Stochastic programming for responsive production operations under uncertain disruptions

Manufacturing systems aim to be streamlined and produce innovative and high-quality products just in time to meet consumer needs. Just-in-time manufacturing processes have suffered significantly from disruptions in the supply chain, demand uncertainty, shop floor break downs, product quality failures, etc. To be responsive to all possible disruption scenarios in the future, first we need to recognize and assess the consequences of any changes we will have to make under these disruptions. Then, by use of an optimization method, we need to minimise the impact of these unexpected disturbances. For this purpose, we observe all these disruptions under several possible scenarios and develop a stochastic programming formulation. The objective function of this formulation minimises the total expected costs of a production operation that consists of production costs, inventory holding costs, inspection costs, and the penalty costs for the uncompleted orders. The uncertainties in this formulation stem from machine break downs, product quality loss, and demand fluctuations. Since the developed stochastic quadratic integer formulation is not efficient to solve large instances with a large set of scenarios, we study a heuristic solution approach based on scenario reduction logic. The generated optimization tool will support people in production industries to observe the consequences of different scenarios with alternative solutions and to make the best decision in terms of imposed costs.