Maw-Sheng Chern

On the computational complexity of reliability redundancy allocation in a series system

Finding the optimal redundancy that maximizes the system reliability is one of the important problems in reliability theory. A good deal of effort has been done in this field. In this paper, we prove that some reliability redundancy optimization problems are NP-hard. We also derive alternative proofs for the NP-hardness of some special cases of the knapsack problem.

Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand

In this paper, we extend the inventory lot-size models to allow for inflation and fluctuating demand (which is more general than constant, increasing, decreasing, and log-concave demand patterns). We prove that the optimal replenishment schedule not only exists but is also unique. Furthermore, we show that the total cost associated with the inventory system is a convex function of the number of replenishments. Hence, the search for the optimal number of replenishments is simplified to finding a local minimum. Finally, several numerical examples are provided to illustrate the results.

The fuzzy shortest path problem and its most vital arcs

Abstract The shortest path problem is to find the shortest distance between two specified nodes in a network. An arc is called a single most vital arc in the network, if its removal from the network results in the greatest increase in the shortest distance. The availability of arcs plays a key role in network problems. The most vital arcs problems provide a means by which the importance of arcs availability can be measured. In the traditional shortest path problem, the arc lengths are assumed to be crisp numbers. In this paper, we consider the case that the arc lengths are fuzzy numbers. In particular, we derive the membership function of the shortest distance by using a fuzzy linear programming approach. Based on this result, we then propose an algorithm for finding the single most vital arc in a network.

Deterministic lot-size inventory models with shortages and deterioration for fluctuating demand

We establish various inventory replenishment policies. We then analytically identify the best alternative among them based on the minimum total relevant costs. Finally, we prove that the relevant cost is convex with the number of replenishments. Consequently, the search for the optimal replenishment number is reduced to finding a local minimum.

A two-machine flowshop sequencing problem with limited waiting time constraints

Abstract We consider a two-machine flowshop sequencing problem with limited waiting time constraints. This means that for each job the waiting time between two machines cannot be greater than a given upper bound. The objective is to minimize the makespan. There are efficient algorithms for the special cases of infinite waiting time and zero waiting time. The two-machine flowshop sequencing problem with limited waiting time constraints is shown to be NP-hard. A branch-and-bound algorithm is proposed, and computational experiments are provided.

Two-machine flowshop group scheduling problem

Abstract This paper considers a two-machine flowshop group scheduling problem. The jobs are classified into groups and the jobs in the same group must be processed in succession. Each group requires a set up time and removal time on both machines. A transportation time is required for moving the jobs from machine 1 to machine 2. The objective is to minimize the maximum completion time (makespan). A polynomial time algorithm is proposed to solve the problem. This generalizes the algorithms proposed by Baker and others. Scope and purpose Recently, an important class of scheduling problem is characterized by a group scheduling constraint where the jobs are classified into groups by the same operation requirements or characters. Each group requires a setup time and removal time on both machines. That is, each machine needs a time to set up or to remove the tools, jigs and fixtures when the group starts processing or completes processing. A transportation time is required to move the jobs between the machines. The objective is to find a sequence of groups and jobs in each group such that the maximum completion time (makespan) is minimized. Baker provided an optimal algorithm for this problem in the case of two-machine flowshop group scheduling without considering the removal and transportation times. But, in some manufacturing environments, it is required to consider the group removal time and job transportation time. The main contribution of this paper is to develop a polynomial time algorithm, which generalizes the algorithms proposed by Baker and others.

Reliability Optimization Problems with Multiple Constraints

This paper presents a class of reliability optimization problems with multiple-choice constraints. We assume that at least one design alternative can be chosen as redundancy for each subsystem. A 2-phase solution method is presented for solving these problems. In phase I, we decompose a problem into n subproblems. These subproblems can be solved by dynamic programming, independently. That is, these subproblems can be solved by parallelism. In phase II, we solve a 0-1 multiple-choice knapsack problem which is generated from phase I. We use a combinatorial tree which always satisfies the multiple-choice constraints. The 2-phase solution method is illustrated with a numerical example.

A Note on Approximation Schemes for Multidimensional Knapsack Problems

Polynomial and fully polynomial approximation algorithms for single-dimensional knapsack problems have been extensively studied and a number of such algorithms constructed. This note shows that the problem of finding a fully polynomial approximation algorithm for multidimensional knapsack problems is NP-hard.

Retailer's optimal ordering policies with trade credit financing

In this article, we extended Goyals model to develop an Economic Order Quantity (EOQ) model in which the supplier offers the retailer the permissible delay period M, and the retailer in turn provides the trade credit period N (with N ≤ M) to his/her customers. In addition, we assume that (1) the retailers selling price per unit is necessarily higher than its unit cost, and (2) the interest rate charged by a supplier or a bank is not necessarily higher than the retailers investment return rate. We then establish an appropriate EOQ model with trade credit financing, and provide an easy-to-use closed-form solution to the problem. Furthermore, we find it is possible that a well-established buyer may order a lower quantity and take the benefit of the permissible delay more frequently, which contradicts to the result by the previous researchers. Finally, we perform some sensitivity analyses to illustrate the theoretical results and obtain some managerial results.

An optimal recursive method for various inventory replenishment models with increasing demand and shortages

We establish various inventory replenishment policies to solve the problem of determining the timing and number of replenishments. We then analytically compare various models, and identify the best alternative among them based on minimizing total relevant costs. Furthermore, we propose a simple and computationally efficient optimal method in a recursive fashion, and provide two examples for illustration.