Aggregate inventory formulation

Aggregate inventory formulation

Class: ULSAlgorithms.Exact.Formulations.AggregateInventoryFormulationSolver

Family: Solver-backed mathematical formulation
Time: Solver-dependent
Memory: O(T) model + solver
Applicability: General classical ULS

Description

Aggregate inventory formulation is an exact solver-backed ULS strategy. It builds a mathematical formulation and delegates the optimization step to the selected external engine while keeping the common IUlsSolver result contract.

Mathematical model

Equations use periods 1,...,T for readability; the C# API is zero-based.

\[\min \sum_{t=1}^{T}\left(f_t y_t+p_t x_t+h_t I_t\right) \]

subject to

\[I_{t-1}+x_t-I_t=d_t, \qquad t=1,\ldots,T, \]

\[x_t\le D_{t,T}y_t, \qquad D_{t,T}=\sum_{k=t}^{T}d_k, \]

\[I_0=0,\qquad I_T=0,\qquad x_t\ge0,\ I_t\ge0,\ y_t\in\{0,1\}. \]

For the formulation taxonomy and historical context, see Mathematical Programming Formulations.

Minimal API

IUlsSolver solver = new AggregateInventoryFormulationSolver();
UlsSolveResult result = solver.Solve(problem);

Scientific source

Wagner & Whitin (1958), Dynamic Version of the Economic Lot Size Model, Management Science 5(1), 89-96; Brahimi, Dauzere-Peres, Najid & Nordli (2006), Single Item Lot Sizing Problems, European Journal of Operational Research 168(1), 1-16

Full class reference

Use the Doxygen Classes index for constructors, members and source-level documentation.