Asia-Pacific Journal of Operational Research

A two-unit cold standby system is considered. The failure rate of a unit is a constant and the repair time distribution is a two-stage Erlang distribution. Measures of system performance such as reliability, mean time before failure, system availability, and steady-state availability are derived. Also, a consistent asymptotically normal estimator and a 100(1-α)% asymptotic confidence interval for the steady-state availability of the system are obtained.

This paper deals with the three-dimensional container packing problem (3DCPP), which is to pack a number of items orthogonally onto a rectangular container so that the utilization rate of the container space or the total value of loaded items is maximized. Besides the above objectives, some other practical constraints, such as loading stability, the rotation of items around the height axis, and the fixed loading (unloading) orders, must be considered for the real-life 3DCPP. In this paper, a sub-volume based simulated annealing meta-heuristic algorithm is proposed, which aims at generating flexible and efficient packing patterns and providing a high degree of inherent stability at the same time. Computational experiments on benchmark problems show its efficiency.

Hyper Sensitivity Analysis (HSA) is an intuitive generalization of conventional sensitivity analysis, where the term "hyper" indicates that the sensitivity analysis is conducted with respect to functions rather than numeric values. In this paper Composite Concave Programming is used to perform HSA in the area of Portfolio Optimization Problems. The concept of HSA is suited for situations where several candidates for the function quantifying the utility of (mean, variance) pairs are available. We discuss the applications of HSA to two types of mean–variance portfolio optimization problems: the classical one and a discrete knapsack-type portfolio selection problem. It is explained why in both cases the methodology can be applied to full size problems.

An order level inventory model is developed for deteriorating items with a constant rate of deterioration and vendor offering delay in payments. The model is developed under probabilistic demand. It is shown that the model derived can be related to the existing model for non-deteriorating items and when delay in payments is not permissible. The model is supported by a probability distribution function.

Several Software Reliability Growth Models (SRGMs) have been developed in the literature to account for exponential and S-shaped growth curves. There are others, which can account for both depending on the testing environment. Such models are termed as flexible models. Most of the models use calendar/execution time as the testing time. Very few SRGMs have been developed which define explicitly the testing effort functions into the modeling. Testing effort/resource may be computer time and manpower needed during testing. The aim of this paper is twofold.

1. Develop an SRGM with testing efforts which is also flexible

2. Use model in (1) to allocate optimally the testing resource to a modular software subject to different constraints.

Model developed in (1) is validated on different data sets and predictive validity is established. Optimization problems in (2) are mathematical programming problems having the sum of fractional functions as the common objective. These are solved using a dynamic programming approach and closed form solutions have been obtained. Finally, numerical illustrations are provided for two optimization problems.

Resource constrained scheduling problems are concerned with the allocation of limited resources to tasks over time. The solution to these problems is often a sequence, resource allocation, and schedule. When human workers are incorporated as a renewable resource, the allocation is defined as the number of workers assigned to perform each task. In practice, however, this solution does not adequately address how individual workers are to be assigned to tasks. This paper, therefore, provides mathematical models and heuristic techniques for solving this multi-period precedence constrained assignment problem. Results of a significant numerical investigation are also presented.

The inconsistency of judgments in the fuzzy Analytic Hierarchy Process (AHP) is a crucial issue. To make the appropriate decision, the inconsistency in decision maker's (DM) judgments needs to be eliminated or reduced. This paper proposes two mathematical models to deal with inconsistency in fuzzy AHP. In the first model, the DM's judgments are modified where the preference order of the DM's judgments remained unchanged. The second model allows reversing the preference orders of judgments. The proposed models aim to eliminate or reduce the inconsistency of fuzzy AHP by changing judgments. The models cause fewer changes for the high certain judgments. Two examples solved by the proposed models are included for purposes of illustration.

For the asset market with finite numbers of investors whose utility functions are general concave functions, we derive a necessary and sufficient condition for the existence and uniqueness of the nonnegative equilibrium price vector that clears the asset market, through considering the expected utility maximization problem under the assumption that the joint distribution of risky assets' returns is an elliptical distribution. An explicit formula for the equilibrium price is given. We also discuss the economic implication of the given condition and demonstrate that our necessary and sufficient condition can be regarded as a necessary condition to maintain the stability of the asset market. These results extend some results about the equilibrium analysis of the asset market.

Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.