in surface mining. They are employed to remove the overburden near the surface, giving access to a seam of the target mineral or coal underneath. Their excavation productivity is significantly affected by the high-level operation strategy of where to position the dragline, what to dig at each position and where to dump the removed material. This letter explores the potential of using the Monte-Carlo tree search (MCTS) algorithm for planning this operation strategy. To this end, we adapt the MCTS algorithm to compute the dragline positioning sequences when a fixed digging and dumping strategy is applied at each position. The performance of the adapted MCTS algorithm is compared to a previously developed A* search algorithm and a greedy algorithm. Simulation results show that the MCTS algorithm is able to find near-optimal positioning sequences using significantly less time and memory than the A* algorithm. The solutions from the MCTS algorithm also largely outperform the solutions from the greedy algorithm in all the test scenarios. These results suggest that the MCTS algorithm can be used to plan the operation strategy when decisions about the digging and dumping operations are also considered.

A matching algorithm with applications to bus operations.

Abstract We present an approach for solving to optimality the budget-constrained Dynamic Uncapacitated Facility Location and Network Design problem (DUFLNDP). This is a problem where a network must be constructed or expanded and facilities placed in the network, subject to a budget, in order to satisfy a number of demands. With the demands satisfied, the objective is to minimise the running cost of the network and the cost of moving demands to facilities. The problem can be disaggregated over two different sets simultaneously, leading to many smaller models that can be solved more easily. Using disaggregated Benders decomposition embedded in a branch-and-cut framework, we solve many instances to optimality that have not previously been solved. We use an analytic procedure to generate Benders optimality cuts that are provably Pareto-optimal.