Asia-Pacific Journal of Operational Research

Multiple equilibria (equilibrium excursion) affects the auction proceeds, and is bad for estimating auction efficiency. This paper examines the relationship between bidding behavior and equilibrium excursion. We analyze a uniform price auction mechanism based on a rationing strategy and common value information. In this uniform price auction mechanism, bidders (strategic and non-strategic) participate in an auction simultaneously, and the auctioneer rations the strategic bidders after observing their bids. The conclusions drawn suggest that a rationing strategy can effectively limit the strategic bidders from manipulating the auction, and the Nash equilibrium may not be unique (i.e., there exists an equilibrium excursion). As the number of bidders increases, or when the quantity that can be allocated to the non-strategic bidders is unconstrained, there exists asymptotically a unique equilibrium price which is the highest price the auctioneer could obtain. Based on these conclusions, we provide some strategies and suggestions on how to induce the equilibrium excursion state to a desired unique equilibrium state.

This paper discusses the applicable conditions of two capacity procurement sub-strategies with two ordering opportunities, namely, sub-strategy I in which only increasing purchase quantity is allowed during the second ordering opportunity, and sub-strategy II in which either increasing or reducing order quantities is possible when the second order is placed. Our research is in the context of a logistics service supply chain (LSSC) consisted of a logistics service integrator (LSI) and a functional logistics service provider (FLSP). LSI purchases first a service capacity from FLSP long before demand is realized and then adjusts this ordering quantity based on demand updating. We developed the profit models for LSI and FLSP which also include the constraints of rational expectations. Based on the assumption of Bayesian updating, this paper investigates the conditions for sub-strategy II outperforming sub-strategy I. The main results are verified through numerical analysis. Counter-intuitively, sub-strategy II is not necessarily always better than sub-strategy I. When using sub-strategy II, LSI needs to purchase more service the first time of placing orders, but the expected profits increase for both LSI and FLSP only with certain conditions, which have been derived as propositions in this paper.

In this paper, we propose a symmetric alternating method of multipliers for minimizing the sum of two nonconvex functions with linear constraints, which contains the classic alternating direction method of multipliers in the algorithm framework. Based on the powerful Kurdyka–Łojasiewicz property, and under some assumptions about the penalty parameter and objective function, we prove that each bounded sequence generated by the proposed method globally converges to a critical point of the augmented Lagrangian function associated with the given problem. Moreover, we report some preliminary numerical results on solving $l_{1/2}$ regularized sparsity optimization and nonconvex feasibility problems to indicate the feasibility and effectiveness of the proposed method.

This paper studies the stochastic differential Stackelberg game in a continuous-time newsvendor problem with a return policy, in which one supplier sells products to one retailer and the two parties make the decisions sequentially to maximize their own expected profits. When the demand process is a general jump-diffusion process, we provide a general formula for the equilibrium if it exists. When the demand rate is an Ornstein–Uhlenbeck (O–U) process, we prove the existence and uniqueness of the equilibrium and find an explicit expression for the equilibrium. Computational results show that the return policy has significant impact on the Stackelberg equilibrium.

An important area of research involving the benchmarking methodology data envelopment analysis (DEA), concerns the modeling of multistage situations. In the usual multistage settings, it is generally assumed that all decision-making units (DMUs) have the same number and configuration of stages. However, in many real-world examples, this assumption does not hold. Consider, for example, a supply chain setting where for some DMUs, products are shipped directly from a supplier to a retailer (single-stage), while for other DMUs, products can be transshipped through distribution centers (two or more stages). In the current paper, we investigate an efficiency measurement situation where the DMUs exhibit a mix of single and two-stage setups. The particular case examined involves a set of high technology firms that can be thought of as falling into two groups; those firms where the output of interest is the annual revenue generated, and those that not only generate revenue, but as well invest a portion of that revenue in R&D. Firms in the first group can be viewed as being single-stage DMUs while those in the other group are of the two-stage type. The modeling complication here is that the set of DMUs do not explicitly form a homogeneous set of units. We develop a DEA-style model aimed at measuring efficiency in the presence of such nonhomogeneous two-group structures.

Multicommodity network problems appear in numerous applications, such as telecommunications, logistics, transportation, distribution and production planning networks. The piecewise linear multicommodity network flow problem is a multicommodity network flow problem with piecewise linear costs corresponding to multiple resources, such as communication lines, vehicles and production lines. In the present paper, for the piecewise linear multicommodity network continuous flow problem, we present a path-based formulation and an arc-based formulation, and develop a combined matheuristic approach, which combines capacity scaling, a column and row generation technique, restricted branch-and-bound and a local branch method.

We model and apply a stochastic-simulation-based methodology to optimize the machine allocation of a flexible flow shop (FFS) dedicated to integrated circuit (IC) packaging. This contrasts with most previous research on non-deterministic FFS problems wherein stochastic simulation is mostly used to estimate throughput, cycle time, delay cost, or some other measure(s) in order to compare the performances of already-existing heuristic-based algorithms. The methodology applied in this research, called progressive simulation metamodeling for IC Packaging (IC-PSO), while rooted in the traditional metamodeling technique known as Response Surface Methodology (RSM), contrasts with RSM in that it is equipped with well-designed mechanisms to ensure an ever-increasing solution quality in an attempt to achieve the desirable optimality. The computational efficiency that IC-PSO affords IC packaging companies is demonstrated via a numerical study. Meanwhile, an empirical study based on real data was conducted to validate the viability of the proposed methodology in real settings.

In data envelopment analysis (DEA), calculating the distances of decision making units (DMUs) from the weak efficient boundary of a production possibility set (PPS) is a very important subject which has attracted increasing interest of researchers in recent years. The distances of DMUs to the weak efficient boundary of the PPS can be used to evaluate the performance of DMUs, obtain the closest efficient patterns and also assess the sensitivity and stability of efficiency classifications in DEA. The present study proposes some new models which compute the distances of DMUs from the weak efficient boundary of a PPS for both convex and nonconvex PPSs using Hölder norms. In fact, the presented models assist a DMU to improve its performance by an appropriate movement towards the weak efficient boundary.

This paper contributes to the literature of single server queueing models with a vacationing server. We have incorporated many features for a better control over the system. The server implements the N-policy, takes both single and multiple vacations, and is subject to breakdowns. The embedded Markov chain technique is used to obtain the pgf of the system size at a service completion epoch in the steady-state. The semi-regenerative technique is used to obtain the pgf of the system size at an arbitrary instant of time in the steady-state.