A feasibility evaluation approach for time-evolving multi-item production–distribution networks

Abstract

Time-dependent multi-item problems arise frequently in management applications, communication systems, and production–distribution systems. Our problem belongs to the last category, where we wish to address the feasibility of such systems when all network parameters change over time and product. The objective is to determine whether it is possible to have a dynamic production–shipment circuit within a finite planning horizon. And, if there is no such a flow, the goal is to determine where and when the infeasibility occurs and the approximate magnitude of the infeasibility. This information may help the decision maker in their efforts to resolve the infeasibility of the system. The problem in the discrete-time settings is investigated and a hybrid of scaling approach and penalty function method together with network optimality condition is utilized to develop a network-based algorithm. This algorithm is analysed from theoretical and practical perspectives by means of instances corresponding to some electricity transmission-distribution networks and many random instances. Computational results illustrate the performance of the algorithm.

Keywords:

• mathematical programming
• nonlinear optimization
• network programming
• approximation algorithm

Acknowledgements

We thank the associated editor for his comments and two anonymous referees for their numerous valuable suggestions leading to improvements in this article's exposition.

Additional information

Funding

This work was supported in part by the Kempe Foundation, Sweden, under grant number SMK-1354.