Asia-Pacific Journal of Operational Research

A continuous approach using NCP function for approximating the solution of the max-cut problem is proposed. The max-cut problem is relaxed into an equivalent nonlinearly constrained continuous optimization problem and a feasible direction method without line searches is presented for generating an optimal solution of the relaxed continuous optimization problem. The convergence of the algorithm is proved. Numerical experiments and comparisons on some max-cut test problems show that we can get the satisfactory solution of max-cut problems with less computation time. Furthermore, this is the first time that the feasible direction method is combined with NCP function for solving max-cut problem, and similar idea can be generalized to other combinatorial optimization problems.

A retail category management model that considers the interplay of optimal product assortment decisions, space allocation and inventory quantities is presented in this paper. Specifically, the proposed model maximizes the total net profit in terms of decision variables expressing product assortment, shelf space allocation and common review period. The model takes into consideration several constraints such as the available shelf space, backroom inventory space, retailer's financial resources, and estimates of rate of demand for products based on shelf space allocation and competing products. The review period can take any values greater than zero. Results of the proposed model were compared with the results of the current industry practice for randomly generated product assortments of size six, ten and fourteen. The model also outperformed the literature benchmark. The paper demonstrates that the optimal common review period is flexible enough to accommodate the administrative restrictions of delivery schedules for products, without significantly deviating from the optimal solution.

In this paper, a novel genetic algorithm — dynamic ring-like agent genetic algorithm (RAGA) is proposed for solving global numerical optimization problem. The RAGA combines the ring-like agent structure and dynamic neighboring genetic operators together to get better optimization capability. An agent in ring-like agent structure represents a candidate solution to the optimization problem. Any agent interacts with neighboring agents to evolve. With dynamic neighboring genetic operators, they compete and cooperate with their neighbors, and they can also use knowledge to increase energies. Global numerical optimization problems are the most important ones to verify the performance of evolutionary algorithm, especially of genetic algorithm and are mostly of interest to the corresponding researchers. In the corresponding experiments, several complex benchmark functions were used for optimization, several popular GAs were used for comparison. In order to better compare two agents GAs (MAGA: multi-agent genetic algorithm and RAGA), the several dimensional experiments (from low dimension to high dimension) were done. These experimental results show that RAGA not only is suitable for optimization problems, but also has more precise and more stable optimization results.

This study addresses a two-stage flowshop with a batch machine in stage 1 and a discrete machine in stage 2, subject to the constraint that the input buffer of the discrete machine can only host limited number of jobs. The batch machine processes a batch of jobs simultaneously, and the discrete machine processes one job at a time. The objective function of the problem is the makespan minimization. Several properties are proposed to solve the special case of the problem optimally. An effective heuristic is presented, and a branch-and-bound procedure is proposed for benchmarking. Extensive experimentation shows that the heuristic yields good results.

In this paper, a use of s-quasimonotonicity [introduced in Optimization, Vol. 55 (2006)] in an economics model is presented. We introduce a strong version of Wald's Axiom of excess demand functions , namely "there exists σ > 0 such that p, q ∈ P, q^T Z(p) - δ ≤ 0,|δ| < σ, and Z(q) ≠ Z(p) imply p^TZ(q) + δ > 0". Under some assumptions, Z satisfies the strong version of Wald's Axiom iff -Z is a s-quasimonotone function. Consequently, an excess demand function Z satisfies the strong version of Wald's Axiom iff -Z is stable with respect to the pseudomonotonicity property (i.e. there exists ∊ > 0 such that -Z + a fulfills the pseudomonotonicity property for all a ∈ ℝⁿ satisfying ‖a‖ < ∊). Some properties on the measure of the strong version of Wald's Axiom of excess demand functions are also presented.

This paper analyzes a continuous-review inventory system with random supply interruptions and stochastic lead time. In such a system, a monopolistic supplier alternates between random ON and OFF periods. The variable (r,q)-policy is used. With a constant demand rate, the leadtime may be interrupted by a random number of OFF periods of the supplier. Using the regenerative cycle analysis, a long-run average cost function is obtained and shown to have some important properties. Accordingly, an effective search algorithm is proposed to find the sub-optimal inventory policy. In the end, we also investigate the effects on the average cost of the uncertain order delay which attribute to both the supply interruptions and the random leadtime. Numerical examples are presented to demonstrate the effectiveness of the search algorithm.

We study static repair priorities in a system consisting of one repair shop and one stockpoint, where spare parts of multiple, critical repairables are kept on stock to serve an installed base of technical systems. Demands for ready-for-use parts occur according to Poisson processes, and are accompanied by returns of failed parts. The demands are met from stock if possible, and otherwise they are backordered and fulfilled as soon as a ready-for-use part becomes available. Returned failed parts are immediately sent into repair. The repairables are assigned to static priority classes. The repair shop is modeled as a single-server queue, where the failed parts are served according to these priority classes. We show that under a given assignment of repairables to priority classes, optimal spare parts stock levels follow from Newsvendor equations. Next, we develop fast and effective heuristics for the assignment of repairables to priority classes. Subsequently, we compare the performance of the system under these static priorities to the case with a First-Come First-Served (FCFS) service discipline. We show that in many cases static priorities reduce total inventory holding and backordering costs by more than 40%. Finally, we analyse the effect of the number of priority classes. We show that 2 priority classes suffice to obtain 90% of the maximal savings via static priorities.