Scheduling Problems: About Professor Camino R. Vela’s Presentation on

Heuristic Strategies for Resolving Scheduling Problems at the University of Malaga

Juan Antonio Martín Checa

Computer Science Department

Campus Teatinos University of Malaga 29071 Málaga, Spain

jamcheca@telefonica.net

Abstract. Professor Camino R. Vela is a recognized researcher on the field of the so called Scheduling Problems from the Computing Technologies Group at the University of Oviedo in Spain. On November 16th 2010, Professor Vela made a presentation on this topic at the University of Malaga, Spain, in the frame of the Master in Software Engineering & Atificial Intelligence organized by the Computer Science Department. In this paper, we will briefly summarize the contents treated, and will comment on the topics under study.

Keywords: B&B Search Algorithm, DF Search Algorithm, G&T Algorithm, Genetic Algorithm, Heuristics, Job Shop Scheduling, Makespan, Operators, Scheduling, Setup Times, Simple Local Search, Tasks, Triangular Fuzzy Numbers, Vicinity.

1 Introduction

Contrary to what some may think, and as described by Professor Vela, scheduling problems are still a hot topic nowadays. Indeed, several work groups from different countries are researching intensively on how to improve scheduling algorithms performance. As an example, Professor Vela’s group, at the University of Oviedo, has long studied different strategies for resolving this type of problems. Her mastery on the topic was palpable along the entire presentation, structured in two parts: an overview of the foundations on scheduling problems, and specific details on her research group’s work.

1.1 An Overview of Scheduling Problems

An scheduling problem can be defined as the “temporal resources assignation to a number of tasks under certain restrictions [...] in order to optimize one or more

objectives” [1]. This is, for instance, exemplified by the Classic Job Shop reference problem. This problem models a ‘system’ (i.e. the production chain in an automobile factory) composed of a number of tasks, each of them with a predefined duration, forming different jobs in a specific unalterable order, and competing for the necessary machines to be carried out. Requirements (restrictions) of different nature may exist (i.e. maximum duration for all the jobs to be finished, specific machines for specific tasks, etc). The goal is to optimize the objective function (make-span, total flow time, weighted delay, etc). The solution graph makes special emphasis in critical tasks, critical blocks, and the critical path. The general resolution strategies can be classified into approximate techniques (greedy algorithms, such as Giffler & Thompson's G&T, or metaheuristics, such as genetic and memetic algortihms, simple local search, and taboo search) and exact techniques (such as Brucker’s B&B - branch & bound -, and first in depth).

1.2 Professor Vela’s Research Group

Different approaches can be adopted in order to solve specific scheduling problems, four of which are the main strategies or research lines within Professors Vela’s group: Job Shop with Partially Informed DF, Job Shop with Fuzzy Times, Job Shop with Setup Times, and last but not least, Job Shop with Operators. Job Shop with Partially Informed DF is an extension of the B&B algorithm, using arcs in a disjunctive graph to represent the schedules, which are limited by both lower and upper bounds modeling the restrictions, and expands the graph from the initial state, by computing possible candidate tasks and spreading out the restrictions. Job Shop with Fuzzy Times introduces the concept of uncertainty in times by assuming we do not actually have a complete knowledge of times in our system, but only ranges and the most probable values for each. At this point, it is to be pointed out that while the initial and final times, together with the makespan are considered as fuzzy, the processing order for tasks itself is precise. Professor Vela’s group’s contribution focuses on a local search algorithm with different vicinities, as well as on a memetic algorithm. Job Shop with Setup Times is based on the called setup operations, meaning those operations that are necessary for a machine that has already processed one task, in order to process the next one. It may be or not case that the duration of the current task depends on the duration of the previous and next tasks. Finally, Job Shop with Operators on its side, considers that all the tasks need to be supervised by a non-specialist operator, who is capable of controlling only one task at a time.

2 Conclusions

There are many daily situations when we need to do some scheduling. If we take one minute to think about it, most of our activities, routinely or not, are to certain degree, scheduled in some way. Since we wake up and until we go to bed, we follow a preconceived plan which enumerates a number of tasks, and the times when those

tasks should actually be done along the day time. Our agenda is nothing else than our personal and private scheduler. Most of people in the world use certain level of organization in the activities they have to perform on a daily basis. Schedules, timetables, agendas, etc. are the rulers of our lives, and the means by which people are capable of working efficiently together as coordinated groups of individuals, all of them on the same page.

But far from being just important, if not essential, for individuals, scheduling is critical in most of companies, organizations, or institutions of any kind worldwide. Not only that, but it is also present on the foundations of most of technologies or technological systems or devices, such as communication protocols, programming languages, operating systems, and practically any gadget we could imagine.

Said this, it seems evident the great importance of the scheduling process by itself, which in many common daily situations is either unnoticed or uncared at all by us, but still is there for us to get the most of our 24-wonderful-hours day. Putting the bread in the toaster before putting the milk in the microwave, and getting the butter or jelly from the fridge, is, as most of people know, a good way to save a little bit of time in our hasty daily breakfast.

In a more scientific or technological arena, the constant necessity of many companies of any field for cutting down production or labor costs, demands from the scientific community scheduling algorithms capable of outperforming the existing ones, or even better, those of the competence. Requirements of CPU’s cycles, memory, channel throughput in broadband communications, transmission of multimedia information, HD videoconferencing, etc. are just some representative examples that come to support energetically the necessity of further research on the field of scheduling. It is only through continuous and extensive research that the scientific community would come up with more and more refined strategies and algorithms to make a more efficient use of time.

References

1. R. Vela, Camino, Estrategias Heurísticas para la Resolución de Problemas de Scheduling.

Computing Technologies Department, University of Oviedo.