Effect of bucket size on lead time discretization error in multi-level production planning systems

Abstract

Production planning systems are models that hold and analyze planning and controlling of physical transformation and transferral processes in production systems. These systems consist of various planning models such as Material Requirements Planning (MRP) and Job Shop Scheduling (JSS). These models generally use a discretized time frame to determine replenishment times of items or starting times of operations. To discretize time frame, planning horizon is divided into time buckets such as shifts, days, weeks or months. Length of time buckets may not be equal to Greatest Common Divisor (GCD) of the lead times, and they are typically larger than GCD of the lead times. This phenomenon results in errors in rounding of the lead times of the items or operations. In this thesis, we propose a mathematical model that can be applied to problems that have an acyclic Bill of Materials (BOM) structure, or precedence relations with minimization of sum of all cumulative errors objective. Hence, we aim to make optimal rounding choices of the lead times that result in less errors for all items and less error uctuations through item chains. We also develop a constructive heuristic for the optimal rounding problem. These approaches are applicable to MRP-type problems but thay are not applicable for JSS type models since rounding of processing times does not give su cient sequence information for JSS problems. There may occur some ties between starting times of the operations. Thus, we develop a second phase model that consist of a mathematical model and a heuristic. We compare the results of second phase model with JSS model in terms of error introduced and Central Processing Unit (CPU) time of the solutions. Our results show that the model can have good discretization scheme with an acceptable rate of errors for the sake of less CPU times. There is negative correlation between bucket size and solution quality in general.