set PROD; # products param T > 0; # number of weeks param rate {PROD} > 0; # tons per hour produced param inv0 {PROD} >= 0; # initial inventory param commit {PROD,1..T} >= 0; # minimum tons sold in week param market {PROD,1..T} >= 0; # limit on tons sold in week param avail_min {1..T} >= 0; # unpenalized hours available param avail_max {t in 1..T} >= avail_min[t]; # total hours available param time_penalty {1..T} > 0; param prodcost {PROD} >= 0; # cost per ton produced param invcost {PROD} >= 0; # carrying cost per ton of inventory param revenue {PROD,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, t in 1..T} >= 0, <= market[p,t]; # tons sold var Use {t in 1..T} >= 0, <= avail_max[t]; # hours used maximize total_profit: sum {p in PROD, t in 1..T} (revenue[p,t]*Sell[p,t] - prodcost[p]*Make[p,t] - invcost[p]*Inv[p,t]) - sum {t in 1..T} <> Use[t] - sum {p in PROD, t in 1..T} <> (Sell[p,t],commit[p,t]); # Objective: total revenue less costs in all weeks subj to time {t in 1..T}: sum {p in PROD} (1/rate[p]) * Make[p,t] = Use[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] = Sell[p,t] + Inv[p,t]; # Tons produced and taken from inventory # must equal tons sold and put into inventory