In this paper, a bi-objective model is presented for dynamic and integrated network design of a new entrant competitive closed-loop supply chain. To consider dynamism and integration in the network design problem, multiple long-term periods are regarded during planning horizon, so that each long-term period includes several short-term periods. Furthermore, a chain to chain competition between t...

This paper presents a competitive supply chain network design problem in which one, two, or three supply chains are planning to enter the price-dependent markets simultaneously in uncertain environments and decide to set the prices and shape their networks. The chains produce competitive products either identical or highly substitutable. Fuzzy multi-level mixed integer programming is used to mo...

In 1986, W. S. Griffith [2] proposed reliability model and described a Markov chain approach for computing the reliability in the system. F. K. Hwang and S. Papastavridis gave a closed-form formula for this reliability in 1991, by counting the number of n-dimensional binary vectors containing exactly k non-overlapping m-tuples of consecutive ones. In 1988, T. M. Apostol [1] established recursiv...