Asia-Pacific Journal of Operational Research

We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m ≥ 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m ≥ 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.

It is well-known that the linear rate of convergence can be established for the classical augmented Lagrangian method for constrained optimization problems without strict complementarity. Whether this result is still valid for other nonlinear Lagrangian methods (NLM) is an interesting problem. This paper proposes a nonlinear Lagrangian function based on Fischer–Burmeister (F–B) nonlinear complimentarity problem (NCP) function for constrained optimization problems. The rate of convergence of this NLM is analyzed under the linear independent constraint qualification and the strong second-order sufficient condition without strict complementarity when subproblems are assumed to be solved exactly and inexactly, respectively. Interestingly, it is demonstrated that the Lagrange multipliers associating with inactive inequality constraints at the local minimum point converge to zeros superlinearly. Several illustrative examples are reported to show the behavior of the NLM.

Understanding the effect of variation of the coefficient matrix in linear optimization problem on the optimal solution and the optimal value function has its own importance in practice. However, most of the published results are on the effect of this variation when the current optimal solution is a basic one. There is only a study of the problem for special perturbation on the coefficient matrix, when the given optimal solution is strictly complementary and the optimal partition (in some sense) is known. Here, we consider an arbitrary direction for perturbation of the coefficient matrix and present an effective method based on generalized inverse and singular values to detect invariancy intervals and corresponding transition points.

This paper considers a single machine scheduling with both deterioration and positional effects and due-window assignment problem. The job-dependent due-windows are obtained by the common flow allowance criterion. The objective is to schedule the jobs, and the due-windows so as to minimize the sum of earliness, tardiness, and due-window starting time and due-window size costs. We introduce a polynomial solution for the problem. Furthermore, we show how the solutions can be extended to the setting with job rejection.

In this paper, we study the control problem of optimal assignment of tasks to servers in a multi-server queue with inhomogeneous servers. In order to improve the performance of the system, we use a periodic deterministic sequence of job assignments to servers called a billiard sequence. We then use a genetic algorithm (GA) for computing a near-optimal billiard sequence. By means of a recent result obtained in the area of ordinal optimization, we show that the solution found by the GA belongs to the top 1% of possible choices for such a billiard sequence. As illustrated by numerical examples, not only is the performance under a billiard sequence better than that of the corresponding randomized policy, the optimal billiard sequence even outperforms the billiard implementation of the optimal randomized policy. The framework we introduce in this paper is suitable for general optimization problems over (periodic) deterministic decision sequences. Given the significant performance improvement that a switch from randomized policies to billiard sequences yields, this framework is of importance in practical applications. Finally, we show that constrained or multi-objective optimization can be dealt with in our framework as well.

One of the most important operational management problems of a cross docking system is the truck scheduling problem. Cross docking is a logistics management concept in which products delivered to a distribution center by inbound trucks are immediately sorted out, routed and loaded into outbound trucks for delivery to customers. The truck scheduling problem in a multi-door cross docking system considered in this paper comprises the assignment of trucks to dock doors and the determination of docking sequences for all inbound and outbound trucks in order to minimize the total operation time. A mathematical model for optimal solution is derived, and the genetic algorithms (GAs) and the adaptive genetic algorithms (AGAs) as solution approaches with different types of chromosomes are proposed. The performance of the meta-heuristic algorithms are evaluated using randomly generated several examples.

Obtaining exact blocking probabilities for tandem queues with finite capacities is not a trivial problem. In this paper, we propose a computational approximation method using max-plus algebra for computing blocking probability in a Poisson-driven 2-node tandem queue with finite capacities and constant service times. The blocking probability of a finite-capacity queueing system can be obtained from either the tail probability of stationary waiting time or the difference between two expected stationary waiting times at the first node of the corresponding extended 3-node tandem queue. The computational results in this study show that the proposed approach provides a good approximation of the blocking probability, and in particular, it works well under moderately to heavily loaded situations. The proposed approach is not limited to a particular blocking policy, system structure, or service time; hence, it is applicable to general queues with finite buffer capacities and various blocking policies.

Freight forwarders plan shipping logistics for client shipments based on available transport networks where logistics agents move commodities from origins to destinations. Forwarders typically have the option of assigning shipments to in-house agents or to sub-contracting agents. When making such assignment decisions, consolidation of shipments is a plausible cost-saving consideration. In this paper, we consider assignments of shipments to agents as well as shipment routing choices on a network. We formulate the problem as a nonlinear program where unit costs charged by agents are described as nonlinear functions. The special case with piecewise constant unit costs is formulated as a mixed integer program. We then develop a two-echelon heuristic algorithm to solve the nonlinear program. The upper echelon of the heuristic assigns shipments to suitable agents by adopting a set of neighborhood policies, while the lower echelon improves the routing plan by consolidating jobs along (sub) paths. The feasibility and validity of the heuristic are examined based on randomly generated instances. Computational results show that the heuristic is able to obtain good solutions in manageable computation time. The effects of network density and iteration limits on the performance of the heuristic are also characterized.

Recent advances in simulation optimization research and explosive growth in computing power have made it possible to optimize complex stochastic systems that are otherwise intractable. In the first part of this paper, we classify simulation optimization techniques into four categories based on how the search is conducted. We provide tutorial expositions on representative methods from each category, with a focus in recent developments, and compare the strengths and limitations of each category. In the second part of this paper, we review applications of simulation optimization in various contexts, with detailed discussions on health care, logistics, and manufacturing systems. Finally, we explore the potential of simulation optimization in the new era. Specifically, we discuss how simulation optimization can benefit from cloud computing and high-performance computing, its integration with big data analytics, and the value of simulation optimization to help address challenges in engineering design of complex systems.

The whole panel industry has been impacted profoundly by global recession from 2007 to 2009, and the TFT–LCD industry is not an exception. Currently, the major TFT–LCD manufacturers cluster in South Korea, Taiwan and Japan, which totally contribute more than 80% sales in global market. All these TFT–LCD manufacturers face the five industry characteristics, including intensive capital, intensive technology, short product life cycle and fast technology advancement, fluctuating prices easily influenced by market demand/supply and business cycle, and international collaboration. In view of rapid growth of global demand, TFT–LCD manufacturers face a tremendous competition environment. Therefore, how to configure the best resource allocation and create more profits tend to be an essential issue for the managers of TFT–LCD industry. This paper employs improved DEA and VIKOR to evaluate the dynamic operation performances for TFT–LCD manufacturers in Taiwan, South Korea and Japan from 2002 to 2009. Research results show that South Korean firms have relatively better stable operation performances, while the performance of the firms in Taiwan and Japan are relatively worse and varied over time. After referring to the disclosure statements and industrial experts' opinions, this paper also portraits the reason of Sony with great performance in 2007 was resulted from the sales boost of high-level touch panels which leads to 50% high gross profit ratio and rapidly increasing pre-tax profit in 2007. As a result, how to develop high-level or multi-function panels might be an essential issue for the TFT–LCD manufacturers in Taiwan.