Asia-Pacific Journal of Operational Research

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, to analyze the effect of different rules on the effectiveness of the beam search algorithms.

The computational results show that using better rules improves the performance of the beam search heuristics. The detailed, filtered beam search (FBS) and recovering beam search (RBS) procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, the detailed beam search (DBS) algorithm requires excessive computation times, and the RBS procedure then becomes the heuristic of choice.

This paper studies the fluid model of a special kind of multi-type queueing network with type priority. The fluid of the same type in the same station is operated under last buffer first served (LBFS) policy. The stability of this kind of fluid model is proved via the Lyapunov function.

We consider the problem of minimizing the total late work on an unbounded batch processing machine, where V_j = min {T_j, p_j} and T_j = max {C_j - d_j, 0}. The batch processing machine can process up to B (B ≥ n) jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time, respectively. For a batch of jobs, the processing time of the batch is equal to the largest processing time among the jobs in this batch. In this paper, we prove that the problem is NP-hard.

Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions defined on the positive definite cone . Using some appealing and mild conditions of the new class, we prove with simple analysis that the new class-based large-update primal-dual IPMs enjoy an iteration bound to solve SDO problems with special choice of the parameters of the new class.

In recent years, as a result of environmental legislation and an increasing interest in economics, many producers have been forced to implement the PTB (Products Tack Back) program. In this paper, we employ the basic (R, Q) model to control a single-item single-echelon inventory system with return flow. Based on the assumption that the return and the demand are independent Poisson processes, we derive a simple approximate algorithm to determine the optimal control parameters. The numerical examples show that the presented algorithm is more tractable than the exact algorithm and more accurate than other approximate algorithms, such as normal approximation.

In this paper we focus on two types of risks, the risk of malfunctioning of a product quantified by its reliability, and the risk of misunderstanding the features and qualities of a product while deciding whether to buy it. The later risk is caused by the information asymmetry, which is a natural property of any communication process. We discuss the relationship between these risks and product warranty. We begin with an overview of warranties from the decision-makers' viewpoint. We elaborate on the purposes, legalities, and types of warranties and follow with a summary of mathematical models and concepts for quantifying the financial implications of warranties of malfunctioning. Further, we propose a model for quantifying the risk of misinforming and elaborate on the relationship between this risk and product warranty.

This work presents an optimization model to support decisions in the production planning and control of the electrofused grain industry. A case study was carried out in a Brazilian company with the aim of helping to increase productivity and improve customer service concerning meeting deadlines. A mixed integer linear programming model combining known models of process selection and single-stage lot sizing were applied to the production scheduling of electrofused grains. Optimizing this scheduling is not a simple task mainly because of the scale of the equipment setup times, the diversity of the products and the deadlines of the order due dates. A constructive heuristic is also proposed as an alternative solution method, particularly for large-sized instances. The results show that the model and the heuristic can produce better solutions than the ones currently used by the company.