Tamás Hajba

37115531500

Publications - 8

MILP models of a patient transportation problem

Tamás Hajba Adrian Horváth Martin Tóth

Publication Name: Central European Journal of Operations Research

Publication Date: 2024-12-01

Volume: 32

Issue: 4

Page Range: 903-922

Description:

With ageing societies and increasing number of patients, there is a growing need for quality services that help transporting non-urgent patients to hospitals. In logistics, patient transportation problems are usually modeled as a dial-a-ride problem. In a Dial-a-Ride problem, a fleet of vehicles is providing the delivery services between the loading points and the delivery destinations. The demands are known in advance. In most cases the total travel distance of the vehicles is to be minimized. In this paper, we consider a specific dial-a-ride problem, where a single vehicle is used to transport patients to the same hospital. In determining the optimal route, the multiple and different travel needs of patients, such as their maximum travel time, are also taken into consideration. We introduce 4 different mixed integer linear programming models of the routing problem. Finally, the efficiency of the four models was compared using some real-life problems by solving them with a commercial solver.

Open Access: Yes

DOI: 10.1007/s10100-023-00902-z

A MILP approach combined with clustering to solve a special petrol station replenishment problem

Tamás Hajba Bálint Psenák Dániel Heitz Zoltán Horváth

Publication Name: Central European Journal of Operations Research

Publication Date: 2024-03-01

Volume: 32

Issue: 1

Page Range: 95-107

Description:

Vehicle routing problem is a well-known optimization problem in the logistics area. A special case of the vehicle routing problem is the station replenishment problem in which different types of fuel types have to be transported from the depots to the customers. In this paper we study the replenishment problem of a European petrol company. The problem contains several additional constraints such as time windows, different sized compartment vehicles, and restrictions on the vehicles that can serve a customer. We introduce a mixed integer linear programming model of the problem. To reduce the size complexity of the MILP model the customers are clustered and, based on the clusters, additional constraints are added to the MILP model. The resulting MILP model is tested on real problems of the company. The results show that combining the MILP model with clustering improves the effectiveness of the model.

Open Access: Yes

DOI: 10.1007/s10100-023-00849-1

MILP models for the optimization of real production lines

Tamás Hajba Zoltán Horváth

Publication Name: Central European Journal of Operations Research

Publication Date: 2015-12-01

Volume: 23

Issue: 4

Page Range: 899-912

Description:

A special class of the permutation flow shop problems (PFSPs) with makespan minimization which contains repeated jobs, limited buffer sizes between the machines and fixed number of palettes that carry the jobs on the production line is introduced in this paper. We define the related PB-R-PFSP, the Permutation with Repetition Flow Shop Problem with Palettes and Buffers, and construct new mixed integer linear programming (MILP) models for this problem. The effectiveness of the MILP models and the influence of the number of palettes and buffers on the problems are investigated experimentally.

Open Access: Yes

DOI: 10.1007/s10100-014-0337-8

New effective MILP models for PFSPs arising from real applications

Tamás Hajba Zoltán Horváth

Publication Name: Central European Journal of Operations Research

Publication Date: 2013-12-01

Volume: 21

Issue: 4

Page Range: 729-744

Description:

Permutation flow shop problems (PFSPs) with makespan minimization that model production lines working in industry often have some special features: they are typically large-scale and the jobs can be sorted into types so that jobs of the same type have equal processing time values at each machine. We define the related R-PFSP, the Permutation with Repetition Flow Shop Problem, which is of less complexity if the number of types is bounded. Moreover, a subproblem set of R-PFSPs, the RL-PFSP is considered too, where only those permutations are in the design space in which subsequent tuples of a certain size contain jobs of the same type. We construct adequate new MILP models for R-PFSPs and RL-PFSPs and investigate their effectiveness experimentally. We demonstrate that via our new MILP models significantly larger problems can be solved than via the classical MILP models. © 2012 Springer-Verlag.

Open Access: Yes

DOI: 10.1007/s10100-012-0263-6

Solution of the convex programming problem via second order differential equation system

Tamás Hajba M. Kovács

Publication Name: Miskolc Mathematical Notes

Publication Date: 2012-01-01

Volume: 13

Issue: 1

Page Range: 23-37

Description:

In this paper we investigate a family of second order differential equations which can be considered as the continuous versions of the Fletcher-Reeves iteration for minimization applied to a regularized and penalized convex programming problem. We show that synchronizing the parameter functions of the differential equation the stationary limit point of the trajectories is the minimal norm solution of the given convex programming problem. © 2012 Miskolc University Press.

Open Access: Yes

DOI: 10.18514/mmn.2012.327

Optimizing second-order differential equation systems

Tamás Hajba

Publication Name: Electronic Journal of Differential Equations

Publication Date: 2011-05-09

Volume: 2011

Issue: Unknown

Page Range: 1-16

Description:

In this article we study some continuous versions of the Fletcher-Reeves iteration for minimization described by a system of second-order differential equations. This problem has been studied in earlier papers [19, 20] under the assumption that the minimizing function is strongly convex. Now instead of the strong convexity, only the convexity of the minimizing function will be required. We will use the Tikhonov regularization [28, 29] to obtain the minimal norm solution as the asymptotically stable limit point of the trajectories. c 2011 Texas State University - San Marcos.

Open Access: Yes

DOI: DOI not available

Sustainability in Manufacturing: MILP Models of a Production Line Optimization Problem

Tamás Hajba

Publication Name: Chemical Engineering Transactions

Publication Date: 2025-01-01

Volume: 121

Issue: Unknown

Page Range: 55-60

Description:

In modern factories, the optimization of production lines is essential to reduce energy consumption and costs. A well-known model of production line optimization is the Permutation Flow Shop Problem (PFSP) with makespan minimization. PFSP instances arising in industry often have some special features: the problem may contain jobs whose processing times are equal on every machine. Such jobs are said to be of the same type. Due to technological reasons, some of the permutations may be forbidden. For example, only those job permutations are allowed in which, for each job type, the length of a maximal block of jobs from that type is divisible by a prescribed number (the lot size of that type). Considering these features, this paper introduces a generalization of the Permutation Flow Shop with Repetition and Lot Size Problem, in which different types of jobs have different lot sizes. We present two new mixed integer linear programming formulations of the problem and compare their effectiveness on a set of benchmark problems. Both models found the optimal solution within a few seconds for all problem instances involving 10 machines, 100 jobs, and five different types. These results show that even large-scale problems containing a small number of different jobs can be solved using these models.

Open Access: Yes

DOI: 10.3303/CET25121010

OPTIMIZING PATIENT TRANSPORT UNDER INFECTION CONTROL CONSTRAINTS: A MILP-BASED DIAL-A-RIDE APPROACH

Tamás Hajba Adrian Horváth Martin Tóth

Publication Name: Communications Scientific Letters of the University of Zilina

Publication Date: 2026-01-01

Volume: 28

Issue: 1

Page Range: E13-E20

Description:

With aging populations and rising healthcare demands, efficient patient transportation has become a critical challenge, particularly in the context of infection control. In this paper an extended mixed-integer linear programming (MILP) model for optimizing patient transport in urban environments is presented, with a focus on the separate transportation of infectious and non-infectious individuals. The model incorporates time windows, maximum allowable ride durations, and mandatory vehicle disinfection requirements. Experimental results obtained using CPLEX demonstrate that incorporating infection control measures significantly influences both route planning and computational complexity. The proposed approach provides a scalable foundation for future multi-vehicle extensions and cost-based optimization strategies.

Open Access: Yes

DOI: 10.26552/com.C.2026.008