Multi-Stage Stochastic Optimisation for Managing Major Production Incidents

摘要

A mining company has entered into contractual commitments to supply certain quantities of itsrnproduct to clients in each time period. Failure to fulfi l its obligations would damage its reputationrnas a reliable supplier. The planned production would normally be suffi cient unless major problemsrnsuch as highwall failures, roof falls, natural disaster, or strikes that interrupt production or delays inrnobtaining environmental permits, occur. To overcome these diffi culties, the company may be able tornobtain more of the commodity:rn1. from its strategic stockpile (if there is suffi cient there);rn2. by buying it on the spot market; orrn3.for some commodities such as gold and uranium, by leasing it.rnTwo sources of uncertainty, the spot price of the commodity and the occurrence of serious incidentsrnthat interrupt production, are considered. For simplicity it is assumed that the commodity pricernfollows a geometric Brownian motion, that productions incidents have a binomial distribution, thatrnthey are independent from one time period to another and that they do not affect prices. A branchingrntree structure is used to model the joint evolution of prices and production incidents.rnThe aim of this research project was to evaluate the company’s options for fulfi lling its contractualrncommitments. When evaluating these options, multi-stage stochastic programming with recoursernwas used to solve this problem because in addition to providing the dollar value of the project, itrngives decision-makers the ‘roadmap’ to reach the optimal value. That is, how much material shouldrnbe bought/sold on the spot market, how much to add to/subtract from the stockpile, how much tornlease and in the worst case what the shortfall would be, for each time period as a function of therncurrent spot price and breakdown status. A case-study over a fi ve-year period is used to illustraternthe proposed procedure. In this study the production would be suffi cient to cover the company’srncontractual commitments unless production incidents occur. Focus is on evaluating the impact of thernquantity initially in the stockpile on the value of the project when the commodity market is tight, thatrnis, when only small quantities can be bought on the spot market or by leasing.