In this paper, a tactical Production-Distribution Planning (PDP) has been handled in a fuzzy and stochastic environment for supply chain systems (SCS) which has four echelons (suppliers, plants, warehouses, retailers) with multi-products, multi-transport paths, and multi-time periods. The mathematical model of fuzzy stochastic PDP is a NP-hard problem for large SCS because of the binary variables which determine the transportation paths between echelons of the SCS and cannot be solved by optimization packages. In this study, therefore, two new meta-heuristic algorithms have been developed for solving fuzzy stochastic PDP: Ant Colony Optimization (ACO) and Genetic Algorithm (GA). The proposed meta-heuristic algorithms are designed for route optimization in PDP and integrated with the GAMS optimization package in order to solve the remaining mathematical model which determines the other decisions in SCS, such as procurement decisions, production decisions, etc. The solution procedure in the literature has been extended by aggregating proposed meta-heuristic algorithms. The ACO and GA algorithms have been performed for test problems which are randomly generated. The results of the test problem showed that the both ACO and GA are capable to solve the NP-hard PDP for a big size SCS. However, GA produce better solutions than the ACO.

Airlines face the imperative of resource management to curtail costs, necessitating the solution of several optimization problems such as flight planning, fleet assignment, aircraft routing, and crew scheduling. These problems present some challenges. The first pertains to the common practice of addressing these problems independently, potentially leading to locally optimal outcomes due to their interconnected nature. The second challenge lies in the inherent uncertainty associated with parameters like demand and non-cruise time. On the other hand, airlines can employ a strategy known as codesharing, wherein they operate shared flights, in order to minimize these challenges. In this study, we introduce a novel mathematical model designed to optimize flight planning, fleet assignment, and aircraft routing decisions concurrently, while accommodating for codesharing. This model is formulated as a three-stage non-linear mixed-integer problem, with stochastic parameters representing the demand and non-cruise time. For smaller-scale problems, optimization software can effectively solve the model. However, as the number of flights increases, conventional software becomes inadequate. Moreover, considering a wide array of scenarios for stochastic parameters leads to more robust results; however, it is not enabled because of the limitations of optimization software. In this work, we introduce two new simulation-based metaheuristic algorithms for solving large-dimensional problems, collectively called “simheuristic.” These algorithms integrate the Monte Carlo simulation technique into Simulated Annealing and Cuckoo Search. We have applied these simheuristic algorithms to various problem samples of different flight sizes and scenarios. The results demonstrate the efficacy of our proposed modeling and solution approaches in efficiently addressing flight scheduling, fleet assignment, and aircraft routing problems within acceptable timeframes.

Production‐Distribution Problem (PDP) in Supply Chain Management (SCM) is an important tactical decision. One of the challenges in this decision is the size and complexity of supply chain system (SCS). On the other side, a tactical operation is a mid‐term plan for 6–12 months; therefore, it includes different types of uncertainties, which is the second challenge. In the literature, the uncertain parameters were modeled as stochastic or fuzzy. However, there are a few studies in the literature that handle stochastic and fuzzy uncertainties simultaneously in PDP. In this paper, the modeling and solution approaches of PDP which contain stochastic and fuzzy uncertainties simultaneously are investigated for a SCS that includes multiple suppliers, multiple products, multiple plants, multiple warehouses, multiple retailers, multiple transport paths, and multiple time periods, which, to the best of the author’s knowledge, is not handled in the literature. The PDP contains deterministic, fuzzy, fuzzy random, and random fuzzy parameters. To the best of the author’s knowledge, there is no study in the literature which considers all of them simultaneously in PDP. An analytic solution approach has been developed by using possibilistic programming and chance‐constrained programming approaches. The proposed modeling and solution approaches are implemented in a numerical example. The solution has shown that the proposed approaches successfully handled uncertainties and produce robust solutions for PDP.