This project focuses on a new framework of models that have scheduling features as well as inventory features. The framework proposed contains a large class of models with a number of new models lying in between already well established inventory models and scheduling models. The new models appear to be of real practical significance. A model typically assumes a number of different product types. Of each product type there is a given demand stream for a number of units with given delivery due dates. Each unit of a given product type must be delivered by a specific due date. The due dates may be regular or irregular. The time to produce any unit of a given type is fixed. Each product type has an earliness cost and atardiness cost. If a machine (or facility) is being set up to produce a run (or batch) of products of a given type a setup cost is incurred. The objective is to minimize all production costs including earliness costs, tardiness costs and setup costs. The machine (or facility) environments to be considered include: (i) the single machine, (ii) parallel machines, (iii) machines in series,(iv) flexible flow shops.
The proposed work has various objectives. First, it is important to determine which models in the proposed class can be solved in polynomial time and where the borderline lies between the problems that are solvable in polynomial time and the problems that are NP-hard. Second, it is of interest to design and test heuristics for the problems that are NP-hard. Third, we intend to apply the heuristics developed to real world data that will be provided to us by colleagues in industry.
The intellectual merit of the proposed activity is based on the fact that the models are meaningful generalizations of existing, well-established models and that a number of the new models appear to have interesting new properties that allow for polynomial time solutions. The polynomial time algorithms as well as the heuristics for the NP-hard cases are expected to exhibit interesting new structures.
The broader impact of the proposed activity is based on the fact that the research team has strong ties with various companies that are genuinely interested in the models and in the solutions. The companies involved include Dash Optimization with which the project team has very close ties. Furthermore, the research will be disseminated at conferences to be held at the various institutions of the Principal Investigators; these conferences have, in the past, typically been attended by academicians as well as by people from industry.
