(!****************************************************** Mosel Example Problems ====================== file f3landing.mos `````````````````` Schedule plane landings Ten planes are scheduled to arrive at a large airport. Each plane has an earliest and latest arrival time. Within this time window, there is a target arrival time. Penalties are assigned to each minute a flight is early or late. Between each landing, there is a required security time interval. Which schedule minimizes the total arrival penalty given the arrival time windows and required separating intervals? This problem calculates a specific BigM per index tuple for use in the formulation of the disjunctive constraints on landing times. Note that the obvious pair of 'START' and 'END' for the time windows cannot be used because 'END' is a reserved word in Mosel. (c) 2008 Fair Isaac Corporation author: S. Heipcke, Mar. 2002 *******************************************************!) model "F-3 Landing schedule" uses "mmxprs" declarations PLANES = 1..10 ! Set of airplanes START, STOP: array(PLANES) of integer ! Start, end of arrival time windows TARGET: array(PLANES) of integer ! Planned arrival times CEARLY, CLATE: array(PLANES) of integer ! Cost of earliness/lateness DIST: array(PLANES,PLANES) of integer ! Minimum interval between planes M: array(PLANES,PLANES) of integer ! Sufficiently large positive values prec: array(PLANES,PLANES) of mpvar ! 1 if plane i precedes j land: array(PLANES) of mpvar ! Arrival time early,late: array(PLANES) of mpvar ! Earliness/lateness end-declarations initializations from 'f3landing.dat' START STOP TARGET CEARLY CLATE DIST end-initializations forall(p,q in PLANES) M(p,q):= STOP(p) + DIST(p,q) - START(q) ! Objective: total penalty for deviations from planned arrival times Cost:= sum(p in PLANES) (CEARLY(p)*early(p) + CLATE(p)*late(p)) ! Keep required intervals between plan arrivals forall(p,q in PLANES | p>q) land(p) + DIST(p,q) <= land(q) + M(p,q)*prec(q,p) forall(p,q in PLANES | p<q) <=land(q) Relations between and effective arrival time in do>= TARGET(p) - land(p)
  late(p) >= land(p) - TARGET(p)
  land(p) = TARGET(p) - early(p) + late(p)
 end-do

 forall(p in PLANES) do
  START(p) <= land(p); land(p) <= STOP(p)
  early(p) <= TARGET(p)-START(p)
  late(p) <= STOP(p)-TARGET(p)
 end-do
 
 forall(p,q in PLANES | p<q) prec(p,q) is_binary ! Solve the problem minimize(Cost) ! Solution printing writeln("Total deviation cost: ", getobjval) writeln("Plane Arrival Target Deviation") forall(p in PLANES) writeln(strfmt(p,3), strfmt(getsol(land(p)),8), strfmt(TARGET(p),8), strfmt(getsol(land(p))-TARGET(p),8)) end-model