Cerry M. Klein

Fuzzy shortest paths

Abstract Shortest Paths are one of the simplest and most widely used concepts in nonfuzzy networks. Fuzzy shortest paths also have a variety of applications but are hampered by the possibility that the fuzzy shortest length may not correspond to an actual path in the network. In this paper we present new models based on fuzzy shortest paths that circumvent this problem and we also give a general algorithm based on dynamic programming to solve the new models. In addition we analyze the fuzzy shortest path algorithms in terms of submodular functions. The analysis concepts developed for fuzzy shortest paths are also discussed in terms of general fuzzy mathematical programming.

An efficient approach to solving fuzzy MADM problems

Abstract An approach using defuzzifying methods is proposed for the fuzzy multiple attribute decision-making (MADM) problem. The computational effectiveness and efficiency of six defuzzifying methods combined with the simple additive weighting (SAW) method are evaluated based on a comparison to the improved fuzzy weighted average (IFWA) followed by four fuzzy ranking methods. Numerical examples are discussed to demonstrate the implementation and effectiveness of the methods.

New algorithm for the ranking procedure in fuzzy decision-making

In order to rank three or more fuzzy numbers it is necessary to consider not only the accuracy and effectiveness of the method but also its numerical efficiency. An algorithm designed to rank any number of fuzzy numbers is presented. The algorithm is verified by testing it on the set of 13 cases of paired examples, which are normal and convex fuzzy numbers, given in T.Y. Tseng and C.M. Klein (1988). The results are compared with those of W. Kolodziejczyks R1 index (1986), and the performance of both algorithms is evaluated. It is concluded that the present algorithm is both accurate and efficient. >

Optimal inventory policies under decreasing cost functions via geometric programming

Abstract In this paper, we establish and analyze two economic order quantity (EOQ) based inventory models under total cost minimization and profit maximization via geometric programming (GP) techniques. Through GP, optimal solutions for both models are found and managerial implications on the optimal policy are determined through bounding and sensitivity analysis. We investigate the effects on the changes in the optimal order quantity and the demand per unit time according to varied parameters by studying optimality conditions. In addition, a comparative analysis between the total cost minimization model and the profit maximization model is conducted. By investigating the error in the optimal order quantity of these two models, several interesting economic implications and managerial insights can be observed.

Single-machine scheduling with sequence dependent setup to minimize total weighted squared tardiness

This paper addresses the NP-hard problem of scheduling N independent jobs on a single machine with release dates, due dates, sequence dependent setup times, and no preemption where the objective is to minimize the weighted sum of squared tardiness. A Lagrangian relaxation based approach is developed for single-machine scheduling with sequence dependent setup times that is based on a list scheduling concept in conjunction with Lagrangian relaxation. Sequence dependent setup times are formulated as capacity constraints, and then are relaxed using Lagrangian multipliers. The primal problem is decomposed into job-level subproblems which are solved optimally and an approximate dual problem is then solved using a sub-gradient technique. The result of the relaxation is a list of jobs sequenced by beginning times that is then improved via a three-way swap. Experimental results are compared with EDD (Earliest Due Date) and ATCS (Apparent Tardiness Cost with Setups) dispatching rules, a four-way swap local search, tabu search, and simulated annealing. The adopted approach results in superior solution quality with respect to EED, ATCS, four-way swap, and tabu search results. It has comparable solution quality to the simulated annealing results, but is substantially more computationally efficient. Overall, the approach is capable of dealing with realistically sized single machine scheduling problems with release dates, due dates, and sequence dependent setup times.

Single machine stochastic scheduling to minimize the expected number of tardy jobs using mathematical programming models

This paper studies the single machine scheduling problem for the objective of minimizing the expected number of tardy jobs. Jobs have normally distributed processing times and a common deterministic due date. We develop new approaches for this problem that generate near optimal solutions. The original stochastic problem is transformed into a non-linear integer programming model and its relaxations. Computational study validates their effectiveness by comparison with optimal solutions.

A new algorithm for fuzzy multicriteria decision making

Abstract An algorithm for fuzzy multicriteria decision making is developed that allows the use of linguistic ratings as well as numeric ratings. This algorithm is based on and maintains the advantages of weighted-average rating methods and implied conjunction methods. The proposed algorithm is tested against another method and is shown to be precise and efficient.

Optimal inventory policies for an economic order quantity model with decreasing cost functions

In this paper, three total cost minimization EOQ based inventory problems are modeled and analyzed using geometric programming (GP) techniques. Through GP, optimal solutions for these models are found and sensitivity analysis is performed to investigate the effects of percentage changes in the primal objective function coefficients. The effects on the changes in the optimal order quantity and total cost when different parameters of the problems are changed is also investigated. In addition, a comparative analysis between the total cost minimization models and the basic EOQ model is conducted. By investigating the error in the optimal order quantity and total cost of these models, several interesting economic implications and managerial insights can be observed.

A new rule for minimizing the number of tardy jobs in dynamic flow shops

In this paper we present a new scheduling rule for minimizing the number of tardy jobs in a dynamic flow shop consisting of m machines. Jobs with processing times and due dates randomly arrive to the system. We assume that job arrival or release dates are not known in advance. The new rule is derived by dividing the m machine problem into several one-machine sub-problems, and optimally solving each one-machine sub-problem by applying a variation of the Moore–Hodgson algorithm. Computational results indicate that the proposed rule performs 15–20% better than SPT, which is currently one of the most effective methods for minimizing the number of tardy jobs in dynamic flow shops. Results are given for 10, 20, and 50 jobs and 2, 5, and 10 machines under various shop conditions.

Minimizing the expected number of tardy jobs when processing times are normally distributed

This paper studies the single machine scheduling problem for the purpose of minimizing the expected number of tardy jobs. The effect of variance of processing time is evaluated, and a dynamic policy based on a myopic approach is developed. The conditions for the optimality and the worst case analysis are provided.