Heng-Soon Gan

Scheduling two parallel machines with a single server: the general case

This paper considers the problem of scheduling two-operation non-preemptable jobs on two identical semi-automatic machines. A single server is available to carry out the first (or setup) operation. The second operation is executed automatically, without the server. The general problem of makespan minimization is NP-hard in the strong sense. In earlier work, we showed that the equal total length problem is polynomial time and we also provided efficient and effective solutions for the special cases of equal setup and equal processing times. Most of the cases analyzed thus far have fallen into the category of regular problems. In this paper we build on this earlier work to deal with the general case. Various approaches will be considered. One may reduce the problem to a regular one by amalgamating jobs, or we may apply the earlier heuristics to (possibly regular) job clusters. Alternately we may apply a greedy heuristic, a metaheuristic such as a genetic algorithm or the well known Gilmore-Gomory algorithm to solve the general problem. We report on the performance of these various methods.

Equal processing and equal setup time cases of scheduling parallel machines with a single server

This paper considers the deterministic problem of scheduling two-operation non-preemptable jobs on two identical semi-automatic machines. A single server is available to carry out the first (or setup) operation. The second operation is executed automatically, without the server. The general problem of makespan minimization is NP-hard in the strong sense. Two special cases which arise in practice, the equal processing times and regular equal setup times problems turn out to be closely linked to the restricted set partitioning problem. This link is used to show that they are NP-hard in the ordinary sense, and to construct a tight lower bound and two highly effective O(n log n) heuristics.

Get me out of here: collaborative evacuation based on local knowledge

Evacuation is one of the most urgent measures of disaster response. It requires spatiotemporal decision making by many individual agents under circumstances that include an unknown impact of the disaster on the environment, which impedes the evacuation planning, and potentially destroyed, blocked or lacking communication infrastructure, which impedes central management. This paper suggests and investigates a novel paradigm for evacuation planning: decentralized planning based on sharing local knowledge. The paradigm is not only independent from infrastructure, and adapts to dynamic disasters, but also is as successful as centralized management in many scenarios.

A branch-and-price algorithm for the general case of scheduling parallel machines with a single server

We consider the strongly NP-hard problem of scheduling two-operation non-preemptable jobs on two identical parallel machines. A single server, that can handle at most one job at a time, is available to carry out the first (or setup) operation. The second operation, to be carried out on the same machine but without the server, must be executed immediately after the setup. The objective is to minimize the makespan. We apply a column generation method to a population of partial schedules, in turn generated by some well known heuristics, to achieve effective and efficient solutions. We compare the performance of this method with those proposed earlier and also suggest future work.

Comparing deterministic, robust and online scheduling using entropy

We conjecture that when the uncertainty of scheduling information increases, one should change from deterministic, through robust to, finally, online scheduling techniques. Previously, extensive mathematical investigations have been carried out on the stability of a deterministic schedule for uncertain operation processing times. In this paper, we will use an empirical approach and an entropy measure to justify the transition between deterministic, robust and online scheduling. The use of an entropy measure in our context can be perceived, in a broader sense, as a pro-active approach to deal with changes in the level of information uncertainty and relative importance of each term in the total schedule execution cost. The level of information uncertainty may change due to the performance deterioration of processors (machines or human) and the replacement of old machines with new ones; and the changes in relative importance of cost elements may be due to changes in shop floor priorities and pressure from partners in the supply chain network. One can decide upon the scheduling strategies to be employed based on the latest entropy value of the information considered and the relative importance of each cost term.

Integration of simulation and optimization for evacuation planning

Abstract Evacuation is a time critical process in which the highest priority is to get those people who may be affected by a disaster out of the danger zone as fast as possible. For disaster-prone areas, authorities often distribute evacuation plans well in advance, or encourage the population to prepare themselves for eventual disasters. This paper presents an approach to such planning ahead for evacuation that tightly couples optimization and traffic simulation in order to determine optimal evacuation time and exit from the area for each evacuee. In this paper, we discuss the approach’s properties and illustrate its performance using two case studies of wildfire-prone areas in the state of Victoria, Australia. The results show that our approach can lead to significant improvements when compared to ad-hoc evacuation, but these improvements also strongly depend on population density and road network topology. More generally, our research highlights the significant benefits of tightly coupling optimization and simulation for evacuation modeling.

Robust economic-statistical design of X-bar control chart

Control charts are developed to monitor the service and production processes. The fact that many processes have uncertain parameters is a barrier to obtain the best design of the control charts. In this paper, economic statistical design (ESD) of the X-bar control chart utilising robust optimisation approach that considers interval estimates of uncertain parameters is investigated. A heuristic algorithm is developed to obtain the robust scheme of the control chart. Robust design for an industrial problem is compared with traditional ESD, and heuristic design. Numerical analyses and simulation study show that the proposed X-bar control chart offers a better approach and more reliable solutions for practitioners.

Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by π ( G , R ) . The edge-forwarding index π ( G ) is the minimum of π ( G , R ) over all possible all-to-all routings R, and the arc-forwarding index π ? ( G ) is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by w ( G , R ) the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colours. The optical index w ( G ) is defined to be the minimum of w ( G , R ) over all possible R, and the directed optical index w ? ( G ) is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for 4-regular circulant graphs with connection set { ? 1 , ? s } , 1 < s < n / 2 . We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of 4-regular circulant graphs.

Heuristic stability: A permutation disarray measure

Heuristic performance has been mainly measured by effectiveness (near optimality) and efficiency (computational complexity). More recently researchers have begun the difficult task of evaluating heuristic stability, or sensitivity, to perturbations in the problem specifications. Various stability measures have been proposed. Here we consider how Spearmans footrule, a measure of permutation disarray, may shed some further light on this, not as yet well understood, problem.