Considering that the demand requirementsare fuzzy demand in each period during the planning horizon, this paper focuses on a novel approach to modelling multi-product aggregate production planning (APP) problems with fuzzy demands and fuzzy capacities. The objective of the problem considered is to minimize the total costs of quadratic production costs and linear inventory holding costs. By means of formulation of fuzzy emand, fuzzy addition and fuzzy equation, the productioninventory balance equation in single stage and dynamic balance equation are formulated as soft equations in terms of a degree of truth, and interpreted as the levels of satisfaction with production and inventory plan in meeting market demands. As a result, the multi-product aggregate production planning problem with fuzzy demands and fuzzy capacities can be modelled into a fuzzy quadratic programming with fuzzy bjective and

The current models and methods for PLP are usually restricted on some special types and usually the same type of possibilistic distribution. This paper focuses on linear programming problems with general possibilistic resources (GRPLP) and linear programming problems with general possibilistic objective coe cients (GOPLP). By introducing some new concepts of the largest most possible point, the smallest most possible point, the most optimistic point and the most possible decision, a new approach for formulating possibilistic constraints through general possibilistic resources and a satisfactory solution method will be discussed in this paper. A most possible decision method for GRPLP and a dual approach for GOPLP will be proposed for solving complex industrial decision problems.

This paper reports on a collaboratively developed user interface. The user interface has been coded as a Microsoft Windows-based and user-friendly computer software system using the Quality Function Deployment (QFD) method and linear programming technique. By using the user interface, a product development team can rapidly specify a product to meet customer requirements and needs, and optimally allocate the team members'time to achieve the various technical features of the defined product so that maximum overall customer satisfaction is achieved. This paper uses an industrial case to illustrate the basic principles behind the user interface and the industrial implementation results are discussed.

Quality Function Deployment (QFD) is a well-known customer-oriented methodology that is widely used to assist decision-making in product design and development in various types of production including highly customized One-of-a-Kind Production (OKP), batch production as well as continuous/mass production. Determining how and to what extent (degree) certain characteristics/technical attributes (TA) of products are to be met with a view to gaining a higher level of overall customer satisfaction is a key to successful product design and development. Most of the existing approaches and models for QFD planning seldom consider the resource constraints in product design, nor do they normally take into account the impacts of the correlation among various TA. In other words, most of the existing QFD applications assume that the resources committed fully to attaining the design target for one TA have no impacts on those for other TA. Hence, the costs/resources required are usually worked out individually by linear formulation. In practice, design resource requirements should be expressed in fuzzy terms to accommodate the imprecision and uncertainties innate in the design process, such as ill-de

ln this paper, a nonsymmetric model for a type of fuzzy nonlinear programming problems with penalty coefficients (FNLP-PC) is proposed. Based on a fuzzy optimal solution set and an optimal decision et, a satisfying solution method and a crisp optimal solution method with a GA for FNLP-PC is developed. Finally, the analysis of simulation results of an actual production problem example are also given.