(!****************************************************** Mosel Example Problems ====================== file transship.mos `````````````````` TYPE: Production planning with time-dependent production cost (transshipment flow formulation) DIFFICULTY: 3 FEATURES: MIP problem, representation of multi-period production as flow; encoding of arcs, `exists', `create', `isodd', `getlast', inline `if' DESCRIPTION: A company wishes to plan the production of a product for the next six weeks. The weekly demand is known for the entire planning period. The production capacity and the production and storage costs take different values depending on the time period. Which is the production plan that minimizes the total cost of production and storage? FURTHER INFO: `Applications of optimization with Xpress-MP', Section 8,5 `Planning the production of fiberglass' (c) 2008 Fair Isaac Corporation author: S. Heipcke, 2002, rev. Nov. 2017 *******************************************************!) model "Transshipment" uses "mmxprs", "mmsvg" declarations NODES: range ! Production and demand nodes ! odd numbers: production capacities ! even numbers: demands ARC: dynamic array(NODES,NODES) of real ! Cost of flow on arcs WEIGHT: array(NODES) of integer ! Node weights (capacities/demand) flow: dynamic array(NODES,NODES) of mpvar ! Flow on arcs end-declarations initializations from 'transship.dat' ARC WEIGHT end-initializations forall(m,n in NODES | exists(ARC(m,n))) create(flow(m,n)) ! Objective: total cost of production and storage Cost:= sum(m,n in NODES | exists(ARC(m,n))) ARC(m,n)*flow(m,n) ! Satisfy demands (flow balance constraints) forall(n in NODES | isodd(n)=FALSE) Balance(n):= if(n>2, flow(n-2,n), 0) + flow(n-1,n) = if(n<getlast(NODES), Production capacities in NODES <=WEIGHT(n) Solve the problem Solution printing cost:=",getobjval)
 write(" not writeln drawing svgaddgroup("Prod",="Production">0) then
   svgaddarrow(t*2, 4, t*2, 1)
   svgaddtext(t*2, 2.5, 
                text(getsol(sum(m in NODES) flow(t*2-1,m))))
  end-if
  
 svgaddgroup("Store", "Storage", svgcolor(0,0,120)) 
 forall(t in 1..integer(getlast(NODES)/2)-1)
  if (getsol(sum(m in NODES) flow(t*2,m))>0) then
   svgaddarrow(t*2, 1, (t+1)*2, 1)
   svgaddtext(t*2+1, 1.1, 
                text(getsol(sum(m in NODES) flow(t*2,m))))
  end-if
  
 svgaddgroup("Cap", "Capacities", SVG_ORANGE) 
 svgsetstyle(SVG_TEXTANCHOR, "middle")
 forall(n in NODES | isodd(n)) do
  svgaddpoint(n+1, 4)
  svgaddtext(n+1, 4.2, string(WEIGHT(n)))
 end-do
 
 svgaddgroup("Dem", "Demands", SVG_BROWN) 
 svgsetstyle(SVG_TEXTANCHOR, "middle")
 forall(n in NODES | not isodd(n)) do
  svgaddpoint(n, 1)
  svgaddtext(n, 0.5, string(WEIGHT(n)))
 end-do

 svgsave("transship.svg")
 svgrefresh
 svgwaitclose("Close browser window to terminate model execution.", 1)
end-model