Possibilistic compositions and state functions: application to the order promising process for perishables

Abstract

In this paper, we propose the concepts of the composition of possibilistic variables and state functions. While in conventional compositional data analysis, the interdependent components of a deterministic vector must add up to a specific quantity, we consider such components as possibilistic variables. The concept of state function is intended to describe the state of a dynamic variable over time. If a state function is used to model decay in time, it is called the ageing function. We present a practical implementation of our concepts through the development of a model for a supply chain planning problem, specifically the order promising process for perishables. We use the composition of possibilistic variables to model the existence of different non-homogeneous products in a lot (sub-lots with lack of homogeneity in the product), and the ageing function to establish a shelf life-based pricing policy. To maintain a reasonable complexity and computational efficiency, we propose the procedure to obtain an equivalent interval representation based on α-cuts, allowing to include both concepts by means of linear mathematical programming. Practical experiments were conducted based on data of a Spanish supply chain dedicated to pack and distribute oranges and tangerines. The results validated the functionality of both, the compositions of possibilistic variables and ageing functions, showing also a very good performance in terms of the interpretation of a real problem with a good computational performance.

Keywords:

• composition of possibilistic variables
• state function
• ageing function
• order promising process
• perishability
• lack of homogeneity in the product
• uncertainty

Acknowledgments

We would also thank Dr. José De Jesús Arias García for useful discussions during the development of this work.

ORCID

H. Grillo http://orcid.org/0000-0001-8621-930X

M.M.E. Alemany http://orcid.org/0000-0002-0992-8441

A. Ortiz http://orcid.org/0000-0001-5690-0807

B. De Baets http://orcid.org/0000-0002-3876-620X

Additional information

Funding

This research has been supported by the Ministry of Science, Technology and Telecommunications, government of Costa Rica (MICITT), through the Program of Innovation and Human Capital for Competitiveness (PINN) (contract number PED-019-2015-1). We acknowledge the partial support of the project 691249, RUCAPS: “Enhancing and implementing knowledge based ICT solutions within high risk and uncertain conditions for agriculture production systems”, funded by the European Union’s research and innovation programme under the H2020 Marie Skłodowska-Curie Actions.