Optimum Spacing of Supply Centers

The costs for relocating material sources and processing plants is offset by a reduction in hauling costs. Elementary cost minimizing methods give simple algebraic expressions that optimize constraints. The following rule evolves: The optimum distance between relocations of supply centers is when the total variable cost (distance dependent) to haul material from these sources equals the total cost to establish all of these supply centers. The theoretical solution is illustrated with a solved problem employing the derived formulas as well as by iteration for comparison and sensitivity. The solution to this problem as well as the one relating to Optimum Working Time, published elsewhere in this Journal, is based on the approach made popular a century ago by Lord William T. Kelvin.