Pricing decisions in a two-echelon decentralized supply chain using bi-level programming approach

Abstract Pricing is one of the major aspects of decision making in supply chain. In the previous works mostly a centralized environment is considered indicating the retailers cannot independently apply their decisions on the pricing strategy. Although in a two-echelon decentralized environment it may be possible that supply chain contributors have encountered with different market power situations which provide that some of them try to impose their interests in pricing and/or volume of the products. In such situations the leader-follower Stackelberg game or more specifically bi-level programming seems to be the best approach to overcome the problem. Furthermore, in this study we consider the impacts of disruption risk caused by foreign exchange uncertainty on pricing decisions in a multi-product two-echelon supply chain. Also it is assumed that the market is partitioned to domestic and international retailers with segmented market for each retailer. The purpose of this paper is to introduce decisions policy on the pricing such that the utility of both manufacturer and retailers is met. Since the proposed bi-level model is NP-hard, a simulated annealing method combining with Tabu search is proposed to solve the model. A numerical example is presented to investigate the effect of foreign exchange variation on the decision variables through different scenarios. The results from numerical example indicate that the international retailers are indifferent to the manufacture undergoes changes where the domestic retailers react to changes, dramatically

Un algoritmo basado en la búsqueda dispersa para resolver el problema de producción distribución de una cadena de suministro

En este trabajo nosotros consideramos el problema de planeación de producción y distribución de una cadena de suministro en una red, que consiste de un conjunto de centros de distribución que buscan dar servicio a un conjunto de minoristas, y dichos centros de distribución abastecidos por un conjunto de plantas, buscando minimizar los costos de transportación en la red y de operación en las plantas, basado en el problema propuesto por Herminia y Calvete en 2011. El problema es formulado como un programa matemático binivel donde el nivel superior (líder) consiste en fijar las rutas de distribución de productos enviados de los centros de distribución a los minoristas, satisfaciendo sus demandas sin exceder de un tiempo límite de duración de cada ruta. Por otro lado, en el nivel inferior (seguidor) se reciben las órdenes de cada centro de distribución y se deciden cuales plantas producirán estas órdenes satisfaciendo las demandas allí conjuntadas sin sobrepasar las capacidades de producción de las plantas. La función objetivo del nivel superior minimiza los costos incurridos en el envío de los productos desde los centros de distribución hacia los minoristas y los costos asociados al envío desde las plantas hasta los centros de distribución considerando un costo de descarga por artículo. En el nivel inferior se busca minimizar los costos de operación en las plantas. En este trabajo proponemos un algoritmo heurístico basado en el equilibrio de Stackelberg y la Búsqueda Dispersa. El algoritmo propuesto consiste en aplicar la búsqueda dispersa en las variables del nivel superior encontrando la mejor respuesta del nivel inferior para cada solución obtenida por la búsqueda dispersa obteniendo así un equilibrio entre estos dos niveles. Nuestro algoritmo ha mostrado ser competitivo y brinda buenos resultados comparados con los publicados por Herminia y Calvete en 2011

Three essays on multi-level optimization models and applications

The general form of a multi-level mathematical programming problem is a set of nested optimization problems, in which each level controls a series of decision variables independently. However, the value of decision variables may also impact the objective function of other levels. A two-level model is called a bilevel model and can be considered as a Stackelberg game with a leader and a follower. The leader anticipates the response of the follower and optimizes its objective function, and then the follower reacts to the leader\u27s action. The multi-level decision-making model has many real-world applications such as government decisions, energy policies, market economy, network design, etc. However, there is a lack of capable algorithms to solve medium and large scale these types of problems. The dissertation is devoted to both theoretical research and applications of multi-level mathematical programming models, which consists of three parts, each in a paper format. The first part studies the renewable energy portfolio under two major renewable energy policies. The potential competition for biomass for the growth of the renewable energy portfolio in the United States and other interactions between two policies over the next twenty years are investigated. This problem mainly has two levels of decision makers: the government/policy makers and biofuel producers/electricity generators/farmers. We focus on the lower-level problem to predict the amount of capacity expansions, fuel production, and power generation. In the second part, we address uncertainty over demand and lead time in a multi-stage mathematical programming problem. We propose a two-stage tri-level optimization model in the concept of rolling horizon approach to reducing the dimensionality of the multi-stage problem. In the third part of the dissertation, we introduce a new branch and bound algorithm to solve bilevel linear programming problems. The total time is reduced by solving a smaller relaxation problem in each node and decreasing the number of iterations. Computational experiments show that the proposed algorithm is faster than the existing ones

A tabu search based approach for solving a class of bilevel programming problems in chemical engineering

In this paper an approach based on the tabu search paradigm to tackle the bilevel programming problems is presented. The algorithm has been tested for a number of benchmark problems and the results obtained show superiority of the approach over the conventional methods in solving such problems