http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Thu, 23 May 2013 11:49:01 +0000 http://www.hindawi.com/isrn/or/2013/495378/ We present a nonmonotone trust region algorithm for nonlinear equality constrained optimization problems. In our algorithm, we use the average of the successive penalty function values to rectify the ratio of predicted reduction and the actual reduction. Compared with the existing nonmonotone trust region methods, our method is independent of the nonmonotone parameter. We establish the global convergence of the proposed algorithm and give the numerical tests to show the efficiency of the algorithm. Zhensheng Yu and Jinhong Yu Copyright © 2013 Zhensheng Yu and Jinhong Yu. All rights reserved. Tue, 23 Apr 2013 15:50:24 +0000 http://www.hindawi.com/isrn/or/2013/203032/ Two difficulties arise when solving the set covering problem (SCP) with metaheuristic approaches: solution infeasibility and set redundancy. In this paper, we first present a review and analysis of the heuristic approaches that have been used in the literature to address these difficulties. We then present a new formulation that can be used to solve the SCP as an unconstrained optimization problem and that eliminates the need to address the infeasibility and set redundancy issues. We show that all local optimums with respect to the new formulation and a 1-flip neighbourhood structure are feasible and free of redundant sets. In addition, we adapt an existing greedy heuristic for the SCP to the new formulation and compare the adapted heuristic to the original heuristic using 88 known test problems for the SCP. Computational results show that the adapted heuristic finds better results than the original heuristic on most of the test problems in shorter computation times. Nehme Bilal, Philippe Galinier, and Francois Guibault Copyright © 2013 Nehme Bilal et al. All rights reserved. Thu, 18 Apr 2013 16:04:08 +0000 http://www.hindawi.com/isrn/or/2013/738270/ Although a smoothly running supply chain is ideal, the reality is to deal with imperfectness in transportations. This paper tries to propose a mathematical model for a supply chain under the effect of unexpected disruptions in transport. Supplier offers the retailer a trade credit period and the retailer in turn offers his customers a permissible delay period. The retailer offers his customers a credit period and he receives the revenue from to , where is the cycle time at the retailer. Under this situation, the three cases such as , , and are discussed. An EPQ-based model is established and retailer's optimal replenishment policy is obtained through mathematical theorems. Finally, numerical examples and sensitivity analysis are presented to felicitate the proposed model. A. Thangam Copyright © 2013 A. Thangam. All rights reserved. Tue, 16 Apr 2013 13:09:37 +0000 http://www.hindawi.com/isrn/or/2013/393482/ Orthogonal distance regression is arguably the most common criterion for fitting a model to data with errors in the observations. It is not appropriate to force the distances to be orthogonal, when angular information is available about the measured data points. We consider here a natural generalization of a particular formulation of that problem which involves the replacement of norm by norm. This criterion may be a more appropriate one in the context of accept/reject decisions for manufacture parts. For distance regression with bound constraints, we give a smoothing Newton method which uses cubic spline and aggregate function, to smooth max function. The main spline smoothing technique uses a smooth cubic spline instead of max function and only few components in the max function are computed; hence it acts also as an active set technique, so it is more efficient for the problem with large amounts of measured data. Numerical tests in comparison to some other methods show that the new method is very efficient. Li Dong and Bo Yu Copyright © 2013 Li Dong and Bo Yu. All rights reserved. Thu, 04 Apr 2013 09:59:40 +0000 http://www.hindawi.com/isrn/or/2013/631427/ Some seasonal products have limited sales season, and the demand of such products over the sales season is of increasing-steady-decreasing type. Customers are highly sensitive to the prices of the products. In such situation, adjustment of unit selling price is needed to accelerate inventory depletion rate and for determining order quantity for the sales season. In this paper, we focus on the issue by jointly determining optimal unit selling prices and optimal lot size over the sales season. Unlike the conventional inventory models with pricing strategy, which were restricted to prespecified pricing cycle lengths, that is, fixed number of price changes over the time horizon, we allow the number of price changes to be a decision variable. The mathematical model is developed and existence of optimal solution is verified. A solution procedure is developed to determine optimal prices, optimal number of pricing cycles, and optimal lot size. The model is illustrated by a numerical example. Sensitivity analysis of the model is also carried out. S. Panda and S. Saha Copyright © 2013 S. Panda and S. Saha. All rights reserved. Wed, 27 Mar 2013 11:45:09 +0000 http://www.hindawi.com/isrn/or/2013/230717/ Firstly, we give the Karush-Kuhn-Tucker (KKT) optimality condition of primal problem and introduce Jordan algebra simply. On the basis of Jordan algebra, we extend smoothing Fischer-Burmeister (F-B) function to Jordan algebra and make the complementarity condition smoothing. So the first-order optimization condition can be reformed to a nonlinear system. Secondly, we use the mixed line search quasi-Newton method to solve this nonlinear system. Finally, we prove the globally and locally superlinear convergence of the algorithm. Zhuqing Gui, Chunyan Hu, and Zhibin Zhu Copyright © 2013 Zhuqing Gui et al. All rights reserved.