Asia-Pacific Journal of Operational Research

In this paper, we study the problem of unrelated parallel machine scheduling with controllable processing times and deteriorating maintenance activity. The jobs are nonresumable. The processing time of each job is a linear function of the amount of a continuously divisible resource allocated to the job. During the planning horizon, there is at most one maintenance activity scheduled on each machine. Additionally, if the starting time of maintenance activity is delayed, the length of the maintenance activity required to perform will increase. Considering the total completion times of all jobs, the impact of maintenance activity in the form of the variation in machine load and the amounts of compression, we need to determine the job sequence on each machine, the location of maintenance activities and processing time compression of each job simultaneously. Accordingly, a polynomial time solution to the problem is provided.

In this paper, we propose a new approach to rank two-stage production systems in data envelopment analysis based on performance of the stages. To do this, a method is devised to compare the stages performance of a special two-stage unit with the corresponding stages performance of other units. The relative performance of two-stage production units is investigated under new definitions of weak and strong relations and a new ranking criterion is introduced as the result. The most important features of our method is the ability to achieve ranking intervals for two-stage production units based on the introduced relations over all feasible weights, as well as the ability to generate accurate information about sources of inefficiency of two-stage production units.

In this paper, we give an application of the perturbation inequality to the low rank matrix recovery problem and provide a condition on the linear map of underdetermined linear system that every minimal rank symmetric matrix $X\in {ℝ}^{m\times n}$ can be exactly recovered from the linear measurement $b={𝒜}(X)\in {ℝ}^q$ via some Schatten $p_0$ norm minimization. Moreover it is shown that the explicit bound on exponent $p_0$ in the Schatten $p_0$ norm minimization can be exactly extracted.

In this paper, we study recycling, remanufacturing, and pricing strategies of a manufacturer in a closed-loop supply chain. Different from traditional list-price transaction, a name-your-own-price auction is introduced into the recycling process where consumers offer a bid for their own used items and the manufacturer decides whether to accept the bid. We first analyze the consumers’ behavior and find that their bids increase with the dealing cost. Next, we build a newsvendor framework to investigate the manufacturer’s optimal manufacturing with pricing strategies and find that the stocking factor influences the recycling quantity and manufacturing policy. Moreover, we find that a larger salvage value motivates the manufacturer to set a higher stocking factor and thus recycle more as well as manufacture new products. We further investigate the effect of the demand uncertain level and the dealing cost on the system.

Many networked systems involve multiple modes of transport. Such systems are called multimodal, and examples include logistic networks, biomedical phenomena and telecommunication networks. Existing techniques for determining minimal paths in multimodal networks have either required heuristics or else application-specific constraints to obtain tractable problems, removing the multimodal traits of the network during analysis. In this paper weighted colored-edge graphs are introduced for modeling multimodal networks, where colors represent the modes of transportation. Minimal paths are selected using a partial order that compares the weights in each color, resulting in a Pareto set of minimal paths. Although the computation of minimal paths is theoretically intractable and ${𝒩}{𝒫}$-complete, the approach is shown to be tractable through experimental analyses without the need to apply heuristics or constraints.

In this paper, we present a novel sequential sampling methodology for solving multi-objective optimization problems. Random sequential sampling is performed using the information from within the non-dominated solution set generated by the algorithm, while resampling is performed using the extreme points of the non-dominated solution set. The proposed approach has been benchmarked against well-known multi-objective optimization algorithms that exist in the literature through a series of problem instances. The proposed algorithm has been demonstrated to perform at least as good as the alternatives found in the literature in problems where the Pareto front presents convexity, nonconvexity, or discontinuity; while producing very promising results in problem instances where there is multi-modality or nonuniform distribution of the solutions along the Pareto front.

In this paper, a new class of cooperative fuzzy games named fuzzy games with convex combination form is introduced. This kind of fuzzy games considers two aspects of information. One is the contribution of the players to the associated crisp coalitions; the other is their participation levels. The explicit expression of the Shapley function is given, which is equal to the production of the Shapley function on crisp games and the player participation levels. Meanwhile, the relationship between the fuzzy core and the Shapley function is studied. Surprisingly, the relationship between them does coincide as in crisp case. Furthermore, some desirable properties are researched. Finally, an example is provided to illustrate the difference in fuzzy coalition values and the player Shapley values for four types of fuzzy games.