Mixed Integer Nonlinear Mathematical Model Research Articles

A bi-objective multi-period series-parallel inventory-redundancy allocation problem with time value of money and inflation considerations

A large number of existing research studies on reliability redundancy allocation problems do not take into consideration the time value of the money and the inflations costs associated with the component inventories. In this study, we formulate a multi-component multi-period series-parallel inventory redundancy allocation problem (SPIRAP) as a mixed-integer nonlinear mathematical model where: (a) the costs are calculated by considering the time value of money and inflation rates; and (b) the total warehouse capacity to store the components, the total budget to purchase the components and the truck capacity are subject to constraints. The primary goal in this study is to find the optimal order quantity of the components for each subsystem in each period such that the total inventory costs are minimized and the system reliability is maximized, concurrently. A controlled elitism non-dominated ranked genetic algorithm (CE-NRGA), a NSGA-II, and a multi-objective particle swarm optimization (MOPSO) are presented to solve the proposed SPIRAP. A series of numerical examples are used to demonstrate the applicability and exhibit the efficacy of the procedures and algorithms. The results reveal that the CE-NRGA outperforms both NSGA-II and MOPSO.

Vessel scheduling in liner shipping: Modeling transport of perishable assets

International seaborne containerized trade significantly increased over the last years. Some assets transported in a containerized form by vessels are perishable in nature. Perishable assets deteriorate due to certain operational and environmental factors. This paper proposes a novel mixed integer non-linear mathematical model for the vessel scheduling problem in a liner shipping route with perishable assets, which explicitly captures decay of perishable assets on board the vessels. The objective aims to minimize the total route service cost, including the asset decay cost. The original non-linear mathematical model is linearized using a set of piecewise linear secant approximations. CPLEX is used to solve the linearized mathematical model. Numerical experiments are conducted for the French Asia Line 1 route, served by CMA CGM liner shipping company, to evaluate performance of the suggested solution approach and reveal some important managerial insights. Results demonstrate that the developed mathematical model can serve as an effective planning tool for liner shipping companies in designing efficient vessel schedules and reducing decay of perishable assets on board the vessels.

Solving multifacility Huff location models on networks using metaheuristic and exact approaches

In this paper we consider multifacility Huff facility location problem on networks. First, we introduce a slight modification of the existing mixed integer nonlinear mathematical model and confirm its validity by using the solver for nonlinear optimization, KNITRO. Second, since the problem is NP-hard, we develop three methods that are based on three metaheuristic principles: Variable Neighborhood Search, Simulated Annealing, and Multi-Start Local Search. Based on extensive computational experiments on large size instances (up to 800 customers and 100 potential facilities), it appears that VNS based heuristic outperforms the other two proposed methods.

The green vessel schedule design problem: consideration of emissions constraints

The fluctuating demand of international seaborne trade, overcapacity, and increasing attention to environmental issues force liner shipping companies to improve efficiency of their operations, while complying with the established emissions limitations. This paper proposes a mathematical model for the green vessel scheduling problem, imposing constraints on emissions produced by a vessel at each voyage leg of the liner shipping route. The original mixed integer non-linear mathematical model is linearized and solved efficiently using CPLEX. Numerical experiments are conducted to demonstrate changes in the vessel schedule that a liner shipping company has to make for a given shipping route, when emissions constraints are imposed.

Multi-objective parallel machine scheduling problem with job deterioration and learning effect under fuzzy environment

The current paper investigates a non-identical parallel machine multi-objective scheduling problem in which both the deterioration and learning effects have been considered. Due to uncertainty of the parameters in real-world systems, processing times and due dates of jobs are represented here with triangular fuzzy numbers. Using the credibility measure, a nonlinear mathematical model is provided based on fuzzy chance-constrained programming (FCCP) with the aim to minimize two objective functions, namely total earliness/tardiness (ET) and maximum completion time of jobs (makespan). Since it is a mixed integer nonlinear mathematical model, there is no guarantee that the solution will obtain a global optimum. Therefore, a multi-objective branch and bound algorithm is provided by introducing an effective lower bound in order to obtain a Pareto optimal front. Computational results show that the algorithm proposed is especially useful to solve large-scale problems.

A tradeoff model for green supply chain planning:A leanness-versus-greenness analysis

This article presents a tactical supply chain planning model that can be used to investigate tradeoffs between cost and environmental degradation including carbon emissions, energy consumption and waste generation. The proposed model also incorporates other aspects of real world supply chains such as multiple transport lot sizing and flexible holding capacity of warehouses. A solution methodology, the Nested Integrated Cross-Entropy (NICE) method, is developed to solve the proposed mixed-integer nonlinear mathematical model. The application of the model and solution method is investigated in an actual case problem. Analysis of the numerical results focuses on investigating the relationship between lean practices and green outcomes. We find that (1) not all lean interventions at the tactical supply chain planning level result in green benefits, and (2) a flexible supply chain is the greenest and most efficient alternative when compared to strictly lean and centralized situations.

Reconfigurable Dynamic Cellular Manufacturing System: A New Bi-Objective Mathematical Model

Dynamic Cell Formation Problem (DCFP) seeks to cope with variation in part mix and demands using machine relocation, replication, and removing; whilst from practical point of view it is too hard to move machines between cells or invest on machine replication. To cope with this deficiency, this paper addresses Reconfigurable Dynamic Cell Formation Problem (RDCFP) in which machine modification is conducted instead of their relocation or replication in order to enhance machine capabilities to process wider range of production tasks. In this regard, a mixed integer nonlinear mathematical model is proposed, which is NP-hard. To cope with the proposed model’s intractability, an Imperialist Competitive Algorithm (ICA) is developed, whose obtained results are compared with those of Genetic Algorithm’s (GA’s), showing superiority and outperformance of the developed ICA.

Effects of Integration on the Cost Reduction in Distribution Network Design for Perishable Products

Perishable products, which include medical and pharmaceutical items as well as food products, are quite common in commerce and industries. Developing efficient network designs for storage and distribution of perishable products plays a prominent role in the cost and quality of these products. This paper aims to investigate and analyze the impact of applying an integrated approach for network design of perishable products. For this purpose, the problem has been formulated as a mixed integer nonlinear mathematical model that integrates inventory control and facility location decisions. To solve the integrated model, a memetic algorithm (MA) is developed in this study. For verification of the proposed algorithm, its results are compared with the results of an adapted Lagrangian relaxation heuristic algorithm from the literature. Moreover, sensitivity analysis of the main parameters of the model is conducted to compare the results of the integrated approach with a decoupled method. The results show that as the products become more perishable, application of an integrated method becomes more reasonable in comparison with the decoupled one.

Introducing a mixed-integer non-linear fuzzy model for risk management in designing supply chain networks

Nowadays, supply chains play an inevitable role in prompt handling of varying customers’ needs. Administration of a successful supply chain depends on how efficiently the network design is accomplished. Therefore, a supply chain network design problem is considered in this paper. The network addresses an uncertain environment threatened by different risk sources in order to captivate the real world conditions. A mixed-integer non-linear mathematical model is developed in which the uncertainties are represented by the fuzzy set theory. Benders decomposition is then applied to solve the proposed problem; consequently, the model is transformed into a mixed-integer one. Moreover, an interactive resolution method is applied to provide the decision maker with alternative decision plans in regard to different satisfaction degrees. Finally, the accuracy of the proposed model is checked by sensitivity analysis test and its performance is considered by different numerical examples.

Environmentally conscious design of chemical processes and products: Multi-optimization method

This paper presents an environmentally conscious integrated methodology for design and optimization of chemical process especially for separation process, whose energy consumption occupies more than 70% of the whole process. The methodology incorporates environmental factors into the chemical process synthesis at the initial design stage, which is totally different with the traditional end-of-pipe treatment method. Firstly, one rigorous model for simulation of multi-stages and multi-components separation process was developed, and based on our proposed environmental impact assessment method, the calculation methods of the reasonable economic and environment objective are constructed. Then one multi-objective mixed integer non-linear mathematical model was established by considering environmental and economic factors. Finally, the high non-linear model was solved by multi-objective evolutionary algorithm (non-dominated sorting genetic algorithm). It is often difficult to find an optimum for a process that satisfies both economic and environmental objectives simultaneously. Normally, an arrangement of optimal solutions is obtained, which forms a non-inferior set. Identifying the optimum from this non-inferior set is subjective, depending on the preference of decision makers. In this paper, technique for order preference by similarity to ideal solution (TOPSIS) for identifying the set of optimal parameters is developed and used at the decision-making step, in which the preference relation for the decision-maker over the objectives is adopted by trade-off information between objectives. The proposed methodology was highlighted through two industrialized processes, dimethyl carbonate production processes by pressure-swing distillation and extraction distillation process, respectively.

Environmental Benign Design of DMC Production Process

This paper presents an integrated methodology for design and optimization of chemical process based on the green chemical principles, which inherently incorporates environmental factors into the chemical process synthesis. Firstly, the process environmental impact assessment method (EIA) is proposed, which includes two parts, the environmental impact of material flow and that of energy. Secondly, a multi-objective mixed integer non-linear mathematical model was established by considering environmental and economic factors. Finally, the high nonlinear model was solved by multi-objective evolutionary algorithm (non-dominated sorting genetic algorithm or NSGAII). The proposed methodology was highlighted through two DMC production processes, pressure-swing distillation and extraction distillation process.