Facility-location formulation

Facility-location formulation

Class: ULSAlgorithms.Exact.Formulations.FacilityLocationFormulationSolver

Family: Solver-backed mathematical formulation
Time: Solver-dependent
Memory: O(T²) model + solver
Applicability: General classical ULS

Description

Facility-location 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

Let \(q_{tk}\) be the amount of demand in period \(k\) supplied by production in period \(t\), and define

\[c_{tk}=p_t+\sum_{r=t}^{k-1}h_r. \]

Then

\[\min \sum_{t=1}^{T}f_t y_t+\sum_{k=1}^{T}\sum_{t=1}^{k}c_{tk}q_{tk} \]

subject to

\[\sum_{t=1}^{k}q_{tk}=d_k, \qquad k=1,\ldots,T, \]

\[q_{tk}\le d_k y_t, \qquad 1\le t\le k\le T, \]

\[q_{tk}\ge0,\qquad y_t\in\{0,1\}. \]

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

Minimal API

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

Scientific source

Krarup & Bilde (1977), Plant Location, Set Covering and Economic Lot Size: An O(nm)-Algorithm for Structured Problems; 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.