Asia-Pacific Journal of Operational Research

In economic allocation problems, egalitarianism and marginalism are two major thoughts to distribute the benefits of cooperation. The α-CIS value reconciles the two thoughts in some variable extent by a parameter α ∈ [0, 1]. The α-CIS value is the center of gravity of the corresponding α-imputation set given the α-imputation set is nonempty. From the cooperative perspective, we present several axiomatizations of the α-CIS value using α-individual rationality or α-dummifying player property. Finally, we provide a noncooperative interpretation of the α-CIS value by a bidding mechanism.

This paper studies the online hierarchical scheduling problem on two uniform machines with bounded job sizes, where the first machine M₁ receives both low and high hierarchy jobs, while the second machine M₂ only receives high hierarchy jobs. The machines have a speed ratio of s(s ≥ 1), and M₂ runs faster. Jobs are revealed one by one, and before the current job is scheduled, we have no information about next jobs except that the size of any job is in the interval [1, t]. The objective is to minimize the makespan. We present optimal algorithms for all (s, t) pairs.

This paper considers single-machine scheduling with learning effect, deteriorating jobs and convex resource dependent processing times, i.e., the processing time of a job is a function of its starting time, its position in a sequence and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately to minimize a cost function containing makespan, total completion (waiting) time, total absolute differences in completion (waiting) times and total resource cost. It is proved that the problem can be solved in polynomial time.

This paper addresses online scheduling of malleable parallel jobs to minimize the maximum completion time, i.e., makespan. It is assumed that the execution time of a job J_j with processing time p_j is p_j/k + (k-1)c if the job is assigned to k machines, where c > 0 is a constant setup time. We consider online algorithms for the scheduling problem on two identical machines. Namely, the job J_j can be processed on one machine with execution time p_j or alternatively two machines in parallel with execution time p_j/2+c. For the asymptotical competitive ratio, we provide an improved online algorithm with makespan no more than (3/2)C* +c/2, where C* is the optimal makespan. For the strict competitive ratio, we propose an online algorithm with competitive ratio of 1.54, which is close to the lower bound of 1.5.

Linguistic hesitant fuzzy sets (LHFSs) are a very useful and appropriate means of expressing preferences of decision-makers; moreover their basic operations and comparison methods have been defined and applied to the solving of MCDM problems. However, there are a number of limitations in the related studies. In this paper, using information from existing studies, several new operations and a new order relationship are defined; moreover four linguistic hesitant fuzzy Heronian mean operators are proposed: the linguistic hesitant fuzzy arithmetic Heronian mean (LHFAHM) operator; the linguistic hesitant fuzzy weighted arithmetic Heronian mean (LHFWAHM) operator; the linguistic hesitant fuzzy geometric Heronian mean (LHFGHM) operator; and the linguistic hesitant fuzzy weighted geometric Heronian mean (LHFWGHM) operator. Furthermore, some useful and desirable properties of these operators are analyzed in some special cases, with respect to the different parameter values in these operators, are discussed. Additionally, an approach based on the LHFWAHM and LHFWGHM operators for solving MCDM problems is proposed. Finally, an illustrative example is provided to verify the validity and feasibility of the proposed approaches, and a comparison analysis is also presented to demonstrate the influences of different parameters on the results of decision-making.

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

Product design decisions have significant impact on a firm's competitive edge. This paper investigates the condition under which component commonality is a profitable product design strategy for a firm by considering customer-choice behavior in the supply chain environment. The design configuration with commonality can lower manufacturing cost, but it also reduces product differentiation and revenue. While the customer-choice behavior with utility maximization will impact the retailer's product pricing, we analyze a stylized model of the manufacturer who designs a product family consisting of two products for two market segments with different valuations of quality. By explicitly considering the interrelationship between customer's utility and retail price, we find that commonality strategy is conditionally profitable. Theoretical research reveals that the optimal product design strategy depends on the marginal valuations of customer-choice behavior and the cost-coefficient of the common component determined by the supplier. An example is used to illustrate how some supply chain parameters impact the optimal product design strategy.

In this paper, we consider the network loading problem under demand uncertainties with static routing, i.e., a single routing scheme based on the fraction of the demands has to be determined. We generalize the class of metric inequalities to the Γ-robust setting and show that they yield a formulation in the capacity space. We describe a polynomial time exact algorithm to separate violated robust metric inequalities as model constraints. Moreover, rounded and tight robust metric inequalities describing the convex hull of integer solutions are presented and separated in a cut-and-branch approach. Computational results using real-life telecommunication data demonstrate the potential of (tight) robust metric inequalities by considering the integrality gaps at the root node and the overall optimality gaps. Average speed-up factors between 2 and 5 for the compact flow and between 3 and 25 for the capacity formulation in the case of mid-sized instances have been achieved by exploiting robust metric inequalities in the solving process.

We consider a linear time–cost tradeoff problem with multiple milestones and uncertain processing times such that all jobs are completely ordered. The performance measure is expressed as the sum of total weighted number of tardy jobs and total crashing cost. The processing times uncertainty is described through two types of scenarios: discrete and interval scenarios. The objective is to minimize maximum deviation from optimality over all scenarios. For the discrete scenario case, we prove its NP-hardness, develop a pseudo-polynomial time approach, and present a polynomially solvable case. Finally, we show that the interval scenario case is also NP-hard.

This paper adds to the growing remanufacturing literature by investigating a collaborative model in which the manufacturer serves as the remanufacturer's distributor while selling its own product. The paper extends the collaborative model that we have studied previously by characterizing it as a channel power structure under which the manufacturer plays the leader role in the collaboration. Furthermore, the paper compares this collaborative model with a competitive model in which the manufacturer competes with the remanufacturer in the market on pricing, sales volume and profit and finds that even if the manufacturer chooses to collaborate with the remanufacturer, it does not give up its market position; the manufacturer keeps the price of its product unchanged as the remanufactured product becomes increasingly acceptable to the consumer, and its product's sales volume remains unchanged in both models. Finally, this paper observes that the collaborative model benefits the manufacturer more than the competitive model, whereas the competitive model benefits the remanufacturer more than the collaborative model. Obviously, if collaboration benefits both of the manufacturer and remanufacturer, they will choose to collaborate, and the manufacturer will transfer part of its profit to the remanufacturer, but if competition brings them more profit, they will choose to compete in the market, and the remanufacturer will transfer part of its profit to the manufacturer.