Evaluating Typical Algorithms of Combinatorial Optimization to Solve Continuous-Time Based Scheduling Problem

Alexander Lazarev,Ivan Nekrasov,Nikolay Pravdivets

doi:10.3390/a11040050

Abstract

We consider one approach to formalize the Resource-Constrained Project Scheduling Problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original problem into combinatorial setting is based on interpreting each operation as an atomic entity that has a defined duration and has to be resided on the continuous time axis meeting additional restrictions. The simplest case of continuous-time scheduling assumes one-to-one correspondence of resources and operations and corresponds to the linear programming problem setting. However, real scheduling problems include many-to-one relations which leads to the additional combinatorial component in the formulation due to operations competition. We research how to apply several typical algorithms to solve the resulted combinatorial optimization problem: enumeration including branch-and-bound method, gradient algorithm, random search technique.

Highlights

The Resource-Constrained Project Scheduling Problem (RCPSP) has many practical applications.One of the most obvious and direct applications of RCPSP is planning the fulfilment of planned orders at the manufacturing enterprise [1] that is sometimes named Job Shop
The Job Shop scheduling process traditionally resides inside the Manufacturing Execution Systems scope [2] and belongs to principle basic management tasks of any industrial enterprise
Sticking to the industrial scheduling known as the Job Shop problem, let us define the main notions that we will use in the formulation:

Summary

Introduction

The Resource-Constrained Project Scheduling Problem (RCPSP) has many practical applications.One of the most obvious and direct applications of RCPSP is planning the fulfilment of planned orders at the manufacturing enterprise [1] that is sometimes named Job Shop. The Job Shop scheduling problem has two formal mathematical approaches [3]: continuous and discrete time problem settings. We research the continuous-time problem setting, analyze its bottlenecks, and evaluate effectiveness of several typical algorithms to find an optimal solution. The continuous-time Job Shop scheduling approach has been extensively researched and applied in different industrial spheres throughout the past 50 years. One of the most popular classical problem settings was formulated in [4] by Manne as a disjunctive model. This problem setting forms a basic system of restrictions evaluated by different computational algorithms depending on the particular practical features of the model used. The article [5] considers 69 papers dating back to the XX century, revealing the following main trends in Job Shop scheduling: Enumerating techniques

Methods

Results

Discussion

Conclusion