Optimal clustering of frequency-constrained maintenance jobs with shared set-ups

Since maintenance jobs often require one or more set-up activities, joint execution or clustering of maintenance jobs is a powerful instrument to reduce shut-down costs. We consider a clustering problem for frequency-constrained maintenance jobs, i.e. maintenance jobs that must be carried out with a prescribed (or higher) frequency. For the clustering of maintenance jobs with identical, so-called common set-ups, several strong dominance rules are provided. These dominance rules are used in an efficient dynamic programming algorithm which solves the problem in polynomial time. For the clustering of maintenance jobs with partially identical, so-called shared set-ups, similar but less strong dominance rules are available. Nevertheless, a surprisingly well-performing greedy heuristic and a branch and bound procedure have been developed to solve this problem. For randomly generated test problems with 10 set-ups and 30 maintenance jobs, the heuristic was optimal in 47 out of 100 test problems, with an average deviation of 0.24% from the optimal solution. In addition, the branch and bound method found an optimal solution in only a few seconds computation time on average

Model based decision support for planning of road maintenance

In this article we describe a Decision Support Model, based on Operational Research methods, for the multi-period planning of maintenance of bituminous pavements. This model is a tool for the road manager to assist in generating an optimal maintenance plan for a road. Optimal means: minimising the Net Present Value of maintenance costs, while the plan is acceptable in terms of technical admissibility, resulting quality, etc. Global restrictions such as budget restrictions can also be imposed.\ud \ud Adequate grouping of maintenance activities in view of quantity discounts is an important aspect of our model. Our approach is to reduce the complexity of the optimisation by hierarchical structuring in four levels. In the lowest two levels maintenance per lane sector is considered, first with an unbounded planning horizon and next with a bounded planning horizon and time-windows for maintenance. The grouping of maintenance activities for a specific road is the topic of the third level. At the fourth level, which we will not consider in this article, the problem of optimal assignment of the available maintenance budgets over a set of roads or road sections takes place. Here, some results are presented to demonstrate the effects of grouping and to show that this hierarchical approach gives rise to improvements compared with previous work

Agent-based transportation planning compared with scheduling heuristics

Here we consider the problem of dynamically assigning vehicles to transportation orders that have di¤erent time windows and should be handled in real time. We introduce a new agent-based system for the planning and scheduling of these transportation networks. Intelligent vehicle agents schedule their own routes. They interact with job agents, who strive for minimum transportation costs, using a Vickrey auction for each incoming order. We use simulation to compare the on-time delivery percentage and the vehicle utilization of an agent-based planning system to a traditional system based on OR heuristics (look-ahead rules, serial scheduling). Numerical experiments show that a properly designed multi-agent system may perform as good as or even better than traditional methods

Comparison of agent-based scheduling to look-ahead heuristics for real-time transportation problems

We consider the real-time scheduling of full truckload transportation orders with time windows that arrive during schedule execution. Because a fast scheduling method is required, look-ahead heuristics are traditionally used to solve these kinds of problems. As an alternative, we introduce an agent-based approach where intelligent vehicle agents schedule their own routes. They interact with job agents, who strive for minimum transportation costs, using a Vickrey auction for each incoming order. This approach offers several advantages: it is fast, requires relatively little information and facilitates easy schedule adjustments in reaction to information updates. We compare the agent-based approach to more traditional hierarchical heuristics in an extensive simulation experiment. We find that a properly designed multiagent approach performs as good as or even better than traditional methods. Particularly, the multi-agent approach yields less empty miles and a more stable service level

On multi-class multi-server queueing and spare parts management

Multi-class multi-server queuing problems are a generalization of the wellknown M/M/k situation to arrival processes with clients of N types that require exponentially distributed service with different averaged service time. Problems of this sort arise naturally in various applications, such as spare parts management, for example. In this paper we give a procedure to construct exact solutions of the stationary state equations. Essential in this procedure is the reduction of the problem for n = the number of clients in the system > k to a backwards second order difference equation with constant coefficients for a vector in a linear space with dimension depending on Nand k, denoted by d(N,k). Precisely d(N,k) of its solutions have exponential decay for n 00. Next, using this as input, the equations for n ::; k can be solved by backwards recursion. It follows that the exact solution does not have a simple product structure as one might expect intuitively. Further, using the exact solution several interesting performance measures related to spare parts management can be computed and compared with heuristic approximations. This is illustrated with numerical results

On Markovian multi-class, multi-server queueing

Multi-class multi-server queueing problems are a generalisation of the well-known M/M/k queue to arrival processes with clients of N types that require exponentially distributed service with different average service times. In this paper, we give a procedure to construct exact solutions of the stationary state equations using the special structure of these equations. Essential in this procedure is the reduction of a part of the problem to a backward second order difference equation with constant coefficients. It follows that the exact solution can be found by eigenmode decomposition. In general eigenmodes do not have a simple product structure as one might expect intuitively. Further, using the exact solution, all kinds of interesting performance measures can be computed and compared with heuristic approximations (insofar available in the literature). We provide some new approximations based on special multiplicative eigenmodes, including the dominant mode in the heavy traffic limit. We illustrate our methods with numerical results. It turns out that our approximation method is better for higher moments than some other approximations known in the literature. Moreover, we demonstrate that our theory is useful to applications where correlation between items plays a role, such as spare parts management

Analyzing multi-class, multi-server queueing systems with preemtive priorities

In this paper we consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple items, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an approximate method to estimate the steady state probabilities with an approximation error that can be made as small as desired at the expense of some more numerical matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system. We illustrate our method with some numerical examples. Comparison to simulation results shows that with a moderate number of matrix iterations (~20) we can estimate key performance measures, such as the mean and variance of the number of items in the system, with an error less than 1% in most cases

Waiting times at periodically switched one-way traffic lanes - A periodic, two-queue polling system with random setup times

We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules, i.e. the driving direction on the infrastructure is switched between two directions according to a fixed time schedule. We analyse both symmetric and asymmetric systems (I.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random set-up times and periodic (non-exhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1-2% for Poisson arrivals. Also, we indicate how our approximations can be generalised to compound Poisson arrivals