A fuzzy approach to modelling production & inventory planning

Considering that the demand requirements are fuzzy demand in each period, especially in the future period, this paper focuses on a fuzzy approach in modeling production and inventory planning (PIP) problems. The objective of the problem considered is to minimize the total costs of nonlinear production costs and linear inventory holding costs. By taking a fuzzy approach, the production-inventory balance equation is formulated as a soft equation in terms of a degree of truth, which depends on the membership function of fuzzy demand. The fuzzy demand and cumulative demand from the start of the horizon to a period are represented in fuzzy numbers of triangular type. By means of addition of soft equations and some reductions, the production and inventory planning (PIP) problem with fuzzy demand can be modelled into a fuzzy nonlinear programming problem with fuzzy objective and fuzzy constraints.