While the predominant pricing scheme for services is a set of long-term contracts stipulating fixed fee level usage, many service providers now offer flexible contracts. These include flexibility in usage and option to opt out certain time periods. We study effectiveness aligning interests between provider customers presence with different discrete demand distributions. This work develops unifi...

Forecast horizons, i.e long enough planning horizons that ensure agreement of first period optimal production decisions of finite and infinite horizon problems regardless of changes in future demand, are shown to exist in the context of production planning under stochastic demand. The monotonicity of first period optimal production decisions with respect to first order stochastic shifts in dema...