A Generalized MILP Formulation for the Period-Aggregated Resource Leveling Problem with Variable Job Duration

Olga Battaïa,Alain Haït,Ilia Tarasov

doi:10.3390/a13010006

Abstract

We study a resource leveling problem with variable job duration. The considered problem includes both scheduling and resource management decisions. The planning horizon is fixed and separated into a set of time periods of equal length. There are several types of resources and their amount varies from one period to another. There is a set of jobs. For each job, a fixed volume of work has to be completed without any preemption while using different resources. If necessary, extra resources can be used at additional costs during each time period. The optimization goal is to minimize the total overload costs required for the execution of all jobs by the given deadline. The decision variables specify the starting time of each job, the duration of the job and the resource amount assigned to the job during each period (it may vary over periods). We propose a new generalized mathematical formulation for this optimization problem. The formulation is compared with existing approaches from the literature. Theoretical study and computational experiments show that our approach provides more flexible resource allocation resulting in better final solutions.

Highlights

In the field of operations research, project management remains a topic of intensive research from various angles such as scheduling and resource allocation
We focus on the resource leveling problem with several practical enhancements
We propose a new mathematical formulation for a resource leveling problem with a variable duration of jobs

Summary

Introduction

In the field of operations research, project management remains a topic of intensive research from various angles such as scheduling and resource allocation. The resource leveling model with the overload cost and overlapping of jobs with precedence relations was presented by Baydoun et al [10] with a focus on different overlapping rules such as overlapping after implementation of some essential predecessor part. We follow these ideas and study the generalization of models presented by Baydoun et al [10]. The main difference could be presented in the following way In these papers, there is one decision variable (denoted as assigned workload [10] or the fraction [16] of activity in a period) describing the progress made by a given job in a given period, and it defines the requirement for each resource type.

Problem Parameters

Generalized Model Description

Scheduling Constraints

Resource Allocations Constraints and Objective Function

Reduction of Variable Domains

Best Scheduling Constraints Formulation

Structural Model Compliance

Solution Quality

Reasons to Use the Generalized Model

Discrete Resource Case

Objective

Conclusions