Monte Carlo simulation based performance analysis of supply chains

Since supply chain management is one of the most important management practices that impacts the financial results of services and companies, it is important to optimize and analyze the performance of supply chains. Simulation provides a way to get closer to real life complex situations and uses less simplifications and assumptions than needed with analytical solutions. Monte Carlo simulation based optimization and sensitivity analysis of supply chains can handle uncertainties and stochastic nature of the processes and to extract and visualize relationship among the decision variables and the Key Performance Indicators. We utilized our interactive simulator, SIMWARE, capable to simulate complex multi-echelon supply chains based on simple configurable connection of building blocks. A sensitivity analysis technique has been introduced to extract and visualize the relationships among the decision variables and key performance indicators. The proposed robust sensitivity analysis is based on an improved method used to extract gradients from Monte Carlo simulation. The extracted gradients (sensitivities) are visualized by a technique developed by the authors. The results illustrate that the sensitivity analysis tool is flexible enough to handle complex situations and straightforward and simple enough to be used for decision support.

Gabor Belvardi, Andras Kiraly, Tamas Varga, Zoltán Gyozsan, Janos Abonyi, Monte Carlo Simulation Based Performance Analysis Of Supply Chains, International Journal of Managing Value & Supply Chains, vol. 3, no. 2, June 2012.

Determining Optimal Stock Level In Multi-Echelon Supply Chains

Inventory control of Multi-echelon supply chains is a widely researched area. In most cases researchers choose analytic methods to analyze such logistics systems. Simulation is a very useful alternative for analyzing supply chain systems and a well-constructed model can provide a better approach and can give more realistic picture of the complex situation.

We introduced an interactive, configurable simulator to analyze stock levels in a complex supply chain. This new modeling approach (SIMWARE) is capable to simulate complex multi-echelon supply chains where the frequency of stock transfer between the individual levels of the supply chain can be optimized. The authors evaluate different optimization strategies and methods. The introduced SIMWARE method can be used to minimize the environmental impact of the supply chain by minimizing the transportation between the nodes of the supply chain hierarchy. The model provides an optimization methodology where the objective function is the total cost of the supply chain.

András Kiraly, Gabor Belvardi, Janos Abonyi, Determining Optimal StockLevel In Multi-Echelon Supply Chains, Hungarian Journal of Industrial Chemistry, Veszprem, vol. 39(1), 107-112, 2012.

Minimization of Off-Grade Production in Multisite Multiproduct Plants by Solving Multiple Traveling Salesman Problem

Continuous multiproduct plants allow the production of several products (product grades). During grade transitions off-spec products are produced. The economic losses and the environmental impact of these transitions are sequence dependent, so the amount of off-grade products can be minimized by scheduling the sequence of the production of different products. Applying parallel production sites (m) increases the flexibility of multiproduct plants. Since market demands are changing, the production cycles of these sites should be re-scheduled in certain intervals. Therefore, our task is to design m production cycles that contains all required products by minimizing the total length of grade transitions. Most production scheduling problems such as the one considered in this paper are NP-hard. Our goal is to solve realistic problem instances in no more than a couple of minutes. We show that this problem can be considered as a multiple traveling salesmen problem (mTSP), where the distances between the products are based on the time or costs of the grade transitions. The resulted mTSP has been solved by multi-chromosome based genetic algorithm. For demonstration purposes, we present an illustrative example. The results show that multiproduct multisite scheduling problems can be effectively handled as mTSPs, and the proposed problem-specific representation based genetic algorithm can be used in wide range of optimization problems.

Király A., Farsang B., Chován T., Christidou M., Karlopoulos E., Abonyi J., Minimization of Off-Grade Production in Multisite Multiproduct Plants by Solving Multiple Traveling Salesman Problem, CHEMICAL ENGINEERING TRANSACTIONS, 39. (2014) 1825-1830

Optimization of Multiple Traveling Salesmen Problem by a Novel Representation based Genetic Algorithm

The Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem that can be described as follows: given a fleet of vehicles with uniform capacity, a common depot, and several requests by the customers, find a route plan for the vehicles with overall minimum route cost (eg. distance traveled by vehicles), which service all the demands. It is well known that multiple Traveling Salesman Problem (mTSP) based algorithms can also be utilized in several VRPs by incorporating some additional constraints, it can be considered as a relaxation of the VRP, with the capacity restrictions removed. The mTSP is a generalization of the well known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. Because of the fact that TSP is already a complex, namely an NP-hard problem, heuristic optimization algorithms, like genetic algorithms (GAs) need to be taken into account. The extension of classical GA tools for mTSP is not a trivial problem, it requires special, interpretable encoding and genetic operators to ensure efficiency. We reviewed how genetic algorithms can be applied to solve these problems, and propose a novel, easily interpretable and problem-oriented representation and operators, that can easily handle constraints on the tour lengths, and the number of salesmen can vary during the evolution. The elaborated heuristic algorithm is demonstrated by a complete realistic example.

Andras Kiraly, Janos Abonyi, Optimization of Multiple Traveling SalesmenProblem by a Novel Representation based Genetic Algorithm, Intelligent Computational Optimization in Engineering, Mario Köppen, Gerald Schaefer, Ajith Abraham, Wien: Springer-Verlag, Springer Berlin Heidelberg, pp. 241-269, 2011. (ISBN: 9783642217043)

Redesign of the Supply of Mobile Mechanics based on a novel Genetic Optimization Algorithm using Google Maps API

If a mobile mechanic has to travel for material, productive time is lost. This paper presents a novel method to reduce activities regarding material handling with extending of serving locations. The design of the supply system can be considered as a complex combinatorial optimization problem, where the goal is to find a route plan with minimal route cost, which services all the demands from the central warehouses while satisfying the capacity and other constraints. We present a multi-chromosome technique for solving the  multiple Traveling Salesman Problem (mTSP). The new operators based on a problem-specific representation proved to be more effective in terms of flexibility, complexity and transparency, and also in efficiency than the previous methods. The proposed optimization algorithm was implemented in MATLAB and integrated with Google Maps to provide a complete framework for distance calculation, definition of the initial routes, and visualization. This integrated framework was successfully applied in the solution of a real logistic problem, in the supply of mobile mechanics at one of Hungary's biggest energy providers.

Andras Kiraly, Janos Abonyi: Redesign of the Supply of Mobile Mechanics based on a novel Genetic Optimization Algorithm using Google Maps API. Engineering Applications of Artificial Intelligence, 2014.