Multiperiod

Multiperiod refers to analysis, planning, or optimization that explicitly spans more than one time period. In contrast to single-period models, multiperiod frameworks incorporate decisions, constraints, and outcomes across a sequence of time steps, allowing dynamics such as inventory carryover, production capacity usage, and financial cash flows to unfold over time.

In optimization, a multiperiod model includes decision variables for each period and constraints that link consecutive periods, such as stock balances, energy balance, or budget constraints. The objective is usually a cumulative measure over the horizon, such as total cost or total profit, and may be maximized or minimized. Many models distinguish finite horizons from infinite ones and may apply discounting to future costs or revenues.

Applications are widespread across operations research and economics. Multiperiod models are common in inventory control, production planning, workforce scheduling, project management, and energy or resource planning. In finance, multiperiod models analyze cash flows, investments, and risk across multiple future periods.

Methods used to solve multiperiod problems include dynamic programming, stochastic programming, and Markov decision processes. Model predictive control and multi-stage optimization are related approaches that optimize decisions over a rolling horizon. Solutions often require simplifying assumptions to combat the curse of dimensionality.

Challenges include data requirements, model calibration, and computational complexity, especially under uncertainty. Properly specifying the horizon length, discount rates, and scenario structure is crucial for producing robust and actionable plans.