Flow shop scheduling with grid-integrated onsite wind power using stochastic MILP

Abstract

Over the last decade, manufacturing companies have identified renewable energy as a promising means to cope with time-varying energy prices and to reduce energy-related greenhouse gas emissions. As a result of this development, global installed capacity of wind power has expanded significantly. To make efficient use of onsite wind power generation facilities in manufacturing, production scheduling tools need to consider the uncertainty attached to wind power generation along with changes in the energy procurement cost and in the products’ environmental footprints. To this end, we propose a solution procedure that first generates a large number of wind power scenarios that characterise the variability in wind power over time. Subsequently, a two-stage stochastic optimisation procedure computes a production schedule and energy supply decisions for a flow shop system. In the first stage, a bi-objective mixed integer linear programme simultaneously minimises the total weighted flow time and the expected energy cost, based on the generated wind power scenarios. In the second stage, energy supply decisions are adjusted based on real-time wind power data. A numerical example is used to illustrate the ability of the developed decision support tool to handle the uncertainty attached to wind power generation and its effectiveness in realising energy-related objectives in manufacturing.

Keywords:

• production scheduling
• flow shop
• renewable energy
• energy consumption
• wind power

Acknowledgments

The authors are grateful to the editor and the anonymous referees, whose valuable comments on an earlier version of this paper helped to improve this work significantly. The first author further wishes to thank the Division of Environmental and Ecological Engineering of Purdue University, and especially Prof. Dr. John W. Sutherland and Prof. Dr. Fu Zhao, for enabling his research stay at Purdue University.

Notes

1. The cut-in speed corresponds to the wind speed at which the turbine starts to generate power. The rated speed corresponds to the wind speed at which the turbine reaches its maximum level of power generation. The cut-out speed corresponds to the wind speed at which the turbine is shut down to protect it from excessive loads (Burton et al. 2011).

2. Historical wind speed forecasts and observations for the calibration period and wind speed forecasts for the planning horizon are available at https://www.wunderground.com/q/zmw:94580.8.99999.

3. Please note that it is possible that the sets of non-dominated solutions after first-stage decisions dominate the sets of non-dominated solutions associated with the theoretical optimum. This event may occur in case the expected wind power the first-stage decisions are based on exceeds the realised wind power the theoretical optimum is based on.