set PROD; # products
set AREA {PROD}; # market areas for each product
param T > 0; # number of weeks
param rate {PROD} > 0; # tons per hour produced
param inv0 {PROD} >= 0; # initial inventory
param avail {1..T} >= 0; # hours available in week
param market {p in PROD, AREA[p], 1..T} >= 0;
# limit on tons sold in week
param prodcost {PROD} >= 0; # cost per ton produced
param invcost {PROD} >= 0; # carrying cost/ton of inventory
param revenue {p in PROD, AREA[p], 1..T} >= 0;
# revenue per ton sold
var Make {PROD,1..T} >= 0; # tons produced
var Inv {PROD,0..T} >= 0; # tons inventoried
var Sell {p in PROD, a in AREA[p], t in 1..T} >= 0, <= market[p,a,t];
# tons sold
maximize total_profit:
sum {p in PROD, t in 1..T}
(sum {a in AREA[p]} revenue[p,a,t]*Sell[p,a,t] -
prodcost[p]*Make[p,t] - invcost[p]*Inv[p,t]);
# Total revenue less costs for all products in all weeks
subject to time {t in 1..T}:
sum {p in PROD} (1/rate[p]) * Make[p,t] <= avail[t];
# Total of hours used by all products
# may not exceed hours available, in each week
subject to initial {p in PROD}: Inv[p,0] = inv0[p];
# Initial inventory must equal given value
subject to balance {p in PROD, t in 1..T}:
Make[p,t] + Inv[p,t-1] = sum {a in AREA[p]} Sell[p,a,t] + Inv[p,t];
# Tons produced and taken from inventory
# must equal tons sold and put into inventory