Asia-Pacific Journal of Operational Research

In the single machine scheduling problem with job delivery to minimize makespan, jobs are processed on a single machine and delivered by a capacitated vehicle to their respective customers. We first consider the special case with a single customer, that is, all jobs have the same transportation time. Chang and Lee (2004) proved that this case is strongly NP-hard. They also provided a heuristic with the worst-case performance ratio , and pointed out that no heuristic can have a worst-case performance ratio less than unless P = NP. In this paper, we provide a new heuristic which has the best possible worst-case performance ratio . We also consider an extended version in which the jobs have non-identical transportation times and the transportation time of a delivery batch is defined as the maximum transportation time of the jobs contained in it. We provide a heuristic with the worst-case performance ratio 2 for the extended version, and show that this bound is tight.

In most real-world situations for transportation planning decision (TPD) problems, environmental coefficients and parameters are imprecise/fuzzy in nature, and the decision maker (DM) generally faces a multi-objective TPD problem in a fuzzy environment. This work develops an interactive fuzzy linear programming (FLP) method for solving TPD problems with fuzzy goals, available supply and forecast demand. The proposed method attempts simultaneously to minimize the total production and transportation costs and the total delivery time with reference to available supply, machine capacities and budget constraints at each source, as well as forecast demand and warehouse space constraints at each destination. In addition, the proposed method provides a systematic framework that facilitates the DM interactively to modify the imprecise data and related parameters until a satisfactory solution is derived. An industrial case is used to demonstrate the feasibility of applying the proposed method to real-world TPD problems. Especially, several significant characteristics of the proposed FLP method are presented in contrast to those of the main TPD methods.

This paper addresses the multi-period two-echelon integrated competitive/uncompetitive facility location problem in a distribution system design that involves locating regional distribution centers (RDCs) and stores, and determining the best strategy for distributing the commodities from a central distribution center (CDC) to RDCs and from RDCs to stores. The goal is to determine the optimal numbers, locations and capacities of RDCs and stores so as to maximize the total profit of the distribution system. Unlike most of past research, our study allows for dynamic planning horizon, distribution of commodities, configuration of two-echelon facilities, availability of capital for investment, external market competition, customer choice behavior and storage limitation. This problem is formulated as a bi-level programming model and a mutually consistent programming mode, respectively. Since such a distribution system design problem belongs to a class of NP-hard problem, a genetic algorithm-based heuristic (GA) is presented and compared with random search solution and mutually consistent solution (MC) using numerical example. The computational results show that the GA approach is efficient and the values of the performance index were significantly improved relative to the MC.

This paper analyzes the unloader queueing model in which N identical trailers are unloaded by R unreliable unloaders. Steady-state analytic solutions are obtained with the assumptions that trip times, unloading times, finishing times, breakdown times, and repair times have exponential distributions. A cost model is developed to determine the optimal values of the number of unloaders and the finishing rate simultaneously, in order to minimize the expected cost per unit time. Numerical results are provided in which several steady-state characteristics of the system are calculated based on assumed numerical values given to the system parameters and the cost elements. Sensitivity analysis is also studied.

This study evaluates the assignment system by FMCDM for Turkish Army Forces (TAF). TAF personnel are assigned to Garrisons (a headquarter or a certain geographical place in Turkey), for fixed periods. Selecting the optimal Garrison is an important problem for personnel, and is based on a number of alternatives and criteria. The system includes eight city centers, evaluated as alternatives. For defining the criteria, a questionnaire is designed and applied to army officers and sergeants. The criteria weights are determined by four randomly selected experts. Experts described the weights depending on their assessments, which may vary depending on their own necessities, experiences and priorities. They used linguistic weights, such as "very good, good, medium, low, very low". Hence, the assessments are away from certainty. This uncertainty implies fuzziness in weights. Besides, the criteria were determined by factor analysis, applied on the responses of the questionnaire, which also gives a sense of uncertainty. In the analysis under imprecision judgements, the criteria weights are presented as trapezoidal fuzzy numbers to get more reasonable and realistic solutions. Ideal and anti-ideal points are calculated for different optimism indexes and the final results are obtained based on these points. It is observed that different optimality indexes changed the rankings of alternatives.

Since the publication of the Goyal model in 1985, research on the modeling of inventory lot-size under trade credits has resulted in a body of literature. In this paper, we present a review of the advances in inventory literature under conditions of permissible delay in payments since 1985. We classify all related previous articles into five categories based on: (a) without deterioration, (b) with deterioration, (c) with allowable shortage, (d) linked to order quantity, and (e) with inflation. The motivations, extensions and weaknesses of various previous models have been discussed in brief to bring out pertinent information regarding model developments in the past two decades.