prodsp.gms : Stochastic Programming Example

**Description**

The problem consists of determining the product mix for a furniture shop with two workstations: carpentry and finishing. The availability of labor in man-hours at the two stations is limited. There are four product classes, each consuming a certain number of man-hours at the two stations. Each product earns a certain profit and the shop has the option to purchase labor from outside. The objective is to maximize the profit.

**Reference**

- King, A J, Stochastic Programming Problems: Examples from the Literature. In Ermoliev, Y, and Wets, R J, Eds, Numerical Techniques for Stochastic Optimization Problems. Springer Verlag, 1988, pp. 543-567.

**Large Model of Type :** LP

**Category :** GAMS Model library

**Main file :** prodsp.gms

$title Stochastic Programming Example (PRODSP,SEQ=186) $ontext The problem consists of determining the product mix for a furniture shop with two workstations: carpentry and finishing. The availability of labor in man-hours at the two stations is limited. There are four product classes, each consuming a certain number of man-hours at the two stations. Each product earns a certain profit and the shop has the option to purchase labor from outside. The objective is to maximize the profit. King, A J, Stochastic Programming Problems: Examples from the Literature. In Ermoliev, Y, and Wets, R J, Eds, Numerical Techniques for Stochastic Optimization Problems. Springer Verlag, 1988, pp. 543-567. $offtext Sets i product class / class-1*class-4 / j workstation / work-1 *work-2 / s Nodes / s1*s300 / Parameters c(i) profit / class-1 12,class-2 20, class-3 18, class-4 40 / q(j) cost / work-1 5, work-2 10 / h(j,s) available labor t(j,i,s) labor required table trand(j,*,i) min and max values class-1 class-2 class-3 class-4 work-1.min 3.5 8 6 9 work-1.max 4.5 10 8 11 work-2.min .8 .8 2.5 36 work-2.max 1.2 1.2 3.5 44 ; t(j,i,s) = uniform(trand(j,'min',i),trand(j,'max',i)); h('work-1',s) = normal(6000,100); h('work-2',s) = normal(4000, 50); Variables EProfit expected profit x(i) products sold v(j,s) labor purchased positive variable x,v Equations obj expected cost definition lbal(j,s) labor balance; obj.. EProfit =e= sum(i, c(i)*x(i)) - 1/card(s)*sum((j,s), q(j)*v(j,s)); Equation foo(i) dummy stage 0 constraint for OSLSE; foo(i).. x(i) =g= 0; lbal(j,s).. sum(i, t(j,i,s)*x(i)) =l= h(j,s) + v(j,s); model mix / all /; mix.solprint$(card(s) > 10) = %solprint.Quiet%; solve mix using lp maximizing eprofit; display eprofit.l,x.l;