\$title Elementary Production and Inventory Model (ROBERT,SEQ=37) \$onText A manufacturer can produce three different products requiring the storage of two raw materials. Expected profits change over time and remaining raw materials are valued. Fourer, R, Modeling Languages versus Matrix Generators For Linear Programming. ACM Transaction of Mathematical Software 9, 2 (1983), 143-183. Keywords: linear programming, production planning, inventory problem, manufacturing \$offText Set p 'products' / low, medium, high / r 'raw materials' / scrap, new / tt 'long horizon' / 1*4 / t(tt) 'short horizon' / 1*3 /; Table a(r,p) 'input coefficients' low medium high scrap 5 3 1 new 1 2 3; Table c(p,t) 'expected profits' 1 2 3 low 25 20 10 medium 50 50 50 high 75 80 100; Table misc(*,r) 'other data' scrap new max-stock 400 275 storage-c .5 2 res-value 15 25; Scalar m 'maximum production' / 40 /; Variable x(p,tt) 'production and sales' s(r,tt) 'opening stocks' profit; Positive Variable x, s; Equation cc(t) 'capacity constraint' sb(r,tt) 'stock balance' pd 'profit definition'; cc(t).. sum(p, x(p,t)) =l= m; sb(r,tt+1).. s(r,tt+1) =e= s(r,tt) - sum(p, a(r,p)*x(p,tt)); pd.. profit =e= sum(t, sum(p, c(p,t)*x(p,t)) - sum(r, misc("storage-c",r)*s(r,t))) + sum(r, misc("res-value",r)*s(r,"4")); s.up(r,"1") = misc("max-stock",r); Model robert / all /; solve robert maximizing profit using lp;