multiple objective optimization

Data uncertainty and multiple conflicting objectives are two crucial issues that the Decision Makers (DMs) must handle in making Aggregate Production Planning (APP) decisions in real practice. In order to address these two-mentioned issues, this study presents a multi-objective multi-product multi-period APP problem in an uncertain environment. The model strives to minimize the total costs of the APP plan, total changing rate in workforce levels, and total holding inventory and backorder quantities simultaneously through the Robust Possibilistic Chance-Constrained Programming (RPCCP) optimization approach. In this integrated approach, the RPCCP is applied for handling uncertain data. The RPCCP can not only handle any fuzzy position in the fuzzy model but also control the robustness of optimality and feasibility of the fuzzy model. Then, an Augmented Epsilon-Constraint (AUGMECON) technique is used to cope with multiple conflicting objectives. The AUGMECON technique can produce exact Pareto optimal solutions, which offer the DMs different selections to assess against conflicting objectives. Next, an industrial case study is provided to validate the applicability and effectiveness of the proposed methodology. The obtained outcomes indicate that the proposed RPCCP model outperforms the Possibilistic Chance-Constrained Programming (PCCP) model in terms of interested performance measurements (i.e., average and standard deviation of the objective function). In addition, a set of strong Pareto optimal solutions can be generated to accommodate alternative selections according to the DM’s preferences. Finally, by applying the Max-Min method, the best compromised (trade-off) solution is determined through a comparison among the attained Pareto solutions.

In this article, we propose a special case of two-echelon location-routing problem (2E-LRP) in cash-in-transit (CIT) sector. To tackle this realistic problem and to make the model applicable, a rich LRP considering several existing real-life variants and characteristics named BO-2E-PCLRPSD-TW including different objective functions, multiple echelons, multiple periods, capacitated vehicles, distribution centers and automated teller machines (ATMs), different type of vehicles in each echelon, single-depot with different time windows is presented. Since, routing plans in the CIT sector ought to be safe and efficient, we consider the minimization of total transportation risk and cost simultaneously as objective functions. Then, we formulate such complex problem in mathematical mixed integer linear programming (MMILP). To validate the presented model and the formulation and to solve the problem, the latest version of ε-constraint method namely AUGMECON2 is applied. This method is especially efficient for solving multi objective integer programing (MOIP) problems and provides the exact Pareto fronts. Results substantiate the suitability of the model and the formulation.