Asia-Pacific Journal of Operational Research

The flow-shop minimum-length scheduling problem with n jobs processed on two machines is addressed where processing times are uncertain: only lower and upper bounds of the random processing times are given before scheduling, but their probability distributions are unknown. For such a problem, there may not exist a dominant schedule that remains optimal for all possible realizations of the processing times and so we look for a minimal set of schedules that are dominant. We obtain necessary and sufficient conditions for the case when it is possible to fix the order of two jobs in a minimal set of dominant schedules. The necessary and sufficient conditions are proven for the case when one schedule dominates all the others. We characterize also the case where there does not exist non-trivial schedule domination. All the conditions proven may be tested in polynomial time of n.

The generation of Pareto optimal solutions for complex systems with multiple conflicting objectives can be easier if the problem can be decomposed and solved as a set of smaller coordinated subproblems. In this paper, a new decomposition-coordination method is proposed, where the global problem is partitioned into subsystems on the basis of the connection structure of the mathematical model, assigning a relative importance to each of them. In order to obtain Pareto optimal solutions for the global system, the aforementioned subproblems are coordinated taking into account their relative importance. The scheme that has been developed is an iterative one, and the global efficient solutions are found through a continuous information exchange process between the coordination level (upper level) and the subsystem level (lower level). Computational experiments on several randomly generated problem instances show that the suggested algorithm produces efficient solutions within reasonable computational times.

This work presents an extension of the classical EOQ model for items with a fixed shelf life and a declining demand rate due to a reduction in the quality of the item in the course of its shelf-life. The demand rate, reflecting consumer preference for fresh items, is a polynomial function of the remaining time until the expiry date of the item. A mathematical model is developed to maximize the average profit per unit time, subject to shelf-life and marginal profit limitations. We prove that based on these limitations the model has a unique optimal solution and suggest a procedure for finding the optimal cycle length. A numeric example, including a sensitivity analysis, illustrates the model.

In this article, we study the convex hull presentation of a quadratically constrained set. Applying the new result, we solve a kind of quadratically constrained quadratic programming problems, which generalizes many well-studied problems.

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

Reliability evaluation has a vital importance at all stages of processing and controlling modern engineering systems. In most of these modern systems the components have different contributions to the system, which are defined as weights. Among the other weighted systems, a linear consecutive-weighted-k-out-of-n:F system consists of n components, where each component has its own weight and reliability. The system fails if and only if the total weight of the failed consecutive components is at least k. The aim of this paper is to study the reliability of linear consecutive-weighted-k-out-of-n:F system consisting of independent & nonidentical and nonhomogeneous Markov dependent components. Exact formulae are provided for computing the reliability for above mentioned cases. Approximation formulae for the reliability are also presented.

This paper focuses on scheduling problem of a pipe-processing flowshop in a shipyard. The flowshop composes of five stages, including cutting, bending, welding preprocessing, argon-welding and CO₂-welding, and each stage consists of identical parallel machines. Since thousands of pipes are mounted on the hull block before erection, the pipe-processing scheduling is a critical task for shipbuilding to meet the due date of the block erection. A tabu search algorithm is developed for the scheduling problem with the objective of minimizing total tardiness. Computational experiments are performed on the collected real data. Results show that the proposed algorithm is efficient for this problem.

A block preventive maintenance (PM) policy for a multi-unit system composed of identical units is investigated in this paper. The block PM model of this paper considers periodic inspection and periodic imperfect maintenance. The imperfect maintenance effects are formulated using improvement factor and age reduction model. We define variables of maintenance policy as the inspection period and the PM period and obtain an optimal maintenance policy which minimizes the average total cost. A numerical example is presented, and some sensitivity analyses for model parameters are also investigated.