Asia-Pacific Journal of Operational Research

In this paper, we propose a nonmonotone Alternative Direction Method (ADM) based on simple conic model for unconstrained optimization. Unlike traditional trust region method, the subproblem in our method is a simple conic model, where the Hessian of the objective function is replaced by a scalar approximation, the trust region subproblem is solved by ADM which was first proposed by Zhu and Ni. When the trial point isn’t accepted by trust region, line search technique is used to find an acceptable point instead of resolving the trust region subproblem. The new method needs less memory capacitance and computational complexity. The global convergence of the algorithm is established under some mild conditions. Numerical results on a series of standard test problems are reported to show the new method is effective and robust.

Researchers traditionally compute isolated points for an efficient frontier and assume a line which passes through a risk-free asset $r_f$ and is tangent to the frontier. The tangency plays pivotal roles for the capital asset pricing model (CAPM). However, the assumption may not hold in the presence of kinks (as non-differentiable points) on efficient frontiers. Kinks are detected by parametric-quadratic programming only and not by ordinary portfolio optimization. Up until now, there has been no research to theoretically scrutinize kink properties (especially implications to CAPM) and systematically quantify the nonexistence of the tangency. In such an area, this paper contributes to the literature. In theorems and corollaries, we prove the nonexistence of the tangency and substantiate that expected-return axis is composed of piecewisely connected intervals for which the tangency does not exist and intervals for which the tangency exists. Computationally, we reveal universal existence of kinks (e.g., 0.2 to 8.0 kinks for 5-stock to 1800-stock portfolio selections) and the tangency-nonexistence ratios as about 0.066.

In the paper, we give a new non-parameter filled function method for finding global minimizer of global optimization programming problems, the filled function consists of a inverse cosine function and a logarithm function, and without parameter. Its theoretical residences are proved. A new filled function algorithm is given based on the proposed new parameterless filled function, The results of numerical with ten experiments verify the efficient and reliability for the algorithm.

In this paper, we address single-machine scheduling with sum of logarithm processing times-based learning effect. Under exponential past-sequence-dependent delivery times, we proved that the makespan and total completion time minimizations can be solved by the smallest processing time (SPT) first rule. Under the agreeable weight condition and agreeable due date condition, we show that the total weighted completion time minimization and maximum tardiness minimization can be solved in polynomial time, respectively.

Many online retailers have adopted drop-shipping as their main order fulfillment strategy. Against this backdrop, this paper studies the service time and pricing decisions in an online retailing system in which the single retailer is served by either monopolistic or duopolistic suppliers. The suppliers are dominant in the Stackelberg game. We employ the guaranteed service framework to model the intricate relationship between service time and inventory. The model stipulates that the delivery of online orders must be completed within guaranteed service time. The equilibrium service times and prices are derived for both cases of monopolistic and duopolistic suppliers. In addition, we systematically analyze the impact of operational and market factors on service time, respectively, and rich insights have been obtained. Interestingly, we find that the presence of competition does not necessarily lead to more rapid delivery service. Suppliers in the duopoly market tend to adopt a price-based competitive strategy, i.e., they are better off by lowering price at the expense of longer service time, especially for the new entrant. However, as competition intensifies to some extent, suppliers are recommended to leverage on more responsive service to maintain or expand the customer base.

Unreliable suppliers may pose a substantial threat to supply chains, especially when they hold private information of their reliability. We consider a dyadic supply chain where the information of supplier reliability (in the form of random production yield) is asymmetric. We propose a new mechanism-design model and derive the buyer’s optimal procurement contract menu offered to suppliers with private information. We prove that the contract menu is as simple as offering two different inflated order amounts and setting the procuring price sufficiently low to let the suppliers earn zero reservation profits. These results are derived analytically under uniform distribution. We test them numerically under beta distribution and find them hold as well. However, the informational rent will become positive when the supplier’s reservation profit is positive. Positive informational rent is also found when we consider another structure of the supplier’s production cost. This paper provides some new insights into supply chain management under asymmetric information of uncertain supply.

This paper develops a queueing system model to analyze the operations of a hierarchical healthcare system consisting of general hospitals (GHs) and community healthcare centers (CHCs). GHs typically provide a higher level of health care service than CHCs, and thus are preferred choices for many patients’ healthcare service needs. Consequently, GHs are often heavily congested and patients often incur excessive waiting time. In contrast, CHCs are often idle and resources are underutilized. To help balance the utilization of resources in GHs and CHCs, a congestion-based information guidance policy is proposed in this paper to inform patients in the GH service queue about the anticipated delay. Upon being informed the delay for GH service, patients may balk, remain in queue for GH service, or switch to receive service at CHCs. This policy is thus expected to relieve the congestion at GHs and promote CHC usage. To study the effects of the proposed policy, a hierarchical healthcare system is modeled as a queueing system with strategic patients. Stationary performance measures of the system are analytically characterized using a Markov chain model. Stochastic and numerical analyses provide insights on how to design information guidance policy that would help improve overall health care service quality under different scenarios.

We consider the resource allocation problem under a two-machine flow shop environment where the job sequence has been determined in advance. The resource is used to reduce the processing time that is inversely proportional to the resource consumption amount. Furthermore, there exist the lower and upper bounds on the amount of the resources consumed by each job. The objective is to minimize the makespan plus the total resource consumption cost. We show that the problem can be solved in strongly polynomial time.

This paper is devoted to the study of multiobjective semi-infinite programming problems on Hadamard manifolds. We consider a class of multiobjective semi-infinite programming problems (abbreviated as MSIP) on Hadamard manifolds. We use the concepts of second-order Karush–Kuhn–Tucker stationary point and second-order Karush–Kuhn–Tucker geodesic pseudoconvexity of the considered problem to derive necessary and sufficient second-order conditions of efficiency, weak efficiency and proper efficiency for MSIP along with certain generalized geodesic convexity assumptions. Moreover, we formulate the second-order Mond–Weir-type dual problem related to MSIP and deduce weak and strong duality theorems relating MSIP and the dual problem. The significance of our results is demonstrated with the help of non-trivial examples. To the best of our knowledge, this is the first time that second-order optimality conditions for MSIP have been studied in Hadamard manifold setting.

In this paper, we develop some three term nonlinear conjugate gradient methods based on the Hestenes–Stiefel (HS), the Polak–Ribière–Polyak (PRP) and the Liu–Storey (LS) methods. The proposed algorithms always generate sufficient descent directions which satisfy $g_k^T{d}_k=-\parallel g_k{\parallel }^2$. When the Wolfe or the Armijo line search is used, we establish the global convergence of the proposed methods in a concise way. Moreover, the linear convergence rate of the methods is discussed as well. The extensive numerical results show the efficiency of the proposed methods.