base.web-kovalev.ru/scripts In this chapter, multiobjective linear programming and interactive multiobjective linear programming, both incorporating fuzzy goals of the decision maker DM , are introduced. Multiobjective linear programming problems with fuzzy parameters are also formulated and interactive decision making methods, both without and with the fuzzy goals of the DM, for deriving a satisficing solution for the DM efficiently are presented.
Finally, multiobjective linear programming problems involving random variable coefficients, called stochastic multiobjective linear programming problems, are considered. By making use of stochastic models such as a probability maximization model together with chance constrained conditions, the stochastic multiobjective programming problems are transformed into deterministic ones. After determining the fuzzy goals of the DM, interactive fuzzy satisficing methods are introduced for deriving a satisficing solution for the DM.
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Abou-El-Enien and M. Meanwhile, we use a sensitivity analysis to investigate the changes in optimal decision values regarding medical service Item 1 when only one parameter in the dataset changes while others remain unchanged. Springer, Berlin. Plenum Press; , New York. Buy New View Book. Goal programming model: A glorious history and a promising future. For illustrative purposes, a numerical example is presented to verify the effectiveness of the proposed model from experimental data.
Please review our Terms and Conditions of Use and check box below to share full-text version of article. Summary For decision making problems involving uncertainty, there exist two typical approaches: stochastic programming and fuzzy programming. Controlled Vocabulary Terms decision making; fuzzy logic; linear programming; stochastic process; uncertainty. Citing Literature. Related Information.
In recent years, most countries around the world have faced increasing pressures in the realm of emergency management than ever before. Medical service organization selection is one of the most vital facets of emergency management. Meanwhile, during the selection process, many criteria may conflict with one another and information is uncertain, rendering decision-making processes complex.
Hence, multi-objective optimization, fuzzy way and stochastic theories serve as suitable means of addressing such problems. In this paper, a fuzzy multi-objective linear model is developed to overcome medical service organization selection issues and uncertain information. Meanwhile, a fuzzy objective and weight are applied to enable the decision-maker to select suitable schemes while considering stochastic medical service demand.
Moreover, real data cannot been obtained. Hence, according to actual conditions, we assume relative information. For illustrative purposes, a numerical example is presented to verify the effectiveness of the proposed model from experimental data. In recent years, in the field of emergency management, many countries have been confronted with a lack of efficient emergency management and an increase in death tolls.
Therefore, these countries must sustain heavy losses when disasters occur. For example, in the Chinese Wenchuan earthquake killed over 69, people, injured over , people, left over 17, people missing, causing economic losses of over From this perspective, emergency medical service organization selection has become extremely important to countries. In such environments, scholars and managers are more concerned about issues of emergency medical service organization selection than ever before.
In existing studies most scholars of emergency management have paid much more attention to issues of vehicle optimization, supply networks and so on. For example, Sheu proposed a means of designing a seamless centralized emergency supply network by integrating three subnetworks the shelter, medical, and distribution networks to support emergency logistics operations in response to large-scale natural disasters [ 1 ].
Wilson et al. Cheng and Liang examined the locations of emergency rescue problem occurrence for urban ambulance and railway emergency systems [ 3 ]. Wohlgemuth et al. Meanwhile, in practical situations, medical resource services are central to emergency management.
Based on real conditions, Torres presented a novel multi-objective heuristic approach for the efficient distribution of h emergency units [ 5 ]. Topaloglu constructed a multi-objective programming model for scheduling emergency medicine residents [ 6 ]. Walls established a multicenter registry and initiated the surveillance of a longitudinal, prospective convenience sample of intubations at 31 EDs [ 7 ]. This study is one of the first multicenter genetic research protocols designed solely for an Emergency Department ED [ 8 ].
Zakaria created a decision support system for the provision of emergency sanitation [ 9 ]. Cong studied family emergency preparedness plans for severe tornado events [ 10 ]. Zhu studied the standardized management of China's strategic railway emergency plan [ 12 ].
Calixto applied regional emergency plan requirements to the Brazilian case [ 13 ]. Su conducted a case study of emergency medical services deployment in Shanghai [ 14 ]. Moreover, as information is usually uncertain, researchers must consider stochastic data and the vagueness of input information. Araz established a fuzzy multi-objective covering-based vehicle location model for emergency services [ 15 ]. El-Ela established optimal preventive control actions using a multi-objective fuzzy linear programming technique [ 16 ].
Adan improved the operational effectiveness of tactical master plans for emergency and elective patients using stochastic demand and capacitated resources [ 17 ]. However, emergency medical service organization selection is a multicriteria decision-making problem affected by several conflicting factors including costs, degrees of social satisfaction, response times, service qualities, etc. The multiple criteria are usually unequally important. Moreover, information is usually uncertain.
Consequently, scholars must analyze the trade-off among several criteria and the uncertainty of input information. In real situations, objectives, constraints and weight information are usually uncertain. The decision-maker cannot precisely apply relative weights and information during emergency medical service organization selection. Meanwhile, stochastic emergency medical service demand also must be considered during medical service organization selection.
However, most of the above models do not simultaneously consider such conditions. Thus, to generate a more practical and meaningful model for addressing the selection problem, we present a new fuzzy multi-objective medical service organization selection model based on stochastic demand and limited resources. In this model, objectives and weights are assumed to be fuzzy numbers with an interval fuzzy number where demand is stochastic.
Based on practical conditions, emergency medical demand is defined as a stochastic variable. As the main motivation of this study, as information is usually uncertain and as multiple medical services must be considered in real situations, we determine how to optimize emergency medical service organization selection in uncertain environments for the country. Furthermore, in this paper, a numerical example is used to illustrate the validation of the proposed method, as the explored problem is complex and difficult to address in real life.
From this example, we demonstrate that the proposed method is valid. The rest of this paper is organized as follows. In Section 2, a fuzzy multi-objective model and its formulation for the decision-making process are proposed in which the objectives are not equally important and have fuzzy weights. Subsequently, a general linear multi-objective programming model for this problem is formulated and some definitions and appropriate approaches to solving this decision-making problem are discussed.
Section 3 presents the numerical example and describes the results. Finally, concluding remarks are given in Section 4. In emergency management, the manager receives medical resource demand information from the relevant department and allocates corresponding medical services for dealing with this risk.
The challenge here is to allocate medial resource demand and select a suitable medical service organization approach. Notably, emergency medical service organization selection is a multiple criteria decision-making problem, and a multi-objective decision model must be built to allocate medical service demand for sudden risk and to select an organization approach among other potential approaches.
Meanwhile, in developing similar models, researchers have rarely simultaneously considered stochastic demand, fuzzy objective and weight factors. Our model recognizes that these phenomena must be considered to address emergency plan selection problems. The following section discusses our model in detail and presents a flowchart describing the proposed model Fig 1. We first make the following assumptions:.
V tj : The maximum capacity for the tth medical organization to execute the jth service. R tj : The probability of satisfaction with the j-th product offered by the t-th supplier. E x tj : The penalty function for the jth service supplied by the tth medical organization. Meanwhile, to solve an emergency medical organization selection problem, we assume that the objective includes the cost f 1 , degree of social satisfaction f 2 , response time f 3 and service quality level f 4 together with the major constraint that medical services can mostly satisfy stochastic demand.
Each emergency medical organization has its own unit cost, social satisfaction history, response time record and service quality data. However, we assume that life is the most precious resource of all and that costs must been considered. Moreover, medical services are limited. At the same time, in real situations, many factors that shape medical service demand cannot been fully addressed. According to such conditions, we must define a penalty function. Notably, delayed medical services result in losses.
Diverse conditions can result in different costs. With a scenario analysis we construct two penalty functions as follows:. When a delayed medical service can be provided by another organization, the penalty function is equal to zero, i. When a delayed medical service can immediately be replenished, the penalty function is linear as follows:. The aggregate performance measure for the response time objective function is defined as:. In turn, the final form of the multi-objective model for medical service organization selection is as follows:.
Generally, managers do not have exact and complete information related to decision-making criteria and constraints that are fuzzy and stochastic in nature. A new fuzzy multi-objective medical service organization selection model is thus developed to address this problem.
Using the Bellman—Zadeh approach [ 18 , 19 ], the fuzzy set objective functions f p and constraints g i are defined as. From 23 , it is possible to obtain the solution proving the maximum degree. This function is satisfied through the use of membership functions. The construction of 26 or 27 involves solving the following problems:. First, the max—min operator used by Zimmermann [ 20 , 21 ] for fuzzy multi-objective problems is discussed. Then, the convex weighted additive operator that enables DMs to assign different weights to various criteria is described.
The fuzzy solution for all fuzzy objectives and fuzzy constraints may be written as. Under real conditions, different objectives and constraints are of unequal importance to DM and other patterns, and thus weight should be considered. The fuzzy weighted additive model can address this problem as described below. The weighted additive model is widely used in vector-objective optimization problems; the basic premise is to use a single utility function to express the overall preference of DM to draw out the relative importance of criteria [ 23 ]. In this case, multiplying each membership function of fuzzy goals by its corresponding weight and then adding the results together generates a linear weighted utility function.
The fuzzy model proposed by Bellman and Zadeh and Sakawa and the weighted additive model developed by Tiwari are written as [ 24 — 26 ].
Constraint 48 ensures that the relative weights should add up to one. Additionally, fuzzy weights reflect the uncertain relative importance of objectives where the sum of all fuzzy weights should be one, i. On the other hand, if for any j-th objective or constraint is considered a triangular fuzzy number, then w j 1 and w j 2 should be replaced with w j 0 for the j-th objective or constraint. Since we cannot obtain real data on medical service organization selection, all data presented in this paper are experimental.
In this section, for explaining validity of our model, we assume that all relative experimental data are based on real conditions. According to these experimental data, a numerical example is presented to illustrate the above listed model and algorithm. Three medical services are purchased from three medical organizations. Factors such as price, satisfaction, response time, service quality and capacity can be obtained from historical data. Objectives include the cost f 1 , degree of social satisfaction f 2 , response time f 3 and service quality f 4.
All experimental data are included in Table 1 and Table 2. In Table 1 , information on objectives and constraints is provided.
In the previous chapter, we have discussed a variety of computationally efficient approaches for solving crisp multiple objective decision making problems. In this volume, methods and applications of crisp, fuzzy and possibilistic multiple objective decision making are first systematically and thoroughly reviewed and.
As the only stochastic constraint, medical services must almost satisfy demand. From Eq 44 — 52 and relative experimental data we find that our numerical example has interesting implications for medical service organization schemes as illustrated in Table 3 , which shows that the value of the penalty function does not always influence medical service organization selection. Regarding scenario descriptions, under one scenario, it is easy to find alternatives; under the other scenario, although a medical service can be purchased, there is a loss.
Meanwhile, the loss is linearly related to the purchase volume. These scenarios serve as simplified descriptions of real situations. Thus, an interesting result occurs when a selected organization incurs a higher penalty than an unselected one. In Table 3 x 22 and x 23 , we purchase more medical services at higher losses rather than incurring no loss.
This phenomenon is usually inconsistent with what people anticipate.
However, when costs are not the sole factor, we know that this is common. In our model, decisions are influenced by costs, degrees of social satisfaction and so on. This finding means that we must simultaneously consider multiple criteria requirements. A factor cannot always influence the final result. According to this rule, a penalty function cannot can occasionally impact medical service organization selection decisions due to other factors.
Meanwhile, we use a sensitivity analysis to investigate the changes in optimal decision values regarding medical service Item 1 when only one parameter in the dataset changes while others remain unchanged. Moreover, this result simultaneously validates the result shown in Table 3 that the sole parameter occasionally fails to affect decisions.
The model proposed here is reasonable to apply under defined conditions and can solve the decision-making problem of selecting medical organization approaches with uncertain information.