Lot Size Formulation Minimizing Makespan with Transactional and Movement Times


 Lanndon Ocampo, Eppie Clark, Alaine Liggayu

Author affiliation

1 Department of Industrial Engineering, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines
2 Department of Industrial Engineering, University of San Carlos, Cebu City, 6000 Cebu, Philippines


This paper proposes a lot size formulation with the objective of minimizing manufacturing makespan. A simple manufacturing system is considered with single product that is processed through pre-defined task sequence of known tasks, transactional and material handling times. The lot size problem yields a nonlinear optimization model whose solution satisfies the Kuhn-Tucker necessary and sufficient conditions. Results show that lot size is a function of the demand, the transactional activities and the length of the material handling times at the constraint task, and the sum of unconstrained task times. When transactional and material-handling times are considered, optimal lot size is independent of the longest task time but dependent on the sum of the processing times of the unconstrained tasks. The main contribution of this paper is the proposed method of minimizing makespan without spending resources in improving the constraint task but instead, considers developing an optimal lot size. This paper poses relevant applications especially for high-volume manufacturing systems.


lot size; nonlinear optimization; makespan