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Choice of locations for income tax offices Description Choice of locations for income tax offices: linear, 'element', 'occurrence', 'equiv' constraints; search strategy for variables. Further explanation of this example:
'Xpress Kalis Mosel User Guide', Section 3.9 equiv: Location of income tax offices
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Data Files j5tax_ka.mos (!****************************************************** CP Example Problems =================== file j5tax_ka.mos ````````````````` Choice of locations for income tax offices (See "Applications of optimization with Xpress-MP", Section 15.5 Location of income tax offices) The variables build(c) representing the decisions whether to build an office and the variables depend(c) indicating the office associated with a town are linked by `occurrence' and `equivalence' constraints: numdep(c) = |depend(d)=c| numdep(c) >= 1 <=> build(c) = 1 The distances in the objective function are represented through `element' constraints (auxiliary variables depdist(c) indicate the distance from town c to the closest office). *** This model cannot be run with a Community Licence for the provided data instance *** (c) 2008 Artelys S.A. and Fair Isaac Corporation Creation: 2005, rev. Mar. 2013, Apr. 2022 *******************************************************!) model "J-5 Tax office location (CP)" uses "kalis" forward procedure calculate_dist setparam("KALIS_DEFAULT_LB", 0) declarations NC = 12 CITIES = 1..NC ! Set of cities DIST: array(CITIES,CITIES) of integer ! Distance matrix POP: array(CITIES) of integer ! Population of cities LEN: dynamic array(CITIES,CITIES) of integer ! Road lengths NUMLOC: integer ! Desired number of tax offices D: array(CITIES) of integer ! Auxiliary array used in constr. def. build: array(CITIES) of cpvar ! 1 if office in city, 0 otherwise depend: array(CITIES) of cpvar ! Office on which city depends depdist: array(CITIES) of cpvar ! Distance to tax office numdep: array(CITIES) of cpvar ! Number of depending cities per off. totDist: cpvar ! Objective function variable Strategy: array(1..2) of cpbranching ! Branching strategy end-declarations initializations from 'Data/j5tax.dat' LEN POP NUMLOC end-initializations ! Calculate the distance matrix calculate_dist forall(c in CITIES) do build(c) <= 1 1 <= depend(c); depend(c) <= NC min(d in CITIES) DIST(c,d) <= depdist(c) depdist(c) <= max(d in CITIES) DIST(c,d) numdep(c) <= NC end-do ! Distance from cities to tax offices forall(c in CITIES) do forall(d in CITIES) D(d):=DIST(c,d) element(D, depend(c)) = depdist(c) end-do ! Number of cities depending on every office forall(c in CITIES) occurrence(c, depend) = numdep(c) ! Relations between dependencies and offices built forall(c in CITIES) equiv( build(c) = 1, numdep(c) >= 1 ) ! Limit total number of offices sum(c in CITIES) build(c) <= NUMLOC ! Branching strategy Strategy(1):= assign_and_forbid(KALIS_MAX_DEGREE, KALIS_MAX_TO_MIN, build) Strategy(2):= split_domain(KALIS_SMALLEST_DOMAIN, KALIS_MIN_TO_MAX, depdist, true, 5) cp_set_branching(Strategy) ! Objective: weighted total distance ! totDist = sum(c in CITIES) POP(c)*depdist(c) ! Equivalent formulation: totDist = dot(POP,depdist) ! Solve the problem if not cp_minimize(totDist) then writeln("Problem is infeasible") exit(1) end-if ! Solution printing writeln("Total weighted distance: ", getsol(totDist), " (average per inhabitant: ", getsol(totDist)/sum(c in CITIES) POP(c), ")") forall(c in CITIES | getsol(build(c))>0) do write("Office in ", c, ": ") forall(d in CITIES | getsol(depend(d))=c) write(" ",d) writeln end-do !----------------------------------------------------------------- ! Calculate the distance matrix using Floyd-Warshall algorithm procedure calculate_dist ! Initialize all distance labels with a sufficiently large value BIGM:=sum(c,d in CITIES | exists(LEN(c,d))) LEN(c,d) forall(c,d in CITIES) DIST(c,d):=BIGM forall(c in CITIES) DIST(c,c):=0 ! Set values on the diagonal to 0 ! Length of existing road connections forall(c,d in CITIES | exists(LEN(c,d))) do DIST(c,d):=LEN(c,d) DIST(d,c):=LEN(c,d) end-do ! Update shortest distance for every node triple forall(b,c,d in CITIES | c<d ) if DIST(c,d) > DIST(c,b)+DIST(b,d) then DIST(c,d):= DIST(c,b)+DIST(b,d) DIST(d,c):= DIST(c,b)+DIST(b,d) end-if end-procedure end-model | |||||||||||

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