Single-Item Capacitated Economic Lot-Sizing

Online Solver - SAMPLE TEST DATA SETS
(derived from Online Solver without Storage Deterioration )

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 Storage Deterioration

min \sum_{i = 1}^{I} (u_{i} (1- u_{i -1}) a_{i} + u_{i} \sum_{j = 1}^{J_{i}} v_{i}^{j} (x_{i}) (s_{i}^{j} + p_{i}^{j} x_{i}) + \sum_{k = 1}^{K_{i}} w_{i}^{k} (y_{i}) (t_{i}^{k} + h_{i}^{k} y_{i}))

with v_{i}^{j} (x_{i}) = {\begin{matrix} 1 & if x_{i}^{j -1} < x_{i} \leq x_{i}^{j} \\ 0 & otherwise \end{matrix} and w_{i}^{k} (y_{i}) = {\begin{matrix} 1 & if y_{i}^{k -1} < y_{i} \leq y_{i}^{k} \\ 0 & otherwise \end{matrix}

y_{i} = {\begin{matrix} x_{i} - d_{i} + y_{i-1} (1 - b_{i-1}) & if y_{i-1} > 0 \\ x_{i} - d_{i} + y_{i-1} & otherwise \end{matrix}

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  input format: (all values must be integer)                                 * 
 *                                                                             * 
 *  I; u_0; y_0_det; y_I_det; (y_det= inventory level after deterioration)     * 
 *  startup; x_min, p_fix, p_var, (x_up, ...,) x_max; ...                      * 
 *   demand; y_min, h_fix, h_var, (y_up, ...,) y_max; b[‰]; (first period)     * 
 *  ...                                                                        * 
 *  startup; x_min, p_fix, p_var, (x_up, ...,) x_max; ...                      * 
 *   demand; y_min, h_fix, h_var, (y_up, ...,) y_max; b[‰]; (last period)      * 
 *                                                                             * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
 *  output format:                                                             * 
 *                                                                             * 
 *  u, x, y, y_det; (first period)                                             * 
 *  ...                                                                        * 
 *  u, x, y, y_det; (last period)                                              * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

Input:

//This is an example with MOQ=57, max-capacity=80, and max-backlogging=10:
//and 20% deterioration per period = 200 b_pm (bad per mill (per period))
//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 b_pm
   7;     0, 9999, 0, 57, 100, 0,  80;    50;   -10,  0, -3,  0, 0,  2,  999; 200;
   6;     0, 9999, 0, 57, 100, 0,  80;    30;   -10,  0, -3,  0, 0,  2,  999; 200;
   5;     0, 9999, 0, 57, 100, 0,  80;    60;   -10,  0, -3,  0, 0,  2,  999; 200;
   7;     0, 9999, 0, 57, 100, 0,  80;    50;   -10,  0, -3,  0, 0,  2,  999; 200;
   6;     0, 9999, 0, 57, 100, 0,  80;    40;   -10,  0, -3,  0, 0,  2,  999; 200;
   5;     0, 9999, 0, 57, 100, 0,  80;    50;   -10,  0, -3,  0, 0,  2,  999; 200;
   7;     0, 9999, 0, 57, 100, 0,  80;    60;   -10,  0, -3,  0, 0,  2,  999; 200;
   6;     0, 9999, 0, 57, 100, 0,  80;    50;   -10,  0, -3,  0, 0,  2,  999; 200;
   5;     0, 9999, 0, 57, 100, 0,  80;    60;   -10,  0, -3,  0, 0,  2,  999; 200;

solve in memory saving mode (slower) . . . hint: calculation with smaller y_max values may be faster

Output + Model: