Feature: Multi-period optimization with inventory dynamics

[chripiermarini]

Description

The current optimization model is single-period and operates on aggregated (average) demand.
While useful as a first approximation, this approach ignores temporal dynamics and does not capture how demand evolves over time.

The goal of this issue is to extend the model to a multi-period optimization framework that explicitly incorporates time and inventory carry-over.

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Goals

• Introduce a time dimension into the optimization model
• Track inventory across periods
• Capture demand variability over time
• Move from steady-state optimization to dynamic decision-making

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Proposed Model Extension

Decision variables

• flow[o, d, t]: flow from origin o to destination d at time t
• inventory[d, t]: inventory at destination d at time t

Constraints

• Inventory balance: inventory[d, t] = inventory[d, t-1] + inflow[d, t] - demand[d, t]

• Capacity constraints per origin and time period:

• Flows from each origin cannot exceed its capacity at each time step

• Non-negativity constraints:

• All flows and inventory levels must be ≥ 0

Objective

• Minimize total transportation cost across all periods
• (Optional) Include inventory holding costs

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Acceptance Criteria

• Multi-period optimization model implemented (OR-Tools or equivalent)
• Supports time-indexed demand as input
• Inventory carry-over correctly modeled across periods
• Clean interface between forecasting output (time series) and optimization input
• Optional: fallback to single-period model remains available