Here, we developed optimization models to minimize the cost to achieve a target SIL using

integer programming. Optimization Model I focused on component replacement to meet the SIL.

Most researchers applied the exact method such as

integer programming models to obtain an optimum solution to the problem.

Schrijver, Theory of Linear and

Integer Programming, John Wiley & Sons, 1998.

According to Table 2, it can be found that, compared with the traditional branch-and-bound algorithm, SDSA can effectively solve the hybrid

integer programming model SDSPM proposed for solving the shuttle tanker scheduling problem.

In this section, we describe the mixed

integer programming formulation of the PROP proposed by Amaral (2013b).

5 The Algorithms for Solving Neutrosophic

integer Programming Problem (NIPP)

Integer programming is a mathematical modeling technology that addresses problems of this kind by answering questions precisely, such as: "What is the fewest number of agents I can hire, in which groups, in which centers, and at what time of year to meet increased call volumes over the next 18 months?

(1) Based on the min-cost network model, we introduce a novel general mathematical

integer programming formulation for multiobject tracking.

Kim and Park further investigated QCSP by considering various interference possibilities between adjacent cranes and proposed a mixed

integer programming model to determine starting and ending times for each quay crane to serve each ship bay [3].

advanced an interval-fuzzy chance-constrained

integer programming (IFCIP) approach for dealing with uncertainties presented in terms of fuzzy sets, intervals, and random variables [11].

An indexed control method is proposed for RCS preallocation, and a 0-1

integer programming algorithm is designed for RCS control allocation in Section 4.

Ahmad: Second order symmetric duality for nonlinear minimax mixed

integer programming problems, Eur.