Robust Multi-Objective Sustainable Reverse Supply Chain Planning: An Application in the Steel Industry

In the design of the supply chain, the use of the returned products and their recycling in the production and consumption network is called reverse logistics. The proposed model aims to optimize the flow of materials in the supply chain network (SCN), and determine the amount and location of facilities and the planning of transportation in conditions of demand uncertainty. Thus, maximizing the total profit of operation, minimizing adverse environmental effects, and maximizing customer and supplier service levels have been considered as the main objectives. Accordingly, finding symmetry (balance) among the profit of operation, the environmental effects and customer and supplier service levels is considered in this research. To deal with the uncertainty of the model, scenario-based robust planning is employed alongside a meta-heuristic algorithm (NSGA-II) to solve the model with actual data from a case study of the steel industry in Iran. The results obtained from the model, solving and validating, compared with actual data indicated that the model could optimize the objectives seamlessly and determine the amount and location of the necessary facilities for the steel industry more appropriately.This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problem

Distributed Random Convex Programming via Constraints Consensus

This paper discusses distributed approaches for the solution of random convex programs (RCP). RCPs are convex optimization problems with a (usually large) number N of randomly extracted constraints; they arise in several applicative areas, especially in the context of decision under uncertainty, see [2],[3]. We here consider a setup in which instances of the random constraints (the scenario) are not held by a single centralized processing unit, but are distributed among different nodes of a network. Each node "sees" only a small subset of the constraints, and may communicate with neighbors. The objective is to make all nodes converge to the same solution as the centralized RCP problem. To this end, we develop two distributed algorithms that are variants of the constraints consensus algorithm [4],[5]: the active constraints consensus (ACC) algorithm, and the vertex constraints consensus (VCC) algorithm. We show that the ACC algorithm computes the overall optimal solution in finite time, and with almost surely bounded communication at each iteration. The VCC algorithm is instead tailored for the special case in which the constraint functions are convex also w.r.t. the uncertain parameters, and it computes the solution in a number of iterations bounded by the diameter of the communication graph. We further devise a variant of the VCC algorithm, namely quantized vertex constraints consensus (qVCC), to cope with the case in which communication bandwidth among processors is bounded. We discuss several applications of the proposed distributed techniques, including estimation, classification, and random model predictive control, and we present a numerical analysis of the performance of the proposed methods. As a complementary numerical result, we show that the parallel computation of the scenario solution using ACC algorithm significantly outperforms its centralized equivalent