Abstract
This paper deals with the problem of planned lead time calculation in a Material Requirement Planning (MRP) environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered: multi-level serial-production and assembly systems. For the serial production systems (one type of component at each level), a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and several numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.