Fuzzy non-linear programming: Theory and application in manufacturing

A non-linear model for farm optimization with adequate and limited water supplies: Application to the South-east Anatolian Project (GAP) Region

Degradation function of Situ Gede (Lake Gede) becomes crucial at present time compared to its function at initial condition when it was used for tourism, irrigation, and raw water supply within an optimal use. The crucial aspects are related to the decreasing reliability of supply to Situ Gede and increasing sedimentation accumulation. The research concerns with various aspects due to the Situ Gede conservation and restoration that is aimed to increase the potential uses, based on the quantitative and qualitative model by using optimization technique and Analitic Hierarchy Process (AHP). The optimization technique is applied in order to evaluate the amount of monthly water availability within 3 scenarios i.e. tourism ounly (Scenario 1), tourism and irrigation (Scenario 2), and, tourism, irrigation and raw water (Scenario 3), respectively, based on the potency of Situ Gede itself, new additional supply from other sources, and additional supply from Galunggung Crater. In addition, based on simulation of accumulated sedimentation model, that is aimed to identify the effect of firm outflow change of Situ Gede Release, indicates the decrease of firm outflow around 0,5% annually. The priority order based on AHP evaluation shows that the the first priority is Scenario 1, the second is Scenario 3 and the third is Scenario 2. Those priorities based on various criterias such as Investment Cost and Operation Maintenance, Additional Supply Reliability to Situ Gede, and Sedimentation. Sensitiviy analysis is also applied based on the weight change of each criteria in performing the shift possibilities due to the priority order. Key Words : Non Linear Programming Modeling, Simulation, Multi objective-Multi Criteria

Financial incentives are used to improve productivity and quality in manufacturing and service facilities. This improvement in productivity would normally release part of the facility's productive capacity. Without stimulating additional demand to consume this released capacity, the facility would Be unable to tap the full benefits of the improvements in productivity. Hence, yield management is introduced in an attempt to entice more demand and increase revenues. In this paper, we develop a Non Linear Programming (NLP) model to jointly determine the optimum financial incentives and price discount levels for each rate class. The model aims at maximizing net revenues. It includes nonlinear relationships representing the impact of incentives on productivity and quality improvements as well as the effect of price discounts on customer demand in each market segment. The generic nature of our NLP model makes it applicable to all multi-product manufacturing facilities covering sales, production and delivery. The model is applied to determine the optimum incentive and price discount levels for perishable products in a multi-product ready-mix concrete plant. It is demonstrated that the model is useful in maximizing net revenues through productivity improvements and an increase in customer demand.

Fuzzy nonlinear programming approach to the evaluation of manufacturing processes

A fuzzy non-linear programming model is developed for the assessment of filter allocation and replacement strategies in fluid power systems (FPSs) under uncertainty. It can not only handle uncertainties expressed as L—R fuzzy numbers, but also enhance the system robustness by transforming the fuzzy inequalities into inclusive constraints. In modelling formulation, theory of contamination wear is introduced to reflect the interactions between system performance and system contamination level. The developed method has been applied to the planning of filter allocation and replacement for an FPS with a bypass filtration system, and a piecewise linearization approach is proposed for solving model non-linearities. Three different contaminant ingression rates are examined based on a number of filter-installation scenarios. The generated solutions can be used for providing guidance to decision makers to identify better contamination control plans for achieving a minimized system cost and system-failure risk.

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.

Chapter 8 Mathematical programming models and methods for production planning and scheduling

A nonlinear programming (NLP) model has been established to describe the process of low rank coal pyrolysis, and the model was validated through comparison with pilot or semi-industry technologies. Results showed good agreement with actual production values, suggesting that the model can be regarded as a general one for simulating low rank coal pyrolysis. On the basis of this model, the products’ distributions and energy penalties can be obtained from the coal pyrolysis process. In this study, the NLP model was used to simulate typical five pyrolysis processes such as the Toscoal process, Lurgi–Ruhrgas process, Char Oil Energy Development technology, Dalian University of Technology process, and Multistage Rotary Furnace technology from China Coal Research Institute, and Hulunbuir lignite was taken as a coal sample. Combined with the simulation results from the NLP model, effects of the key parameters on the performance of the pyrolysis technologies are investigated and a comprehensive evaluation in terms ...

To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.

This paper develops a fuzzy chance constrained mixed-integer nonlinear programming (FCC-MINLP) model and the solution methods for refinery short-term crude oil scheduling problem under demands uncertainty. To reduce the calculation complexity of the model, it is transformed into its equivalent fuzzy chance constrained mixed-integer linear programming (FCC-MILP) model by using the method of Quesada & Grossmann (1995). After that the FCC-MILP model is solved through its crisp equivalent algorithm and fuzzy simulation algorithm rely on the theory presented by Liu & Iwamura (B. Liu, K. Iwamura, 1998) for the first time in this area. Finally, a case study which has 265 continuous variables, 68 binary variables and 318 constraints is effectively solved in LINGO 8.0 (J. X. Xie and Y. Xue, 2005) with the proposed approaches

In this paper, a Mixed-integer non linear programming (MINLP) model for a multi-facility location problem in the presence of a probabilistic line barrier is presented in which the starting point of the line barrier uniformly distributed. It is supposed that the distances metric is rectilinear. The objective function minimizes the summation of the weighted expected rectilinear barrier distances between the n new facilities and the m existing facilities and also between the new facilities. To show the applicability of the model, a numerical example is provided. It is worth noting that the global optimal solution is found.

This chapter presents a mixed integer non-linear programming (MINLP) model for a fuzzy parallel machine scheduling problem under fuzzy job deterioration and learning effects with fuzzy processing times in order to minimize fuzzy makespan. The uncertainty of parameters such as learning/deterioration effects and processing times in a scheduling problem makes the solution of the problem uncertain. Fuzzy sets can be used to encode uncertainty in parameters. In this chapter, possibilistic distributions of fuzzy parameters and possibilistic linear programming approaches are used in order to create a solution method for MINLP model of fuzzy parallel machine scheduling problem.

Disasters pose a serious threat to people’ lives and urban environment, affecting the sustainable development of society. Then it's crucial to quickly develop an efficient rescue plan for the disaster area. However, disaster rescue is rather difficult due to the requirement to develop the optimal rescue plan as quickly as possible according to the information of trapped people and rescue teams, and the amount of information will continue to increase as the rescue proceeds. At present, most of the rescue plans are manually made based on previous rescue experience. But obviously these plans might be the not optimal one. Considering the real-time location data of trapped people, this paper develops a Mixed Integer Non-linear Programming (MINLP) model to find the highest efficient rescue plan To solve the model accurately and efficiently, a bi-level decomposition (BLD) algorithm is presented to iteratively solve a discretized Mixed Integer Linear Programming (MILP) model and its nonconvex Non-linear Programming (NLP) model until a converged solution is obtained. In addition, since more trapped people could be found over time, the built rescue units should also be considered when making a rescue plan for a new stage. To further improve the solving efficiency, an accelerated bi-level decomposition (ABLD) algorithm is also proposed. Finally, a real-world disaster rescue is given to validate the superiority of the proposed ABLD algorithm relative to particle swarm optimization (PSO) algorithm and BLD algorithm.

A non-linear mathematical approach for solving matrix games with picture fuzzy payoffs with application to cyberterrorism attacks

A master–slave solving method with adaptive model reformulation technique for water network synthesis using MINLP