A rolling horizon approach for material requirement planning under fuzzy lead times

This paper proposes a fuzzy multi-objective integer linear programming (FMOILP) approach to model a material requirement planning (MRP) problem with fuzzy lead times. The objective functions minimise the total costs, back-order quantities and idle times of productive resources. Capacity constraints are included by considering overtime resources. Into the crisp MRP multi-objective model, we incorporate the possibility of occurrence of each uncertain lead time using fuzzy numbers. Then FMOILP is transformed into an auxiliary crisp mixed-integer linear programming model by a fuzzy goal programming approach for each fuzzy lead time combination. In order to defuzzify the set of solutions associated with each fuzzy lead time combination, a solution method based on the centre of gravity concept is addressed. Model validation with a numerical example is carried out by a novel rolling horizon procedure where uncertain lead times are updated during each planning period according to the centre of gravity obtained. For illustration purposes, the proposed solution approach is satisfactorily compared to a rolling horizon approach in which lead times are allocated when the possibility of occurrence is established at one.