# stockcycle.mod   OLR2-AN-480-97
# AMPL coding: S. Leyffer, September 1999.
#
# Source: "A fast heuristic for minimizing total average cycle stock
#	   subject to practical constraints", E.A. Silver & I. Moon, 
#	   JORS 50, 789-796, August 1999. Model uses SOS to express
#	   discrete variables.
#
# Number of variables:   480
# Number of constraints: 97
# Objective nonlinear
# Linear constraints

param n := 48;            # number of items
param m := 9;             # number of possible discrete reorder intervals
param N := 100;		  # max total number of replenishments

set nn := 1..n;
set mm := 1..m;

param Dv {nn};            # demand rate times unit cost of item i
param Y  {mm};            # set of possible number of orders

var y {nn} >= Y[1], <= Y[m], integer;  	# number of orders per unit time
var z {nn,mm} >= 0, <= 1, integer;	# SOS1 to model discrete y

minimize objective: sum{i in nn}( 1.5*Dv[i] / y[i] );

subject to
   capacity:      sum{i in nn}( y[i] )        <= 3*N;
   defy{i in nn}: sum{j in mm}( z[i,j]*Y[j] )  = y[i];
   SOS{i in nn}:  sum{j in mm}( z[i,j] )       = 1;

data;

param:      Y  :=
     1      3
     2      6
     3      9
     4     12
     5     18
     6     36
     7     52
     8     78
     9    156;

param:      Dv := 
	 1   20.04
	 2   21.72
	 3   37.92
	 4   54.12
	 5   61.8
	 6   81.24
	 7   94.2
	 8   119.4
	 9   171.6
	10   208.8
	11   415.27
	12   470.23
	13   1212
   	14   1393.2
	15   1496.4
	16   1600
	17   1702.4
  	18   1714.5
	19   1870.5
	20   1977.8
	21   2647.12
	22   3143.82
	23   4173
   	24   4347.78
	25   4917
	26   5048.3
	27   5397.2
  	28   6692.4
	29   6837.6
	30   8003.1
	31   8449.5
	32   9152
	33   13236.3
   	34   13970
	35   15327.6
	36   16368
	37   19765
  	38   20470.3
	39   23182.2
	40   25026
	41   31675.6
	42   56734.2
	43   69040.4
   	44   75192
	45   97066.5
	46   99803.2
	47   105984
  	48   106465;