The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography.

/pdf/optimization-and-approximation-in-deterministic-sequencing-327pfewdb6.pdf

Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

We survey and extend the results on the complexity of machine scheduling problems. After a brief review of the central concept of NP-completeness we give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity. The problems for which a polynomial-bounded algorithm is available are listed and NP-completeness is established for a large number of other machine scheduling problems. We finally discuss some questions that remain unanswered.

/pdf/complexity-of-machine-scheduling-problems-3kmjz4hlnd.pdf

Complexity of machine scheduling problems

The vehicle routing problem: An overview of exact and approximate algorithms

/pdf/sequencing-and-scheduling-algorithms-and-complexity-lnutyrr3kz.pdf

Sequencing and scheduling: algorithms and complexity

Scheduling subject to resource constraints: classification and complexity

In two recent papers by C. S. Orloff (Networks, 4(1974)35–64, 147–162) general routing problems for one or more vehicles on a graph G = (N,A) are introduced and discussed. The single vehicle problem is to find an optimal tour on G, containing required subsets Q ⊆ N and R ⊆ A. We show that a proposed conversion of required nodes to required arcs is not allowed and that the problem remains polynomial complete if Q = θ. Furthermore, the proposed transformations from M vehicle to single vehicle problems are shown to be incorrect; correct transformations are presented as well.

/pdf/on-general-routing-problems-575f7yqdvo.pdf

On general routing problems

The travelling salesman problem arises in many different contexts. In this paper we report on typical applications in computer wiring, vehicle routing, clustering and job-shop scheduling. The formulation as a travelling salesman problem is essentially the simplest way to solve these problems. Most applications originated from real world problems and thus seem to be of particular interest. Illustrated examples are provided with each application.

/pdf/some-simple-applications-of-the-travelling-salesman-problem-4quw5dpqt6.pdf

Some Simple Applications of the Travelling Salesman Problem

Some simple applications of the travelling salesman problem

Suppose we have n jobs that arrive simultaneously to be processed on a continuously available machine that can handle only one job at a time. Each job has a fixed processing time and a cost function that is nondecreasing in its finishing time. We want to find a schedule that minimizes total costs. After reviewing the relevant work on this problem, we present a new algorithm for a general cost function. The algorithm is tested for the well known case of a weighted tardiness criterion.

Minimizing total costs in one-machine scheduling

/pdf/minimizing-total-costs-in-one-machine-scheduling-3fvertu1qk.pdf

A.H.G. Rinnooy Kan

Papers

On general routing problems

Some Simple Applications of the Travelling Salesman Problem

Some simple applications of the travelling salesman problem

Minimizing total costs in one-machine scheduling

Minimizing Total Costs in One-Machine Scheduling