Solving a lot sizing and scheduling problem byhybrid modelling

The authors propose an analytic-simulation hybrid model (HM) to solve a lot sizing andscheduling problem in a multi-product/dynamic demand/single machine environment. Problemcomplexity is increased due to sequence dependent and relevant setup times as well as to stochasticvariability of both process and setup times. Resource availability is also considered in evaluating capacityat each period of the planning horizon. The analytic model consists of a mixed integer linear programmingmodel obtained by improving a model available in literature; it interacts with a simulation model inorder to meet a production plan that allows minimizing an economic objective function. The approachtries to overcome traditional limits of both analytic and simulation models as each of them fails injointly capturing system complexity and searching for optimal solutions. HM proposed is applied to acase study. It concerns with production of braking systems components for automotive industry. Resultsobtained are compared with those that could have been obtained if only the analytic model adopted inHM was used. Comparison outlines capabilities of HM in facing problem complexity as it is able toevaluate stochastic dependency among manufacturing variables; such a dependency is neglected byanalytic models. Moreover, the iterative procedure adopted in HM reveals an effective tool in searchingfor a good production planning avoiding expensive and low effective “trial and error” procedures requiredby simulation to meet the same goal when a relevant number of decision manufacturing variablesoccurs in a production planning problem in cases of full scale industrial cases.