Single-Item Lot-Sizing With Multiple Capacitated Modules

Online Solver - SAMPLE TEST DATA SETS (derived from Online Solver with Piecewise Linear Production Costs)

Extension of algorithm described at www.lutanho.net/plt/lgrthm/lotsize.html

with Start-up Costs, Multiple Modules with Linear Production Costs and Piecewise Linear Holding Costs

$$min\sum _{i=1}^I(u_i\left(\mathrm{1-}{u}_{i\mathrm{-1}}\right)a_i+u_i\sum _{m=1}^{M_i}{v}_i^m\left(x_i^m\right)(s_i^m+p_i^m{x}_i^m)+\sum _{k=1}^{K_i}{w}_i^k\left(y_i\right)(t_i^k+h_i^k{y}_i))$$
$$0\le x_i^m\le C_i^m,\; with{v}_i^m\left(x_i^m\right)=\{\begin{array}{cc}1& if{x}_i^m>0\\ 0& otherwise\end{array}and{w}_i^k\left(y_i\right)=\{\begin{array}{cc}1& if{y}_i^{k\mathrm{-1}}<y_i\le y_i^k\\ 0& otherwise\end{array}$$

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  input format: (all values must be integer)                                 * 
 *                                                                             * 
 *  I; u_0; y_0; y_I;                                                          * 
 *  startup; x_min, p_fix, p_var, x_max, (first module)                        * 
 *            ...   p_fix, p_var, x_max; (last module)                         * 
 *   demand; y_min, h_fix, h_var, (y_up, ...,) y_max; (first period)           * 
 *  ...                                                                        * 
 *  startup; x_min, p_fix, p_var, x_max, (first module)                        * 
 *            ...   p_fix, p_var, x_max; (last module)                         * 
 *   demand; y_min, h_fix, h_var, (y_up, ...,) y_max; (last period)            * 
 *                                                                             * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  output format:                                                             * 
 *                                                                             * 
 *  u, x, y, n; (first period)                                                 * 
 *  ...                                                                        * 
 *  u, x, y, n; (last period)                                                  * 
 *                                                                             * 
 * (n is the number of pieces in the piecewise linear production cost function)* 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

Input: //This is an example with 2 modules //I u_0 y_0 y_I 5; 0; 0; 0; startup x_min fix var max fix var max demand y_min fix var y_max 0; 0, 400, 5, 40, 300, 10, 50; 60; 0, 0, 2, 999; 0; 0, 400, 5, 40, 300, 10, 50; 50; 0, 0, 2, 999; 0; 0, 400, 5, 40, 300, 10, 50; 60; 0, 0, 2, 999; 0; 0, 400, 5, 40, 300, 10, 50; 60; 0, 0, 2, 999; 0; 0, 400, 5, 40, 300, 10, 50; 40; 0, 0, 2, 999;
solve in memory saving mode (slower) . . . hint: calculation with smaller y_max values may be faster
Output:
T O P M D I SC PC BC IC TC CC