Optimal Planning of Equipment Maintenance and Replacement on a Variable Horizon

In maintenance and replacement planning of an industry, the purchasing of new equipment on the market with some kind of technological improvement over existing equipment should be taken into account. Because of operating cost, ordinary and preventive maintenance expenses may be lower, production rate may be higher and the quality of output may be better, etc. The industry to be considered in this paper is the mining industry and the replaced equipment is the mine shovel. It is assumed that, at most, one new shovel can be purchased before the mine is exhausted. It is possible that the mine is given up before exhausted, because of the disadvantage of the expense and loss of the salvage value of the shovel compared with the value of the remaining mine. There are four decision variables in this problem, as follows: the aintenance policy in each period, the purchase time of the new shovel, the end of the planning horizon or the time to stop the mining and the value of production during each period. The objective is to determine the values of the decision variables so as to maximize the overall discounted profit of the mine over the planning horizon.