Developing a new production inventory model with multiple products and multiple constraints and a new solution method

In this thesis a fuzzy production inventory model with multiple products and multiple fuzzy constraints has been created and it is aimed to seek a solution for cost minimization problems in production industry.Additional to unconstrained optimization problem, some constraints have been added. These constraints are warehouse capacity, production capacity and budget. Total production cost is calculated to minimize under these constraints.The constraints are chosen by considering the priorities of production companies and thus integrated to the model.For the solution of the problem a method has been evaluated which will provide ease and efficiency to companies. With this evaluation it has been decided to use Lagrange multipliers which is rarely applied to optimization problems, but which is also an efficient tool and method.The model has been solved with Lagrange multipliers method and then in parallel the solution has been reached by a Matlab program.In this way, it has been seen that Lagrange multipliers can also be applied efficiently to optimization problems.After finding the solution for the crisp model, the model has been converted to a fuzzy model by fuzzying the total cost formula and the constraints. This fuzzy model has been solved by a Matlab program and thus the optimal solution has been reached.The results of the crisp and fuzzy models have been evaluated at the end.With this thesis, a new economic order quantity model has been developed and thus a new approach has been presented in the academic area.Anahtar kelimeler: Production Inventory Model, Fuzzy Logic, Lagrange, Zimmermann, Optimization, Economic Order Quantity