Integrated Possibilistic Linear Programming with Beta-Skewness Degree for a Fuzzy Multi-Objective Aggregate Production Planning Problem Under Uncertain Environments

Abstract

This study proposes an improved Fuzzy Programming (FP) approach to optimise multi-objective Aggregate Production Planning (APP) problem under uncertain environments. The proposed approach integrates the concept of Possibilistic Linear Programming (PLP) with Beta-Skewness Degree that decision-makers can manipulate the best level of data fuzziness as well as maintain such fuzziness in the optimisation process (by not turning it to deterministic data too early). The effectiveness of the proposed approach is demonstrated through a case study by minimising the highest overall deviation from the ideal solution of total costs under imprecise operating costs, customer demand, labour level, and machine capacity. Our comparative result clearly shows that the obtained solution outperforms the solutions from traditional defuzzification methods. The proposed approach also helps decision-makers not only to know and optimise the most likely situation, but also realise the outcomes in the optimistic and the pessimistic business situations so that decision makers can prepare and take necessary actions for future uncertainty.

An Icon-Based Methodology for the Design of a Prototype of a Multi-Process, Multi-Product, Aggregated Production Planning Software

“…The icon-based methodology has the theoretical potential to be extended to more complex APP models, incorporating multiple objectives such as maximizing quality while minimizing costs (Galankashi et al 2022, [18]). It could also be applied to models using genetic algorithms to address seasonal demands under uncertainty conditions , [1]), the optimization of renewable energy under uncertainty conditions (Islam et al 2022, [15]), fuzzy programming (Sutthibutr et al 2020), [31], or workforce leveling considerations (Jang et al 2020, [33]). Exploring this potential would involve developing new icons to represent the desired implementations.…”

Evaluation of Technical Resilience and Its Estimation by the Least Squares Method

“…The data were centralized on different time intervals delimited to every ten faults that appeared (table 1). R0 represents the resilience scores over the time interval bounded by defects [1][2][3][4][5][6][7][8][9][10], R1 represents the resilience scores over the time interval determined by defects [11][12][13][14][15][16][17][18][19][20] and so on. The graphs of the values of the resilience function as a function of time for every ten defects that appeared in the system after the stabilization period of the technical system operation are presented in Figure 1.…”

“…The metrics used to calculate the resilience characteristic belong to complementary and very diversified fields: probabilistic [12], mathematical [13], Bayesian networks [14], statistical techniques [15], Monte Carlo simulation [5], fuzzy systems -relationships modelled by linguistic expressions and using fuzzy set theory [16]. Such a theory based on fuzzy mathematics constitutes support for the subjective or natural descriptors of the system characteristics and offers a methodology as natural as possible to allow the modelling of resilience from the design process of technical systems, [17]. The present paper proposes an application of a metric for technical resilience based on the least squares method.…”