Load Optimizer in Containers

We were faced with the practical problem of packing tubes in a container, considering that they may be put inside other tubes in a recursive fashion. A variant of the greedy randomized adaptive search procedure is proposed for tackling this problem, and its performance assessed in a set of benchmark instances.

Challenge overview

The FERSIL company (Oliveira de Azeméis, Portugal), a manufacturer of plastic pipes, manually calculated the distribution of the various tubes part of each customer order within a container dimension. This process was carried out by highly skilled and qualified employees by trial and error strategy, with the help of a spreadsheet program. Requiring great response times to pack customers’ orders, this process had high operating costs. After a thorough study of the requirements, an optimization algorithm for container packaging was developed along with its computational implementation. The approach allowed for an automatic solution for the above-mentioned problem.

CMUP research centre and GEMAC

The work was undertaken by the Office of Statistics, Modeling and Computer Applications (GEMAC), which is a service rendering office issued from a partnership between the Mathematics Center of the University of Porto (CMUP) and the Mathematics Department of the Science Faculty (FCUP) of the University of Porto (UP). The GEMAC provides consultancy in Applied Statistics Analysis (Employee Engagement Satisfaction Models, Retail Market Basket Analysis, Applied Survival Analysis, Data Mining) and in Mathematical Modeling and Optimization (Operational Research, Forecast Models, Production Planning, Risk Analysis). It offers short-term training in its areas of competence, taught by specialists, following active and dynamic methodologies, adequate to the needs of the business staff and the academic community.

Implementation of the initiative

  1. Preliminary Studies: characterization of the real needs of the promoters and specification of the software modes of operation, methods and programs to the workflow deliver and further integration into the Fersil Information System.
  2. Study and Distribution Algorithm Development: Mathematical modelling and development of routines for packaging optimization of cylinders into cargo containers. The approach was based on GRASP optimization techniques (random and greedy adaptive search procedure). The codes, developed in Python, implement 3D box packing algorithms, and tube and tube telescoping.
  3. Development of the telescoping module based on the technical documentation restrictions.
  4. Software installation on the Fersil computer Production System and final tests.

Mathematical problem

Recursive circle packing problems (RCPP) has its origins in the tube industry, where shipping costs represent an important fraction of the total product delivery cost. Tubes are produced in a continuous extraction machine and cut to the length of the container inside which they will be shipped. Before being placed in the container they may be inserted inside other thicker tubes, so container space is maximized — a process named telescoping. As all the tubes occupy the full container length, maximizing container load is equivalent to maximizing the area filled with circles (or, more precisely, rings/annuli) in a section of the container. This problem is more general than circle packing, which is known to be NP. In this project a heuristic method was proposed, which has proved to be able to produce very good solutions for practical purposes.


Results and achievements

The implementation of this cargo optimization program to increase, in the short term, the efficiency of the processes associated with cargo budgeting and dispatch, resulted both in a significant cost reduction of these processes and in substantial improvements in the quality of services provided to customers, increasing considerably their level of satisfaction. The impact of this solution for both Commercial and Logistics Fersil’s departments was so relevant that Fersil recognizes that this application is a key instrument for the competitiveness of the company.

The transfer of scientific and technical knowledge with strategic collaboration of CMUP at FCUP ensures the quality and reliability of the developed solution and guarantees its practical applicability. On the other hand, CMUP has developed expertise in that particular research area and has deployed practical application ready and available for business market.


João Nuno Tavares
CMUP – Centre for Mathematics, University of Porto
Mathematics Department, Sciences Faculty, University of Porto
Rua do Campo Alegre s/n
4169-007 Porto
Email: jntavar@fc.up.pt
Site: http://cmup.fc.up.pt/cmup/cv/

João Pedro Pedroso
Departamento de Ciência dos Computadores, Faculdade de Ciências da Universidade do Porto
Rua do Campo Alegre s/n
4169-007 Porto
Email: jjpp@fc.up.pt
Site: http://www.dcc.fc.up.pt/~jpp/JPP/Welcome.html

Industrial partner: FERSIL PORTUGAL
Zona Industrial de Cesar, Rua das Matas
Cesar – Oliveira de Azeméis (Portugal)
Email: fersil@fersil.com
Site: http://www.fersil.com/

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