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Single period product mix Description A firm has 3 workshops, each working 40 hours per week, in
which it can produce two products. A unit of each product
requires a given number of hours in the workshops and a
given number of man hours. The hourly labor cost and the
unit sales prices are known. The objective is to determine
the most profitable operation. Further explanation of this example:
'Applications of optimization with Xpress-MP',
Section 2.3 'Simple resource constraints'
Source Files prodmix_graph.mos (!****************************************************** Mosel Example Problems ====================== file prodmix.mos ```````````````` TYPE: Product mix (single period production planning) DIFFICULTY: 1 FEATURES: simple LP problem DESCRIPTION: A firm has 3 workshops, each working 40 hours per week, in which it can produce two products. A unit of each product requires a given number of hours in the workshops and a given number of man hours. The hourly labor cost and the unit sales prices are known. The objective is to determine the most profitable operation. FURTHER INFO: "Applications of optimization with Xpress-MP", Section 2.3 "Simple resource constraints" (c) 2008 Fair Isaac Corporation author: S. Heipcke, 2001, rev. Sep. 2017 *******************************************************!) model Workshop uses "mmxprs", "mmsvg" declarations NProd = 2 ! Number of products NShop = 3 ! Number of workshops RP = 1..NProd RS = 1..NShop WMAX = 40 ! Maximum weekly working time LABOR = 5 ! Hourly labor cost DUR: array(RP,RS) of integer ! Duration of product p in shop s RES: array(RP) of integer ! Man hours per unit PRICE: array(RP) of integer ! Selling price per unit make: array(RP) of mpvar ! Amount of product p end-declarations DUR :: [ 5, 9, 7, 10, 2, 5] RES :: [10, 8] PRICE:: [108, 84] ! Objective: Maximize Benefit MaxBen:= sum(p in RP) (PRICE(p)-LABOR*RES(p)) * make(p) forall(s in RS) ! Limit on weekly working hours Capacity(s):= sum(p in RP) DUR(p,s)*make(p) <= WMAX maximize(MaxBen) writeln("Objective: ", getobjval) forall(p in RP) write("Product ", p, ":", getsol(make(p)), " ") writeln ! Draw solution FACT:=5 forall(p in RP) do svgaddgroup("P"+p, "Product "+p) svgsetstyle(SVG_FILL,SVG_CURRENT) end-do svgaddgroup("Cap","Capacity",SVG_RED) svgaddline(FACT-1, WMAX, (RS.size+1)*FACT, WMAX) forall(s in RS) do cum:=0.0 forall(p in RP) do svgaddrectangle("P"+p,s*FACT,cum,1*FACT-1,DUR(p,s)*make(p).sol) cum+=DUR(p,s)*make(p).sol end-do end-do svgsetgraphviewbox(0,0,(RS.size+1)*FACT, WMAX+1) svgsetgraphscale(10) svgsetgraphlabels("Workshops", "Resource usage") svgsave("prodmix.svg") svgrefresh svgwaitclose("Close browser window to terminate model execution.", 1) end-model | |||||||||

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