Mixed integer linear programming models for Flow Shop Scheduling with a demand plan of job types

Abstract

This paper presents two mixed integer linear programming (MILP) models that extend two basic Flow Shop Scheduling problems: $$ {\text{Fm}} $$/$$ {\text{prmu}} $$/$$ {\text{C}}_{ \hbox{max} } $$ and $$ {\text{Fm}} $$/$$ {\text{block}} $$/$$ {\text{C}}_{ \hbox{max} } $$. This extension incorporates the concept of an overall demand plan for types of jobs or products. After using an example to illustrate the new problems under study, we evaluated the new models and analyzed their behaviors when applied to instances found in the literature and industrial instances of a case study from Nissan’s plant in Barcelona. CPLEX solver was used as a solution tool and obtained acceptable results, allowing us to conclude that MILP can be used as a method for solving Flow Shop Scheduling problems with an overall demand plan.