Asia-Pacific Journal of Operational Research

Decision-maker (DM) can assign the weights of the distance measures in the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS) for achieving his/her desirable ranking of alternatives. This phenomenon is called strategically setting distance measure weights in this study, which may affect the fairness of the results. In order to prevent this phenomenon, the idea of data envelopment analysis (DEA) is introduced to determine the objective weights of distance measures, and an improved TOPSIS is proposed in this study. The proposed method not only determines weights of the distance measures from an objective perspective and achieves the fully ranking of alternatives, but also provides the directions for improvement. Moreover, in comparison with the other methods, the advantages of the proposed method are analyzed, and the meanings and properties of the new relative closeness are discussed and proved. Finally, an example of evaluating the innovation development of high-tech industries in central and western regions of China is investigated to illustrate the effectiveness and the usefulness of the proposed method.

This paper proposes a group decision making model with individual preferences to investigate the multicriteria ABC inventory classification problem. We first propose a preliminary group decision matrix by means of identifying the individual preference among the classification criteria as a typical decision maker; then analyze the endogenous individual preference structure in terms of exploring the preferential difference and preferential priority, a revised group decision matrix is therefore presented; thirdly, make the use of SMAA-2 to derive the holistic acceptability index for classifying the SKUs. A satisfaction index is developed to manifest the merits of proposed method. A numerical illustration using the data drawn from previous studies is performed to indicate the applicability and feasibility of our method.

The unbalanced assignment problem (UAP) aims to distribute a set of jobs to some workers. The cost of the jobs is different when they are distributed to different workers. The goal is: (1) minimizing the total cost of arranging jobs to workers; (2) making the distribution of jobs as even as possible among all the workers. We transform the UAP into a min-cost network flow problem with squared terms, and apply the belief propagation (BP) algorithm to deal with it. We prove that, when the min-cost network flow problem has a unique optimal solution, the BP algorithm converges to the optimal solution within $O(\frac{\beta n}{𝜀})$ iterations, where $n$ represents the number of vertices of the flow network, $𝜀$ is the difference between value of the optimal solution and the second optimal solution and $\beta$ is the maximum value of the terms of the objective function. Next, we prove that BP converges to the optimal solution in $O({\beta }^2{n}^2\mu mlogn)$ operations, where $m$ represents the number of edges and $\mu$ is the tight upper bound of the slope of the terms of the objective function.

Cooperative advertising (coop-ad) programs with both accrual rates and participation rates are popularly adopted in practice by manufacturers and retailers to share advertising expenditures. However, results from extant literature show that the accrual rates always negatively impact the manufacturers’ performances, indicating a gap between theory and practice. In this paper, we study a coop-ad program in a distribution channel consisting of a manufacturer and a retailer with risk preferences under demand uncertainty. When both the channel members are risk-neutral, we show that an elaborately specified accrual rate can help reach channel coordination, although the accrual rate always negatively impacts the manufacturer’s performance. When the manufacturer is risk-averse and the retailer is risk-neutral, the accrual rate may positively impact the manufacturer’s performance, and in particular, the manufacturer does prefer a coop-ad program with an accrual rate if his risk-averse level is high and/or the demand volatility is high. When both the channel members are risk-averse, numerical examples illustrate that an accrual rate may benefit both members when the retailer has high profitability and low risk-averse level. These findings, seemingly never reported in the literature, provide plausible explanations for the fact that accrual rates are usually included in coop-ad programs in real-world practice.

Most supply chains in reality are composed of multiple enterprises which are independent individuals in terms of organizational structures and operating modes. From the perspective of performance evaluation, optimizing each enterprise’s efficiency independently will probably result in undesired inventory of intermediate products in the supply chain. Taking the two-stage supply chain where the outputs from the upstream supplier are taken as the inputs for the downstream manufacturer as an example, this paper introduces enterprises’ relative dominance into allocating the responsibility of inventory management between two decentralized enterprises. To motivate these enterprises to adopt the allocation strategy, this paper takes the loss aversion of enterprises into account to reveal the utility subjectively perceived by each decentralized enterprise insisting on independence instead of cooperation. Subsequently, a DEA-based cooperative model is developed to readjust the production processes of two decentralized enterprises. We find that adjusting the relevant parameters is able to explore the relationship between the proposed model and the non-cooperative model and the relationship between the proposed model and the centralized model. Finally, a practical example of coordinating sustainable supply chains is applied to illustrate the effectiveness of the proposed model.

We present a unified approach to single-machine scheduling with position-based processing times, an availability constraint, and job rejection. The approach uses two general position-based processing time functions to model both the learning and aging effects in scheduling. In addition, taking machine availability and job rejection into consideration, the models are more realistic, which seek to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. We present fully polynomial-time approximation schemes to address the two NP-hard problems.

In this paper, we prove that the Henig global proper efficient solution map and the Henig global proper efficient perturbation map of a parametric vector optimization problem are second-order semi-differentiable with index $\gamma \in \{0,1\}$ under some suitable qualification conditions. Several examples are given to illustrate the obtained results.

Mathematical program with vertical complementarity constraints (MPVCC) plays an important role in economics and engineering. Due to the vertical complementarity structure, most of the standard constraint qualifications fail to hold at a feasible point. Without constraint qualifications, the Karush–Kuhn–Tucker (KKT) conditions are not necessary optimality conditions. The classical methods for solving constrained optimization problems applied to MPVCC are likely to fail. It is necessary to establish efficient algorithms for solving MPVCC from both theoretical and numerical points of view. We present an algorithm to obtain stationarity of MPVCC by solving a sequence of Scholtes regularized problems. We consider the Scholtes regularization method with the sequence of approximate KKT points only. We prove that, under strictly weaker constraint qualifications, the accumulation point of the approximate KKT points is Clarke (C-) stationary point. In particular, we can get Mordukhovich (M-) or strongly (S-) stationary point under additional assumptions. From these results, we apply an augmented Lagrangian method to obtain a solution of MPVCC and give the convergence analysis. In particular, the accumulation point of the generated iterates is an S-stationary point if some boundedness conditions hold. The numerical results show that it is an effective way to solve MPVCC.

The mathematical program with switching constraints (MPSC), which has been introduced recently, is a difficult class of optimization problems. The reason for the difficulty is that the existence of the switching constraint makes the standard constraint qualifications invalid at local minimizers. This paper proposes the Wolfe-type dual (WD) model of this problem without switching constraints. Under the assumptions of convexity and strict convexity, we derive the weak, strong, converse, restricted converse, and strict converse duality results between MPSC and WD.

The vehicle routing problem (VRP) and its variants are a class of network problems that have attracted the attention of many researchers in recent years, owing to their pragmatic approach to solving issues in logistics management. Most surveys/reviews of the extant literature often focus on specific variants or aspects of the VRP. However, a few reviews of the overall VRP literature are available. The focus of these papers is to identify which VRP literature characteristics are the most popular in recent studies. To this end, we analyze 229 articles published between 2015 and 2017. We provide a systematic literature review evaluating the Scenario Characteristics and Problem Physical Characteristics that are most frequently addressed by VRP researchers, the Type of Study and Data Characteristics that they address, the most cited works that constitute the theoretical pillars of the field, and details of three specific problem variants that have been studied extensively in recent years and their opportunities for future research.