Asia-Pacific Journal of Operational Research

We introduce new classes of higher-order functional, termed higher-order $(F,\alpha ,\rho ,d)-$convex and higher-order $(C,\alpha ,\rho ,d)-$convex functionals. These classes are illustrated by nontrivial examples. A pair of higher-order multiobjective symmetric fractional variational programs with cone constraints and fixed boundary conditions is formulated. Appropriate duality results are discussed utilizing the aforementioned assumptions. The results in this paper are generalizations of the results already existing in literature.

In this paper, our purpose is to use the improvement set to investigate the scalarization and optimality conditions of E-globally proper efficient solution for the set-valued equilibrium problems with constraints. First, the notion of E-globally proper efficient solution for set-valued equilibrium problems with constraints is introduced in locally convex Hausdorff topological spaces. Second, the linear scalarization theorems of E-globally proper efficient solution are derived. Finally, under the assumption of nearly E-subconvexlikeness, the Kuhn–Tucker and Lagrange optimality conditions for set-valued equilibrium problems with constraints are obtained in the sense of E-globally proper efficiency. Meanwhile, we give some examples to illustrate our results. The results obtained in this paper improve and generalize some known results in the literature.

Founded on the idea of subdividing the $(p-1)$-dimensional output space, a branch-and-bound algorithm for solving the sum-of-linear-ratios(SLR) problem is proposed. First, a two-stage equivalent transformation method is adopted to obtain an equivalent problem(EP) for the problem SLR. Second, by dealing with all nonlinear constraints and bilinear terms in EP and its sub-problems, a corresponding convex relaxation subproblem is obtained. Third, all redundant constraints in each convex relaxation subproblem are eliminated, which leads to a linear programming problem with smaller scale and fewer constraints. Finally, the theoretical convergence and computational complexity of the algorithm are demonstrated, and a series of numerical experiments illustrate the effectiveness and feasibility of the proposed algorithm.

Taking into consideration gH-symmetrical derivative, we discuss Fritz John type optimality conditions for E-convex functions in interval-valued optimization problems. By a suitable example, we show that gH-symmetrical derivative is an extension of gH-derivative. We use LU type of order relation in this context.

In this paper, we consider a dual-channel farming supply chain with two farmers and one distributor, where agriculture products produced by farmers have different quality levels. Farmers sell high-quality products to supermarkets and normal-quality products to small retail markets, respectively. Three scenarios are investigated: decentralized selling through the distributor to supermarkets (the DD mode); centralized selling through the distributor to supermarkets (the CD mode); centralized selling directly to supermarkets (the CS mode). Under the CS mode, farmers need to bear some extra sale cost such as inventory and transportation cost. We derive farmers’ optimal strategies of production effort and quality investment. It turns out that as farming scale expands, farmers’ production effort decreases, while quality investment increases. Moreover, two farmers’ quality investments are the highest under the CS mode and the least under the DD mode. black Further analysis indicates that farmers’ total profits are generally the highest under the CS mode, but farmers obtain the highest profits under the CD mode if farmers’ extra sale cost under the CS mode exceeds a certain level. Therefore, to improve farmers’ welfare and agriculture products’ quality simultaneously, the CS mode may be the best choice in most cases, and it leads to a “win–win” situation for farmers and consumers.

The remanufacturing industry is experiencing a gradual increase in international trade. Accordingly, manufacturers are encountering a multitude of regulations in this cross-border trade of remanufactured products, such as import prohibitions/bans, environmental regulations, and tariff barriers. In this paper, we investigated the implications of exporting remanufactured products to the international market with or without trade regulations. Our analysis reveals that, although the international market for remanufacturing invariably benefits the manufacturer, trade regulations are a disadvantage to remanufactured exports. Thus, while the quality of remanufactured products increases, the adverse effect of trade regulations could be weakened. Additionally, we reveal that trade regulations may be detrimental to the environment with a higher rate of used core collection and disposal impact. Thus, policymakers should take care to regulate the international market for remanufactured goods rather than implementing a one-size-fits-all solution.

In this paper, we consider a system of inequalities associated with circular cones. By constructing a new smoothing function, the problem is reformulated as a system of parameterized smooth equations. In addition, we suggest a Newton-type algorithm for solving the smooth equations so that a solution of the problem concerned is found. In particular, the algorithm is proved to be globally and locally quadratically convergent under suitable conditions. The preliminary numerical results demonstrate that the algorithm is effective.

We study single-machine bicriteria scheduling problems with position-dependent weights. Due date costs and penalty costs can affect the decision-maker’s profit. Therefore, how to optimize the benefits and balance of these costs for decision-makers is the focus of this research. This paper discusses three models: weighted-sum scheduling problem, constrained scheduling problem, Pareto scheduling problem. It analyzes the properties of bicriteria schedule, determines the optimal due dates (usually referred to as different due dates: DIF), and gives the corresponding polynomial solvable algorithms.

Among the carbon regulation policy schemes, the cap-and-trade has received more attention because of its efficiency and flexibility. Two primary challenges with the cap-and-trade scheme are determining the correct cap and carbon trading price in the carbon market. This paper presents a bi-level model to investigate these two challenges in the cap-and-trade scheme formed between multiple supply chains and the government. At the first level, the government minimizes the cap in such a way that the costs of the supply chains do not rise too much. At the second level, the supply chains minimize their costs according to their cap and trade the dedicated allowances. An exact and a heuristic method are developed to solve the bi-level model. The computational results on a set of randomly generated instances show the effectiveness of the presented heuristic. Sensitivity analysis demonstrates that the government should choose proper amounts of caps to balance costs and environmental benefits.

This paper investigates a dual-channel supply chain which consists of a capital-constrained manufacturer and an e-commerce platform. The manufacturer sells its products through an offline direct channel and an online platform. The platform can serve as a marketplace or a reseller for the manufacturer, while the platform provides online finance to the manufacturer. We discuss the equilibrium decisions of the manufacturer and the platform when the platform serves as two different roles. We find that when the total production quantity of the manufacturer who with an online marketplace channel exceeds a threshold, the manufacturer tends to choose the platform’s marketplace role for the online channel, unless the wholesale price and the upper limit of demand are high. When production quantity is below this threshold, unless the wholesale price and the upper limit of demand are low, the manufacturer tends to choose the platform’s reseller role for the online channel. The platform tends to choose the role whose production quantity exceeds the threshold. If both are exceeded, the platform chooses the marketplace role when the wholesale price is low, and if both are not exceeded, the marketplace role is better when the wholesale price is high.

Considering the real dilemma of deteriorating items, we explore how to find a balance between the conflicting achievements of enhancing flexibility and reducing costs. We propose a general dynamic model to penetrate customer orders by decoupling point with objective to minimize the cost. The closed forms of optimal solutions are obtained for companies to deal with the integrated problem of customer order decoupling point (CODP) decision and production–inventory plan simultaneously. Applications and numerical experiments are performed to illustrate practical insights for managers. The results show that the truth of zero-inventory policy is to avoid unnecessary inventory instead of absolutely no inventory. The CODP will shift forward with the increasing of customer demand rate and shift backward with the increasing of deterioration rate under the production smoothing policy. However, although it encounters the same changes of demand, the CODP moves with a smaller extent in high deterioration rate than in low. In addition, we find that during the growth phase of product life cycle, the increase of time-sensitive degree of demand is coupled with forward shifting of CODP; while during the decline phase, it is coupled with CODP backward shifting.

In this paper, we consider scheduling problems with slack (different) due-window assignment and time-dependent processing times. The processing time functions are all a proportional linear increasing function of time. On a single-machine setting, the goal is to minimize a cost function that includes earliness, tardiness, due-window starting time and size, and the number of early and tardy jobs. Some relevant optimality properties and polynomial time solution algorithms are proposed to solve these two problems.