Higher-Order optimality conditions for set-valued optimization

2007-2008 > Academic research: refereed > Publication in refereed journa

Second-order necessary conditions of the Kuhn-Tucker type in multiobjective programming problems

In this paper, we are concerned with a multiobjective programming problem with inequality constraints. We develop second-order necessary condition of the Kuhn-Tucker type for effciency and prove that the condition holds under a. constraint qualification. Moreover, we give some conditions which ensure that the constraint qua,lifica.tion holds

Sufficient conditions and duality for multiobjective variational problems with generalized B-invexity

In this paper, we consider the multiobjective variational problem. We propose a class of generalized B-type I vector-valued functions and use this concept to establish sufficient optimality conditions and mixed type duality result

Analysis of the Single-Vehicle Cyclic Inventory Routing Problem

The single-vehicle cyclic inventory routing problem (SV-CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer, selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each, and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximized while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this paper, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV-CIRP.Inventory-Routing, Nonlinear Mixed Integer Programming, Exact Algorithms.