Asia-Pacific Journal of Operational Research

Scheduling problems with variable processing times and past-sequence-dependent delivery times are considered on a single-machine. The delivery times of jobs depend on their waiting times of processing. A job’s actual processing time depends on its position in a sequence, its starting time and its allocation of non-renewable resources. Under the linear resource consumption function, the goal (version) is to determine the optimal sequence and optimal resource allocation such that the sum of scheduling cost and total resource consumption cost is minimized. Under the convex resource consumption function, three versions of the scheduling cost and total resource consumption cost are discussed. We prove that these four versions can be solved in polynomial time, respectively. Some applications are also given by using the scheduling cost, which involve the makespan, total completion time, total absolute differences in completion times (TADC), and total absolute differences in waiting times (TADW).

While nearly all previous algorithms designed to solve simulation optimization problems have treated the outputs of simulation systems at a given design point (input parameter) as being independent of each other, this premise is flawed in that simulated outputs are generally correlated. We propose a decorrelation (DC) procedure that can effectively evaluate and remove the correlation of outputs of a simulation system. The proposed DC procedure is further integrated with STRONG, an improved framework of the well-known Response Surface Methodology (RSM), for tackling the simulation optimization problems with correlated outputs. This integration is particularly synergistic due to the fact that STRONG is a fully automated, response-surface-based procedure possessing appealing convergence properties and DC can take advantage of the concept of trust region as in STRONG to enable the removal of the correlation of outputs at the design points within the same trust region all at once. This is more efficient compared to the traditional approaches where a substantial number of observations are typically required for dealing with correlations. The resulting integrated method, which we call STRONG-DC, requires various adaptations so as to ensure the efficacy and efficiency of the overall framework. STRONG-DC preserves the desirable automation and convergence as STRONG, namely, it does not require human involvements and can be proved to achieve the truly optimal solution(s) with probability one (w.p.1) under reasonable conditions. Moreover, the effectiveness and efficiency of STRONG-DC are evaluated through extensive numerical analyses, along with a case study involving the well-known newsvendor problem.

The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

We study the Markowitz mean-variance portfolio selection model under three types of regularizations: single-norm regularizations on individual stocks, mixed-norm regularizations on stock groups, and composite regularizations that combine the single-norm and mixed-norm regularizations. With mixed-norm regularizations incorporated, our model can accomplish group and stock selections simultaneously. Our empirical results using both US and global equity market data show that compared to the classical mean-variance portfolio, almost all regularized portfolios have better out-of-sample risk-adjusted performance measured by Sharpe ratio. In addition, stock selection and group screening accomplished by adding ${\ell }_1$ and ${\ell }_{2,1}$ regularizations respectively can lead to decreased volatility, turnover rate, and leverage ratio. Yet there are instances in which diversifying across different groups is more favorable, depending on the grouping methods. Moreover, we find a positive correlation between portfolio turnover and leverage. Heavily leveraged portfolios also have high turnover rates and thus high transaction costs.

In this paper, we investigate error bounds of an inverse mixed quasi variational inequality problem in Hilbert spaces. Under the assumptions of strong monotonicity of function couple, we obtain some results related to error bounds using generalized residual gap functions. Each presented error bound is an effective estimation of the distance between a feasible solution and the exact solution. Because the inverse mixed quasi-variational inequality covers several kinds of variational inequalities, such as quasi-variational inequality, inverse mixed variational inequality and inverse quasi-variational inequality, the results obtained in this paper can be viewed as an extension of the corresponding results in the related literature.

Automated material handling systems (AMHS) have been widely used in semiconductor manufacturing. However, the performance of AMHS heavily hinges on vehicle fleet sizing, which is a complex yet crucial problem. For example, a small fleet size may increase the average wait time, but a large fleet size can also result in traffic congestion. This tradeoff is difficult and can be further exacerbated by profound uncertainty in the manufacturing process. In the literature, the existing models are focused on improving the mean-based performance of AMHS, where the resulting optimal vehicle fleet size is fixed, lacking the ability and flexibility to respond to the changes and/or special requirements that suddenly come up in the manufacturing process. Another drawback with the existing models is that they are not able to characterize the upside/downside risks associated with the resulting vehicle fleet size. This paper, motivated by a real project, presents a novel quantile-based decision model to fill the gap. The adjustment of $\alpha$ values in the proposed decision model allows for agile vehicle fleet sizing according to the production situations, resulting in the satisfactory performance of AMHS. We develop a simulation optimization solution method, called ES-AMHS in short, to enable the efficient derivation of the optimal vehicle fleet size. A comprehensive numerical analysis is conducted to evaluate the efficiency and efficacy of the solution method. Finally, an empirical study in cooperation with a wafer fab in Taiwan is presented to show the practical usefulness of this methodology in a real-world setting.

Refined product distribution is an application of the Multi-compartment Vehicle Routing Problem (MCVRP), which simultaneously considers the vehicle routing, the assignment of heterogonous vehicles and loading policies of multi-compartment. First, we develop an optimization model with the objective of delivering on-time and minimizing transportation cost. Then we propose a Multi-objective Variable Neighborhood Descent Algorithm (MOVND), where the $𝜀$-constraint method transforms the original problem into a series of sub-problems of single objective with constraints. Finally, the efficiency of the proposed algorithm is verified by conducting a large number of small and large instances. Mainly including (i) compared with the classical NSGA-2 algorithm for multi-objective VRP, MOVND provides better performance in terms of convergence, spread and distribution; (ii) the multi-compartment vehicles are able to carry a variety of products simultaneously, which can improve the effective utilization of vehicle space and meet the needs of different customers in a single transportation. In addition, heterogonous vehicles that take full advantage of the characteristics of different vehicles are superior to homogeneous ones in terms of operating cost in the practice of the refined product distribution.

In this paper, a complete characterization of the B-subdifferential of the projection onto the generalized simplex is given. This work is accomplished with the help of Han–Sun Jacobian, whose full characterization is also given in this case. The characterizations are given with simple and explicit formulae in terms of the active index set of the projection.

In this paper, we propose a self-adaptive inertial projection and contraction algorithm, by combining backtracking search with the inertial projection and contraction algorithm, for solving monotone variational inequality in Hilbert space. This algorithm not only circumvents the restrictive assumption of Lipschitz continuity of the operator, but also gives more suitable and feasible parameters. Under the assumption that the operator is continuous and monotone, we establish weak convergence for proposed algorithm. Finally, we report some preliminary computational results to show the efficiency and advantage of the algorithm.

Low-rank tensor approximation plays a crucial role in various tensor analysis tasks ranging from science to engineering applications. There are several important problems facing low-rank tensor approximation. First, the rank of an approximating tensor is given without checking feasibility. Second, even such approximating tensors exist, however, current proposed algorithms cannot provide global optimality guarantees. In this work, we define the low-rank tensor set (LRTS) for Tucker rank which is a union of manifolds of tensors with specific Tucker rank. We propose a procedure to describe LRTS semi-algebraically and characterize the properties of this LRTS, e.g., feasibility of tensors manifold, the equations/inequations size of LRTS, algebraic dimensions, etc. Furthermore, if the cost function for tensor approximation is polynomial type, e.g., Frobenius norm, we propose an algorithm to approximate a given tensor with Tucker rank constraints and prove the global optimality of the proposed algorithm through critical sets determined by the semi-algebraic characterization of LRTS.

We study the Pareto optimization scheduling on an unbounded parallel-batch machine with jobs having agreeable release dates and processing times for minimizing makespan and maximum cost simultaneously. The jobs considered in this paper are of two types: batch jobs and drop-line jobs. For batch jobs, the completion time of a job is given by the completion time of the batch containing this job. For drop-line jobs, the completion time of a job is given by the starting time of the batch containing this job plus the processing time of this job. For both of batch jobs and drop-line jobs, we present polynomial-time algorithms for finding all Pareto optimal points.

Motivated by a variety of applications in sharing economy, we study an identical parallel machine scheduling problem with due date-to-deadline window by jointly considering machine sharing and the time value of money. A factory owns a set of parallel identical machines and processes a set of production orders within a finite time period. In the sharing setting, the factory may also rent external machines to handle a part of orders by paying some extra cost. The factory aims to determine the sharing policy of the production orders and the scheduling rule of machines, to maximize its total future value of profits by satisfying the orders. To the best of our knowledge, there are no previous results for this problem. In this work, a mathematical programming model is derived, and a problem-specific genetic algorithm and a heuristic are proposed to solve large-scale instances. Numerical experiments using randomly generated instances are carried out to evaluate the effectiveness and efficiency of the proposed solution methods.