Abstract
A two-echelon supply chain is studied that involves a retailer who faces demand from two or more market segments and enable to set different prices and marketing expenditures and a supplier who desires to find optimal number of shipments through an integrated system. A new mixed-integer non-linear fractional programming (MINLFP) model is developed. In order to solve the resultant MINLFP model, the constrained non-linear programming model is reformulated as an unconstrained one using penalty terms. Two meta-heuristics, namely simulated annealing (SA) and imperialist competitive algorithm (ICA), are applied to solve the relaxed unconstrained model. Numerical results show that ICA can reach better solutions in comparison with SA. However, SA has the ability of providing more robust solutions which are converged to a good solution. The chapter concludes with superiority of SA.
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