Asia-Pacific Journal of Operational Research

This paper is devoted to the study of solutions for multi-choice transferable-utility (TU) games which admit a potential, such as the potential associated with a solution in the context of multi-choice TU games. Several axiomatizations of the family of all solutions that admit a potential are offered and, as a main result, it is shown that each of these solutions can be obtained by applying the weighted associated consistent value proposed in this paper to an appropriately modified game. We also characterize the weighted associated consistent value by means of the weighted balanced contributions and the associated consistency.

When a customer steps into a complete pre-ordered store, he will review the merchandise and consider his demands based on the merchandise price levels and price variability at that point in time. However, after declaring his intention to purchase said merchandise, the store assistant informs him that the merchandise will not be available for a period of time. This is a typical stock-out merchandise scenario in which customers may only place an order for delivery at a later point in time. Therefore, whether or not customer purchases merchandise does not just depend on the price at that moment. It is also influenced by the expected future increase or decrease of the price of the merchandise and the length of time before the store can supply the merchandise. In this study, we will explore how to set price levels at each point in time during the stock-out period in order to maximize the discounted profit after considering the influence of the price level, price variability, and waiting time on customer demand. The main assumption in this study is that customers' potential demand rate function at a given point during the stock-out period is a linear function of the price level and price variability at that point. Also, the ratio function of customers willing to wait for the merchandise is an exponential function of the length of time before the merchandise will be delivered. Constructing a mathematical model that is concrete to discuss the above problem, to derive the optimal price function of the merchandise at each point in time, and to discuss the characteristics of this function are the main parts of this study.

We consider a region suffering from irrigation water scarcity. Candidate crops differ widely in their growth cycles, economic values and water consumption. We develop an integrated dynamic programming-mixed integer programming model to solve for optimal land exploitation over a one year horizon for multiple crops. The model applies deficit irrigation in order to increase the irrigated area at the expense of reducing crop yield per unit area. The dynamic program (DP) guarantees that deficit irrigation is only considered when it is economically efficient. Moreover, it provides optimal combinations of irrigation levels for each growth stage of candidate crops, accounting for the varying impact of water stress over time and the seasonal supply of irrigation water. The output of the DP serves as input to the mixed integer program (MIP). The MIP selects the most profitable crops in the right sequence to benefit the most from the crop-yield dependence on crop predecessor and allocates water and land optimally to maximize total profit. The objective function accounts for the attitude of the decision-maker toward risk by incorporating in its expression a risk-aversion coefficient.

To optimize the design of reliability systems, an analyst is frequently faced with the demand of achieving several targets (i.e., maximization of system reliability, minimizations of cost, volume, and weight), some of which may be in conflict with each other. This paper presents a novel hybrid approach, combining a multi-objective genetic algorithm and a neural network, for multi-objective optimization of a reliability system, namely GANNRS (Genetic Algorithm and Neural Network for Reliability System optimization). The multi-objective genetic algorithm's evolutionary strategy is based on the modified neighborhood design, and is presented to find the Pareto optimal solutions so as to provide a variety of compromise solutions to the decision makers. The purpose of the neural network is to generate a good initial population in order to speed up the searching by genetic algorithm. For demonstrating the feasibility of the proposed approach, four multi-objective optimization problems of reliability system are used, and the outcomes are compared with those from other methods. The evidence shows that the proposed GANNRS is more efficient in computation, and the results from the objectives are appealing.

It is common that prices of raw materials, parts or products decrease significantly after they come onto the market. High technology products are good examples, such as PCs, CPUs, DRAM, and mobile phones. Consequently, the traditional economic production quantity (EPQ) model assuming a constant unit production cost is no longer suitable for today's time-based competition. This study incorporates linearly and exponentially decreasing unit production costs during the mature stage of a product life cycle and presents a mathematical inventory model for production policy. A recursive algorithm is developed to obtain the optimal production schedule and a one-dimension search method is applied to find the optimal number of production cycles. In addition, numerical examples to illustrate the proposed model and its significance with or without considering a continuous reduction in unit production costs for the production policy are discussed as well.

Production Possibility Set (PPS) based on Free Disposal Hull assumption describes the minimum PPS for evaluating efficiency of DMUs and presents one reference for each unit. Tulkens (Journal of Productivity Analysis, 4(1), 183–210) proposed a mathematical program and a procedure for solving FDH model that can be used for only VRS technology. In this paper, we extend the method for solving all four standard technologies (VRS, CRS, NDRS and NIRS) by a numeration algorithm without using LP or MILP regular solving methods.

Queuing models need well defined knowledge on arrivals and service times. However, in real applications, because of some measurement errors or some loss of information, it is hard to achieve deterministic knowledge. Non-deterministic knowledge interferes or complicates analysis of the queuing model. Additionally, when the customers are asked about their impressions on waiting times or service times, mostly the answers are linguistic expressions like "I waited too much", "service was fast", and that the responses are. Linguistic statements and ill defined data make the sense of imprecision in the model. In this study, arrivals and service times are defined as fuzzy numbers in order to represent this imprecision. Fuzzy multi-channel queuing systems and membership functions are introduced in defining the arrivals and service times. Besides, a new membership function based on a probability function is studied. Fuzzy queuing characteristics are calculated via different membership functions and the results are compared on simulations. Among models it is found that, Generalized Beta Distribution membership function is the one that minimized the queuing characteristics.

Weighted additive models are well known for dealing with multiple criteria decision making problems. Fuzzy goal programming is a branch of multiple criteria decision making which has been applied to solve real life problems. Several weighted additive models are introduced to handle fuzzy goal programming problems. These models are based on two approaches in fuzzy goal programming namely goal programming and fuzzy programming techniques. However, some of these models are not able to solve all kinds of fuzzy goal programming problems and some of them that appear in current literature suffer from a lack of precision in their formulations. This paper focuses on weighed additive models for fuzzy goal programming. It explains the oversights within some of them and proposes the necessary corrections. A new improved weighted additive model for solving fuzzy goal programming problems is introduced. The relationships between the new model and some of the existing models are discussed and proved. A numerical example is given to demonstrate the validity and strengths of the new model.