a. Graduate School of Engineering, The University of Tokyo. Bunkyo-ku, Tokyo 113-5656, Japan
b. McKinsey and Company Inc. Japan

Although the general, production scheduling problem, which seeks to maximize the NPV of a cash flow of a multi-period open pit mine development project, can be formulated as an IP problem, it can virtually not be solved by ordinary PCs. Therefore, the 4-D network relaxation method, in which production capacity constraints will be relaxed by a Lagrangian multiplier method so that the problem can be solved by LG method or Max-Flow method and in combination with a subgradient method iteratively converged to the optimum solution, has been developed. Akaike (1999) proposed a new 4-D network relaxation method, in which the processing method of each block will also he optimized, and further revised it to decrease the possibility of gap problem generation.
The algorithm to obtain the optimum production scale and the production schedule at the scale, using this revised 4-D network relaxation method, is proposed. Case study on showed an influence of the discount rate on the optimum production scale. It took two and a half days approximately to solve a 5 period (10 years) project scheduling problem for an ore body model with 129,500 blocks.