Multi-Stage Stochastic Optimisation for Managing Major Production Incident

A mining company has entered into contractual commitments to supply certain quantities of its product to clients in each time period. Failure to fulfil its obligations would damage its reputation as a reliable supplier. The planned production would normally be sufficient unless major problems such as highwall failures, roof falls, natural disaster, or strikes that interrupt production or delays in obtaining environmental permits, occur. To overcome these difficulties, the company may be able to obtain more of the commodity: from its strategic stockpile (if there is sufficient there); by buying it on the spot market; or for some commodities such as gold and uranium, by leasing it. Two sources of uncertainty, the spot price of the commodity and the occurrence of serious incidents that interrupt production, are considered. For simplicity it is assumed that the commodity price follows a geometric Brownian motion, that productions incidents have a binomial distribution, that they are independent from one time period to another and that they do not affect prices. A branching tree structure is used to model the joint evolution of prices and production incidents. The aim of this research project was to evaluate the companyÆs options for fulfilling its contractual commitments. When evaluating these options, multi-stage stochastic programming with recourse was used to solve this problem because in addition to providing the dollar value of the project, it gives decision-makers the æroadmapÆ to reach the optimal value. That is, how much material should be bought/sold on the spot market, how much to add to/subtract from the stockpile, how much to lease and in the worst case what the shortfall would be, for each time period as a function of the current spot price and breakdown status. A case-study over a five-year period is used to illustrate the proposed procedure. In this study the production would be sufficient to cover the companyÆs contractual commitments unless production incidents occur. Focus is on evaluating the impact of the quantity initially in the stockpile on the value of the project when the commodity market is tight, that is, when only small quantities can be bought on the spot market or by leasing.