Expanding Flow Shop Tasks Based on Recursive Functions

TL;DR

This paper introduces a recursive function framework to model and extend flow shop scheduling problems, enabling unified descriptions of multiple problem variants and facilitating optimization techniques like branch and bound.

Contribution

It presents a novel recursive function approach that captures various extensions of flow shop scheduling within a single unified framework.

Findings

Recursive functions can describe multiple flow shop extensions.

The structure of superpositions of recursive functions is characterized.

Demonstrated formulation of new problems and optimization methods.

Abstract

The paper discusses several extensions of the recursive representation of the flow shop scheduling problem. It is shown that recursive functions make it possible to describe multiple extensions in a single problem. The paper considers altogether six extensions. The examples consider three types of recursive functions: functions associated with the machine, functions that adjust the procession time based on constraints, and functions that control the feasibility of the schedule. The structure of the superpositions of these functions is presented, and also descriptions of several objective functions by recursive functions are presented. Then the general requirements for a recursive function are formulated and its properties are described. Finally, a demonstration of the formulation of new problems is provided using examples of simple flow shop extensions and branch and bound optimization.