# American Institue of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

2011 , Volume 7 , Issue 1

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2011, 7(1): 1-18 doi: 10.3934/jimo.2011.7.1 +[Abstract](53) +[PDF](395.3KB)
Abstract:
This paper considers a two-station tandem production system consisting of make-to-stock and make-to-order facilities. The make-to-stock facility produces components which are served for external demands as well as internal make-to-order operations while the make-to-order facility processes customer orders with the option to accept or reject. We address the problem of coordinating the decision of when to accept customer order and when to satisfy component demand that maximizes the total expected discounted profit. To deal with this issue, we present a Markov decision process model of two-station tandem queueing system and characterize the structure of the optimal policy. We investigate the marginal impacts of system parameters on the optimal policy and implement a numerical experiment for comparing the performance between the optimal policy and the static policy with two fixed thresholds.
2011, 7(1): 19-30 doi: 10.3934/jimo.2011.7.19 +[Abstract](33) +[PDF](344.6KB)
Abstract:
In this paper, we study the production time allocation issue for a multi-purpose manufacturing facility. This production facility can produce different types of make-to-order and make-to-stock products. Using a vacation queueing model, we develop a set of quantitative performance measures for a two-parameter time allocation policy. Based on the renewal cycle analysis, we derive an average cost expression and propose a search algorithm to find the optimal time allocation policy that minimizes the average cost. Some numerical examples are presented to demonstrate the effectiveness of the search algorithm. The vacation model used in this paper is also a generalization of some previous vacation queueing models in the literature. The results obtained in this study are useful for production managers to design the operating policy in practice.
Tao Zhang , Yue-Jie Zhang , Qipeng P. Zheng and  P. M. Pardalos
2011, 7(1): 31-51 doi: 10.3934/jimo.2011.7.31 +[Abstract](81) +[PDF](480.0KB)
Abstract:
This paper presents the production planning management architecture for iron-steel manufacturing factories based on Make-To-Order (MTO) and Make-To-Stock (MTS) management ideas. Within this architecture, we discuss the procedures of order planning in details and construct a nonlinear integer programming model for the order planning problem. This model takes into account inventory matching and production planning simultaneously, and considers multiple objectives, such as the total cost of earliness/tardiness penalty, tardiness penalty in delivery time window, production, inventory matching and order cancelation penalty. In order to solve this nonlinear integer program, this paper designs a hybrid Particle Swarm Optimization (PSO) and Tabu Search (TS) algorithm, in which new heuristic rules to repair infeasible solutions are proposed, and then analyzes the parameter settings for PSO and the combined algorithm by simulations. This paper also compares the results of using PSO individually, TS individually, and the hybrid PSO/TS algorithm to solve the models with three different order quantities. Numerical results show that the hybrid PSO/TS algorithm provides better solutions while being computationally efficient.
Li-Xia Liu , Sanyang Liu and  Chun-Feng Wang
2011, 7(1): 53-66 doi: 10.3934/jimo.2011.7.53 +[Abstract](54) +[PDF](396.0KB)
Abstract:
A smoothing Newton method based on the CHKS smoothing function for a class of non-monotone symmetric cone linear complementarity problem (SCLCP) with the Cartesian $P$-property and a regularization smoothing Newton method for SCLCP with the Cartesian $P_0$-property are proposed. The existence of Newton directions and the boundedness of iterates, two important theoretical issues encountered in the smoothing method, are showed for these two classes of non-monotone SCLCP. Finally, we show that these two algorithms are globally convergent. Moreover, they are globally linear and locally quadratic convergent under a nonsingular assumption.
Jing Quan , Zhiyou Wu and  Guoquan Li
2011, 7(1): 67-78 doi: 10.3934/jimo.2011.7.67 +[Abstract](47) +[PDF](310.8KB)
Abstract:
In this paper, some verifiable necessary global optimality conditions and sufficient global optimality conditions for some classes of polynomial integer programming problems are established. The relationships between these necessary global optimality conditions and these sufficient global optimality conditions are also discussed. The main theoretical tool for establishing these optimality conditions is abstract convexity.
Peng Cui , Hongguo Zhao and  Jun-e Feng
2011, 7(1): 79-85 doi: 10.3934/jimo.2011.7.79 +[Abstract](38) +[PDF](278.0KB)
Abstract:
State estimation problem is discussed for discrete-time systems with delays in measurement noise sequence, which is usually seen in network control and geophysical prospecting systems. An optimal recursive filter is derived via state augmentation. Dimensions of the optimal filter just are the sum of dimensions of state and observation vector. Therefore, they are not related to the size of delay. Besides, a sub-optimal recursive filter with same dimension as the original state is designed. The sub-optimal filter realizes instant optimization at current time. One example shows the effectiveness of the proposed approach.
Xiwei Liu , Tianping Chen and  Wenlian Lu
2011, 7(1): 87-101 doi: 10.3934/jimo.2011.7.87 +[Abstract](62) +[PDF](538.8KB)
Abstract:
In this paper, the cluster synchronization for an array of linearly coupled identical chaotic systems is investigated. New coupling schemes (or coupling matrices) are proposed, by which global cluster synchronization of linearly coupled chaotic systems can be realized. Here, the number and the size of clusters (or groups) can be arbitrary. Some sufficient criteria to ensure global cluster synchronization are derived. Moreover, for any given coupling matrix, new coupled complex networks with adaptive coupling strengths are proposed, which can synchronize coupled chaotic systems by clusters. Numerical simulations are finally given to show the validity of the theoretical results.
Roxin Zhang , Bao Truong and  Qinghong Zhang
2011, 7(1): 103-115 doi: 10.3934/jimo.2011.7.103 +[Abstract](45) +[PDF](343.3KB)
Abstract:
A hierarchical optimization (or bilevel programming) problem consists of a decision maker called the leader who is interested in optimizing an objective function that involves with the decisions from another decision maker called the follower whose decisions are based in part on the policies made by the leader. However, if the planning horizon expands into an extended period of time, it may be unrealistic for either players to commit to the original decisions so there is a desire to break the problem into stages and the leader may wish to reevaluate the follower's response at each stage. In this article, we propose a multistage hierarchical optimization problem with the leader's objective consisting of multiple criteria and study the optimality conditions of such problems using an extremal principle of Mordukhovich.
Xiaoming Yan , Ping Cao , Minghui Zhang and  Ke Liu
2011, 7(1): 117-137 doi: 10.3934/jimo.2011.7.117 +[Abstract](36) +[PDF](490.5KB)
Abstract:
In this paper, we consider a firm which maximizes its profit by determining the production and sales policies for a new product during the lifetime of the product. Because of capacity constraint, we extend Bass demand process a more general case including the negative effectiveness of word-of-mouth. We analyze the production and sales policies in two cases: strong negative word-of-mouth and weak negative word-of-mouth. In the case of strong negative word-of-mouth, we show that myopic policy is optimal under some mild conditions. In the case of weak negative word-of-mouth, we show that build-up policy is optimal in a special case of negligible holding cost and discount rate. However, for positive holding cost and discount rate, we compare myopic policy with build-up policy by numerical examples, and show that the build-up policy is no longer a robust approximation to the optimal policy.
Lei Sun and  Lihong Zhang
2011, 7(1): 139-156 doi: 10.3934/jimo.2011.7.139 +[Abstract](45) +[PDF](437.0KB)
Abstract:
In this paper, we study how irrationality affects the investor's consumption and investment decisions. We build a continuous-time financial model, where an irrational investor determines his consumption and investment according to an exogenous price process. The main results are as follows. First, compared with a rational investor, an optimistic irrational investor tends to consume more, while a pessimistic irrational investor tends to consume less. Second, the more irrational the investor, the more volatile his consumption. Third, the extremely irrational investor can get more ex ante expected utility than his rational counterpart, no matter he is optimistic or pessimistic.
Chunrong Chen , T. C. Edwin Cheng , Shengji Li and  Xiaoqi Yang
2011, 7(1): 157-174 doi: 10.3934/jimo.2011.7.157 +[Abstract](48) +[PDF](409.4KB)
Abstract:
In this paper, based on the ordering relations induced by a pointed, closed and convex cone with a nonempty interior, we propose a nonlinear augmented Lagrangian dual scheme for a nonconvex multiobjective optimization problem by applying a class of vector-valued nonlinear augmented Lagrangian penalty functions. We establish the weak and strong duality results, necessary and sufficient conditions for uniformly exact penalization and exact penalization in the framework of nonlinear augmented Lagrangian. Our results include several ones in the literature as special cases.
Chuandong Li , Fali Ma and  Tingwen Huang
2011, 7(1): 175-181 doi: 10.3934/jimo.2011.7.175 +[Abstract](49) +[PDF](281.1KB)
Abstract:
This paper investigates an iterative learning controller for linear discrete-time systems with state delay based on two-dimensional (2-D) system theory. It shall be shown that a 2-D linear discrete Roessor's model can be applied to describe the ILC process of linear discrete time-delay systems. Much less restrictive conditions for the convergence of the proposed learning rules are derived. A learning algorithm is presented which provides much more effective learning of control input, which enables us to obtain a control input to drive the system output to the desired trajectory quickly. Numerical examples are included to illustrate the performance of the proposed control procedures.
Li Wang , Yang Li and  Liwei Zhang
2011, 7(1): 183-198 doi: 10.3934/jimo.2011.7.183 +[Abstract](48) +[PDF](496.2KB)
Abstract:
In this paper, we discuss a system of differential equations based on the projection operator for solving the box constrained variational inequality problems. The equilibrium solutions to the differential equation system are proved to be the solutions of the box constrained variational inequality problems. Two differential inclusion problems associated with the system of differential equations are introduced. It is proved that the equilibrium solution to the differential equation system is locally asymptotically stable by verifying the locally asymptotical stability of the equilibrium positions of the differential inclusion problems. An Euler discrete scheme with Armijo line search rule is introduced and its global convergence is demonstrated. The numerical experiments are reported to show that the Euler method is effective.
Jinyan Fan and  Jianyu Pan
2011, 7(1): 199-210 doi: 10.3934/jimo.2011.7.199 +[Abstract](52) +[PDF](467.7KB)
Abstract:
In this paper we study the convergence rate of the inexact Levenberg-Marquardt method for nonlinear equations. Under the local error bound condition which is weaker than nonsingularity, we derive an explicit formula of the convergence order of the inexact LM method, which is a continuous function with respect to not only the LM parameter but also the perturbation vector. The new formula includes many convergence rate results in the literature as its special cases.
Yi-Kuei Lin and  Cheng-Ta Yeh
2011, 7(1): 211-227 doi: 10.3934/jimo.2011.7.211 +[Abstract](53) +[PDF](447.7KB)
Abstract:
A network constructed by arcs and vertices is a useful tool to model a real-life system, such as a computer/communication, an electric power transmission, a transportation, or a logistics system. Network reliability, the probability to satisfy customers' demand, is a common performance index of such a system. From the quality of service viewpoint, the network reliability optimization is an important objective which many enterprises pursue to maintain their customer satisfaction. Combining with the characteristic of assignment problem, this study is mainly to search for the optimal components assignment with maximal network reliability. A set of components is ready to be assigned to the arcs, each component may have several modes, such as failure, maintenance, or partially reserved by other customers, and thus the network according to any component assignment is multistate. A minimal-cut based genetic algorithm is developed to solve such a problem. In order to show the computational efficiency of the proposed algorithm, a simple computer network and a real one are adopted while comparing with the implicit enumeration method and the approach of random solution generation, respectively.
Yu-Jen Chang and  Ming-Jong Yao
2011, 7(1): 229-251 doi: 10.3934/jimo.2011.7.229 +[Abstract](63) +[PDF](453.8KB)
Abstract:
In this study, we are interested in the economic lot scheduling problem (ELSP) that considers manufacturing of the serviceable products and remanufacturing of the rework products. In this paper, we formulate a mathematical model for the ELSP with reworks using the common cycle approach in which only one manufacturing lot and only one rework lot for each product exist during a common cycle. In order to solve this problem, we propose two heuristics that not only search for the optimal cycle time and an optimal production sequence, but also utilize a simple scheduling heuristic to schedule the starting time of all the manufacturing and rework lots so as to minimize the average total costs. The first heuristic is a simple heuristic that employs a 2-opt search to obtain a close-to-optimal production sequence. The second heuristic, which is a refined version of the simple heuristic, employs a bisection search to look for an optimal cycle time. In our numerical experiments, we compare the effectiveness of both heuristics using randomly generated instances.
2011, 7(1): 253-282 doi: 10.3934/jimo.2011.7.253 +[Abstract](38) +[PDF](536.0KB)
Abstract:
This paper presents two bi-objective simulated annealing procedures to deal with the classical permutation flow shop scheduling problem considering the makespan and the total completion time as criteria. The proposed methods are based on multi-objective simulated annealing techniques combined with constructive and heuristic algorithms. A computational experiment has been carried out and different metrics have been computed to check various attributes of each method. For all the tested instances a net set of potentially efficient schedules has been obtained and compared with previously published results. Results indicate that the proposed algorithms provide efficient solutions with little computational effort which can serve as input for interactive procedures.

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