A brief Summary on and comprchnsivc undcrstanding of fuzzy optimization is presented. This Summary is madc on aspcets of fuzzy modclling and fuzzy optimization. classification and formulation for the fllzzy optimization problems. models and nlcthods The importance of interpretation of the probhlcm and formulation of the optimal sohltion in fuzzy sense arc mphasizcd in the Summry of fhe fuzzy optimization

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

Given the uncertain market demands and capacities in production environment, this paper discusses some practical approaches to modeling multiproduct aggregate production planning problems with fuzzy demands, fuzzy capacities, and financial constraints. By formulating the fuzzy demand, fuzzy equation, and fuzzy capacities, a fuzzy production-inventory balance equation for single period and a dynamic balance equation are formulated as fuzzy/soft equations and they represent the possibility levels of meeting the market demands. Using this formulation and interpretation, a fuzzy multiproduct aggregate production planning model is developed, and its solutions using parametric programming, best balance and interactive techniques are introduced to cater to different scenarios under various decision making preferences. Using the proposed models and techniques, first, the decision maker can select a preferred production plan with a common satisfaction level or different combinations of preferred possibility level and satisfaction levels, according to the market demands and available production capacities, and second, the obtained structure of the optimal solution can help decision maker in aggregate production planning. The decision maker can also make a preferred and reasonable production plan corresponding to one's most concerned criteria. Hence, decision makers not only can come up with a reasonable aggregate production plan with minimum efforts, but also have more choices of making a preferred aggregate plan based on his most concerned criteria. These models can ffectively enhance the capability of an aggregate plan to give feasible family disaggregation plans under different scenarios with fuzzy demands and capacities. Simulation and the results of nalysis on the proposed techniques are also given in detail in this paper.

Quality Function Deployment (QFD) is a wellknown customer-oriented methodology, which is widely used to assist decision making in product design and development in various types of production. etermining how and to what extent certain characteristics or technical attributes (TAs) of products are to be met, with a view to gaining a higher level of overall customer satisfaction, is a key success factor in product design and development. An operational QFD planning problem with resource allocation is considered in this paper. The aim is to plan the attainment of TAs by allocating resources among the TAs with a view to achieving maximized overall customer satisfaction. Taking into account the technical and resource constraints, and the impact of the correlation among TAs, the operational QFD planning with resource allocation is formulated as a linear program and solved by a heuristics-combined Simplex Method. An overall procedure is presented to help a design team to implement this QFD design planning with resource allocation in practice. This model can bridge the gap and conflicts

In the global manufacturing environment, decisions involving production activities and distribution should be made in an integrative manner for substantial savings in the logistics costs. An integrated decision on production assignment, lot sizing, transportation, and order quantity for a multiple-suppliers/multiple-destinations logistics network in a global manufacturing system is discussed in this paper. The integrated decision process can be viewed as a two-layer decision. The first layer is the combined decisions of production assignment and lot sizing (APLS-M), while the second layer is the combined decisions of transportation and order quantity determination (TOQ-M). A two-layer decomposition method combining two heuristics is hence developed to solve the integrated decision model (IDM-M). An assignment heuristic and a transportation heuristic are designed to solve the decision layers APLS-M and TOQ-M, respectively. Simulations were conducted on a practical example in an electronics manufacturing enterprise together with different sizes of problems. The results indicate that the two-layer decomposition method with heuristics is effective and provides a practical way to solve medium and large-scale integrated decision problems.