Stochastic programming

Authors: Gerald Ogbonna (gco27), Hangyu Zhou (hz477), Roohi Menon (rm832), Vikram Raghavan (vr278) (SYSEN 6800 Fall 2021)

Introduction

Stochastic Programming, also referred to as Stochastic Optimization, is a mathematical framework to help decision-making process under uncertainty [1]. With uncertainties being widespread, Stochastic Programming is a risk-neutral mathematical framework that finds application in areas, such as process systems engineering [2]. In process engineering, uncertainties are related to prices, purity of raw materials, customer demands, and yields of pilot reactors, among others. Batch processing has widely been adopted across process industries, and for the stated manufacturing process production scheduling is one of the most crucial decisions to be taken. In a deterministic optimization model, parameters, such as process of raw materials, availability of raw materials, price of different products, operation time and cost, and order demands are considered without factoring uncertainty. However, such assumptions are not realistic because uncertainty doesn’t come with a forewarning. Hence, uncertainty needs to be factored always [4].

In conventional robust optimization, the assumption is made that all decision variables are realized before the realization of uncertainty. Such an approach makes the conventional robust optimization problem overly conservative [4]. Moreover, in manufacturing not all decisions need to be made “in-the-present,” a stagnated approach to decision making [two-stage approach] can also be adopted. Going beyond, Stochastic Programming framework can also be applied to a variety of problems across sectors, such as electricity generation, financial planning, supply chain management, mitigation of climate change, and pollution control [2]. The field has evolved from deterministic linear programming by introducing random variables [7].