This paper details models that determine the efficient allocation of resources on a medical assessment unit (MAU) of a general hospital belonging to the National Health Service (NHS) UK. The MAU was established to improve the quality of care given to acute medical patients on admission, and also provide the organizational means of rapid assessment and investigation in order to avoid unnecessary admissions. To analyse the performance of the MAU, doctors, nurses and beds are considered as the three main resources. Then a model is developed using the goal programming approach in multiobjective decision making and solved to deal with MAU performance. The developed model is solved under three different sets of patient admissions with the same resource levels using past data from the MAU. The results of the model are used to analyse the needed resource levels. Conclusions as to the appropriate staffing levels and functions of the MAU are drawn.
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.
Keywords:Multiobjective linear programming Maximal efficient face Minimal index set Efficiency Finding an efficient or weakly efficient solution in a multiobjective linear programming (MOLP) problem is not a difficult task. The difficulty lies in finding all these solutions and representing their structures. Since there are many convenient approaches that obtain all of the (weakly) efficient extreme points and (weakly) efficient extreme rays in an MOLP, this paper develops an algorithm which effectively finds all of the (weakly) efficient maximal faces in an MOLP using all of the (weakly) efficient extreme points and extreme rays. The proposed algorithm avoids the degeneration problem, which is the major problem of the most of previous algorithms and gives an explicit structure for maximal efficient (weak efficient) faces. Consequently, it gives a convenient representation of efficient (weak efficient) set using maximal efficient (weak efficient) faces. The proposed algorithm is based on two facts. Firstly, the efficiency and weak efficiency property of a face is determined using a relative interior point of it. Secondly, the relative interior point is achieved using some affine independent points. Indeed, the affine independent property enable us to obtain an efficient relative interior point rapidly.
In this paper, a linear programming (LP) problem is considered where some or all of its coefficients in the objective function and/or constraints are rough intervals. In order to solve this problem, we will construct two LP problems with interval coefficients. One of these problems is an LP where all of its coefficients are upper approximations of rough intervals and the other is an LP where all of its coefficients are lower approximations of rough intervals. Via these two LPs, two newly solutions (completely and rather satisfactory) are defined. Some examples are given to demonstrate the results.
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