Single-Item Capacitated Economic Lot-Sizing with Lost Sales

Online Solver - SAMPLE TEST DATA SETS (derived from Online Solver without Lost Sales)

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

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

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

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  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; ls_uc, ls_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; ls_uc, ls_max;           *  
 *   demand; y_min, h_fix, h_var, (y_up, ...,) y_max; (last period)            * 
 *                                                                             * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  output format:                                                             * 
 *                                                                             * 
 *  u, x, l, y; (first period)                                                 * 
 *  ...                                                                        * 
 *  u, x, l, y; (last period)                                                  * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

Input: //Example with MOQ=57, max-capacity=80, max-backlogging=10 and max-lost-sales=25: //I u_0 y_0 y_I 9; 0; 0; 0; startup x_min fix var up fix var x_max ls_uc max demand y_min fix var up fix var y_max 70; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 50; -10, 0, -30, 0, 0, 20, 999; 60; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 30; -10, 0, -30, 0, 0, 20, 999; 50; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 60; -10, 0, -30, 0, 0, 20, 999; 70; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 50; -10, 0, -30, 0, 0, 20, 999; 60; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 40; -10, 0, -30, 0, 0, 20, 999; 50; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 50; -10, 0, -30, 0, 0, 20, 999; 70; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 60; -10, 0, -30, 0, 0, 20, 999; 60; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 50; -10, 0, -30, 0, 0, 20, 999; 50; 0, 99999, 0, 56, 1000, 0, 80; 22, 25; 60; -10, 0, -30, 0, 0, 20, 999;
solve in memory saving mode (slower) . . . hint: calculation with smaller y_max values may be faster
Output + Model:
T O P L D I SC PC LC BC IC TC CC