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

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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 alpha -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, AVAILABLE-TO-PROMISE, SHELF-LIFE, FUZZY, OPTIMIZATION, PRODUCT

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MLA
Grillo, H., et al. “Possibilistic Compositions and State Functions : Application to the Order Promising Process for Perishables.” INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, vol. 57, no. 22, 2019, pp. 7006–31.
APA
Grillo, H., Alemany, M., Ortiz, A., & De Baets, B. (2019). Possibilistic compositions and state functions : application to the order promising process for perishables. INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, 57(22), 7006–7031.
Chicago author-date
Grillo, H, MME Alemany, A Ortiz, and Bernard De Baets. 2019. “Possibilistic Compositions and State Functions : Application to the Order Promising Process for Perishables.” INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 57 (22): 7006–31.
Chicago author-date (all authors)
Grillo, H, MME Alemany, A Ortiz, and Bernard De Baets. 2019. “Possibilistic Compositions and State Functions : Application to the Order Promising Process for Perishables.” INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 57 (22): 7006–7031.
Vancouver
1.
Grillo H, Alemany M, Ortiz A, De Baets B. Possibilistic compositions and state functions : application to the order promising process for perishables. INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH. 2019;57(22):7006–31.
IEEE
[1]
H. Grillo, M. Alemany, A. Ortiz, and B. De Baets, “Possibilistic compositions and state functions : application to the order promising process for perishables,” INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, vol. 57, no. 22, pp. 7006–7031, 2019.
@article{8636553,
  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 alpha -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.},
  author       = {Grillo, H and Alemany, MME and Ortiz, A and De Baets, Bernard},
  issn         = {0020-7543},
  journal      = {INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH},
  keywords     = {composition of possibilistic variables,state function,ageing function,order promising process,perishability,lack of homogeneity in the product,uncertainty,AVAILABLE-TO-PROMISE,SHELF-LIFE,FUZZY,OPTIMIZATION,PRODUCT},
  language     = {eng},
  number       = {22},
  pages        = {7006--7031},
  title        = {Possibilistic compositions and state functions : application to the order promising process for perishables},
  url          = {http://dx.doi.org/10.1080/00207543.2019.1574039},
  volume       = {57},
  year         = {2019},
}

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