ISRN Operations Research The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Discrete-Time State Dependent Bulk Service Queue with Multiple Vacations and Changeover Times Mon, 24 Mar 2014 00:00:00 +0000 This paper presents the analysis of a discrete-time renewal input multiple vacations queue with state dependent service and changeover times under policy. The service times, vacation times, and changeover times are geometrically distributed. The server begins service if there are at least units in the queue and the services are performed in batches of minimum size and maximum size . At service completion instant, if the queue size is less than but not less than a secondary limit , the server continues to serve and takes vacation if the queue size is less than . The server is in changeover period whenever the queue size is at service completion instant and at vacation completion instant. Employing the supplementary variable and recursive techniques, we have derived the steady state queue length distributions at prearrival and arbitrary epochs. Based on the queue length distributions, some performance measures of the system have been discussed. A cost model has been formulated and optimum values of the service and vacation rates have been evaluated using genetic algorithm. Numerical results showing the effect of model parameters on the key performance measures are presented. P. Vijaya Laxmi and D. Seleshi Copyright © 2014 P. Vijaya Laxmi and D. Seleshi. All rights reserved. Inventory with Positive Service Time and Retrial of Demands: An Approach through Multiserver Queues Mon, 17 Mar 2014 09:55:04 +0000 We analyze an inventory with positive service time and retrial of demands by considering the inventory as servers of a multiserver queuing system. Demands arrive according to a Poisson process and service time distribution is exponential. On each service completion, the number of demands in the system as well as the number of inventories (servers) is reduced by one. When all servers are busy, new arrivals join an orbit from which they try to access the service at an exponential rate. Using matrix geometric methods the steady state joint distribution of the demands and inventory has been analyzed and a numerical illustration is given. Anoop N. Nair and M. J. Jacob Copyright © 2014 Anoop N. Nair and M. J. Jacob. All rights reserved. Ascent Trajectories of Multistage Launch Vehicles: Numerical Optimization with Second-Order Conditions Verification Tue, 10 Dec 2013 18:05:51 +0000 Multistage launch vehicles are employed to place spacecraft and satellites in their operational orbits. Trajectory optimization of their ascending path is aimed at defining the maximum payload mass at orbit injection, for specified structural, propulsive, and aerodynamic data. This work describes and applies a method for optimizing the ascending path of the upper stage of a specified launch vehicle through satisfaction of the necessary conditions for optimality. The method at hand utilizes a recently introduced heuristic technique, that is, the particle swarm algorithm, to find the optimal ascent trajectory. This methodology is very intuitive and relatively easy to program. The second-order conditions, that is, the Clebsch-Legendre inequality and the conjugate point condition, are proven to hold, and their fulfillment enforces optimality of the solution. Availability of an optimal solution to the second order is an essential premise for the possible development of an efficient neighboring optimal guidance. Mauro Pontani and Giampaolo Cecchetti Copyright © 2013 Mauro Pontani and Giampaolo Cecchetti. All rights reserved. A Heuristic Approach to Flow Shop Scheduling Problem in Which Processing Times Are Associated with Their Respective Probabilities with No-Idle Constraint Wed, 11 Sep 2013 16:07:55 +0000 This paper is an attempt to study general flow shop scheduling problem in which processing time of jobs is associated with probabilities under no-idle constraint. The objective of this paper is to develop a heuristic algorithm to flowshop scheduling so that no machine remains idle during working for any given sequence of jobs. The proposed algorithm is simple, and easy to understand and provides an important tool in many practical situations for minimizing the expected hiring cost of the machines for a fixed sequence of job processing. A numerical illustration is also given to justify the proposed algorithm. Deepak Gupta and Harminder Singh Copyright © 2013 Deepak Gupta and Harminder Singh. All rights reserved. Dynamic Decision Making and Race Games Wed, 07 Aug 2013 11:06:19 +0000 Frequent criticism of dynamic decision making research pertains to the overly complex nature of the decision tasks used in experimentation. To address such concerns, we study dynamic decision making with respect to a simple race game, which has a computable optimal strategy. In this two-player race game, individuals compete to be the first to reach a designated threshold of points. Players alternate rolling a desired quantity of dice. If the number one appears on any of the dice, the player receives no points for his turn; otherwise, the sum of the numbers appearing on the dice is added to the player's score. Results indicate that although players are influenced by the game state when making their decisions, they tend to play too conservatively in comparison to the optimal policy and are influenced by the behavior of their opponents. Improvement in performance was negligible with repeated play. Survey data suggests that this outcome could be due to inadequate time for learning or insufficient player motivation. However, some players approached optimal heuristic strategies, which perform remarkably well. Shipra De and Darryl A. Seale Copyright © 2013 Shipra De and Darryl A. Seale. All rights reserved. A Two-Period Newsvendor Model with Product Extension and Shortage-Making Strategy Thu, 27 Jun 2013 18:18:18 +0000 This study deals with a two-period newsvendor setting in which the item in the second period is a product extension of the item in the first period. A shortage strategy toward the first item is intentionally made so as to stimulate more sales amounts of the second item. The stochastic demand of these two items is assumed to be a linear-additive pattern comprising a deterministic demand and an error demand, where the deterministic demand consists of a primary demand and a consumer price elasticity, and the error demand is hypothesized to be exponentially distributed. The objective of this study is to optimize system's overall expected profit by jointly determining the optimal order quantities and selling prices of these two items. We first compare our proposed model with the classical newsvendor model in light of profit performances, and it reveals that a higher shifting demand rate makes our model a more profitable setting. Impact on profit performances caused by an increasing primary demand of the second item is then demonstrated by numerical examples that an unthought-of ripple effect of an increasing error demand of the second item also occurs. Kuo-Hsien Wang, Che-Tsung Tung, and Yuan-Chih Huang Copyright © 2013 Kuo-Hsien Wang et al. All rights reserved. EPQ Model for Trended Demand with Rework and Random Preventive Machine Time Sun, 23 Jun 2013 10:39:28 +0000 Economic production quantity (EPQ) inventory model for trended demand has been analyzed with rework facility and stochastic preventive machine time. Due to the complexity of the model, search method is proposed to determine the best optimal solution. A numerical example and sensitivity analysis are carried out to validate the proposed model. From the sensitivity analysis, it is observed that the rate of change of demand has significant impact on the optimal inventory cost. The model is very sensitive to the production and demand rate. Nita H. Shah, Dushyantkumar G. Patel, and Digeshkumar B. Shah Copyright © 2013 Nita H. Shah et al. All rights reserved. A Nonmonotone Trust Region Algorithm Based on the Average of the Successive Penalty Function Values for Nonlinear Optimization Thu, 23 May 2013 11:49:01 +0000 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. A New Formulation of the Set Covering Problem for Metaheuristic Approaches Tue, 23 Apr 2013 15:50:24 +0000 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. Mathematical Modeling of a Supply Chain with Imperfect Transport and Two-Echelon Trade Credits Thu, 18 Apr 2013 16:04:08 +0000 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. A Spline Smoothing Newton Method for Distance Regression with Bound Constraints Tue, 16 Apr 2013 13:09:37 +0000 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. Pricing and Lot Sizing for Seasonal Products in Price Sensitive Environment Thu, 04 Apr 2013 09:59:40 +0000 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. A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem Wed, 27 Mar 2013 11:45:09 +0000 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.