Simulation-Based Robust Revenue Maximization Of Coal Mines Using Response Surface Methodology

Abstract

A robust simulation-based optimization approach is proposed for truck-shovel systems in surface coal mines to maximize the expected value of revenue obtained from loading customer trains. To this end, a large surface coal mine in North America is considered as case study. A data-driven modeling framework is developed and then applied to automatically generate a highly detailed simulation model of the mine in Arena. The framework comprises a formal information model based on Unified Modeling Language (UML), which is used to input mine structural as well as production information. Petri net-based model generation procedures are applied to automatically generate the simulation model based on the whole set of simulation inputs. Then, factors encountered in material handling operations that may affect the robustness of revenue are then classified into 1) controllable; and 2) uncontrollable categories. While controllable factors are trucks locked to routes, uncontrollable factors are inverses of summation over truck haul, and shovel loading and truck-dumping times for each route. Historical production data of the mine contained in a data warehouse is used to derive probability distributions for the uncontrollable factors. The data warehouse is implemented in Microsoft SQL, and contains snapshots of historical equipment statuses and production outputs taken at regular intervals in each shift of the mine. Response Surface Methodology is applied to derive an expression for the variance of revenue as a function of controllable and uncontrollable factors. More specifically, 1) first order and second order effects for controllable factors, 2) first order effects for uncontrollable factors, and 3) two factor interactions for controllable and uncontrollable factors are considered. Latin Hypercube Sampling method is applied for setting controllable factors and the means of uncontrollable factors. Also, Common Random Numbers method is applied to generate the sequence of pseudo-random numbers for uncontrollable factors in simulation experiments for variance reduction between different design points of the metamodel. The variance of the metamodel is validated using leave-one-out cross validation. It is later applied as an additional constraint to the mathematical formulation to maximize revenue in the simulation model using OptQuest. The decision variables in this formulation are truck locks only. Revenue is a function of the actual quality of coal delivered to each customer and their corresponding quality specifications for premiums and penalties. OptQuest is an optimization add-on for Arena that uses Tabu search and Scatter search algorithms to arrive at the optimal solution. The upper bound on the variance as a constraint is varied to obtain different sets of expected value as well as variance of optimal revenue. After comparison with results using OptQuest with random sampling and without variance expression of metamodel, it has been shown that the proposed approach can be applied to obtain the decision variable set that not only results in a higher expected value but also a narrower confidence interval for optimum revenue. According to the best of our knowledge, there are two major contributions from this research: 1) It is theoretically demonstrated using 2-point and orthonormal k-point response surfaces that Common Random Numbers reduces the error in estimation of variance of metamodel of simulation model. 2) A data-driven modeling and simulation framework has been proposed for automatically generating discrete-event simulation model of large surface coal mines to reduce modeling time, expenditure, as well as human errors associated with manual development.