Single-Item Capacitated Economic Lot-Sizing

Online Solver - SAMPLE TEST DATA SETS (Extension: Multiple Modules with Linear Production Costs)

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

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

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

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  input format: (all values must be integer)                                 * 
 *                                                                             * 
 *  I; u_0; y_0; y_I;                                                          * 
 *  startup; x_min, p_fix, p_var, (x_up, ...,) x_max; ...                      * 
 *   demand; y_min, h_fix, h_var, (y_up, ...,) y_max; (first period)           * 
 *  ...                                                                        * 
 *  startup; x_min, p_fix, p_var, (x_up, ...,) x_max; ...                      * 
 *   demand; y_min, h_fix, h_var, (y_up, ...,) y_max; (last period)            * 
 *                                                                             * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  output format:                                                             * 
 *                                                                             * 
 *  u, x, y; (first period)                                                    * 
 *  ...                                                                        * 
 *  u, x, y; (last period)                                                     * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

Input: //This is an example with MOQ=57, max-capacity=80, and max-backlogging=10: //I u_0 y_0 y_I 9; 0; 0; 0; startup x_min fix var up fix var x_max demand y_min fix var up fix var y_max 7; 0, 9999, 0, 56, 100, 0, 80; 50; -10, 0, -3, 0, 0, 2, 9999; 6; 0, 9999, 0, 56, 100, 0, 80; 30; -10, 0, -3, 0, 0, 2, 9999; 5; 0, 9999, 0, 56, 100, 0, 80; 60; -10, 0, -3, 0, 0, 2, 9999; 7; 0, 9999, 0, 56, 100, 0, 80; 50; -10, 0, -3, 0, 0, 2, 9999; 6; 0, 9999, 0, 56, 100, 0, 80; 40; -10, 0, -3, 0, 0, 2, 9999; 5; 0, 9999, 0, 56, 100, 0, 80; 50; -10, 0, -3, 0, 0, 2, 9999; 7; 0, 9999, 0, 56, 100, 0, 80; 60; -10, 0, -3, 0, 0, 2, 9999; 6; 0, 9999, 0, 56, 100, 0, 80; 50; -10, 0, -3, 0, 0, 2, 9999; 5; 0, 9999, 0, 56, 100, 0, 80; 60; -10, 0, -3, 0, 0, 2, 9999;
solve in memory saving mode (slower) . . . hint: calculation with smaller y_max values may be faster
Output:
T O P D I SC PC BC IC TC CC