~jdpipe/ascend/trunk-old

REQUIRE "atoms.a4l";

(*

	Solution of the 'toy' problem given in the GAMS documentation at

	http://www.gams.com/docs/example.htm

	"Here is a standard algebraic description of the problem, which is to 

	minimize the cost of shipping goods from 2 plants to 3 markets, subject 

	to supply and demand constraints."

	This model doesn't currently agree with the GAMS solution when solving using

	CONOPT. We're still debugging it.

*)

MODEL markets;

	(* canning plants *)

	I IS_A set OF symbol_constant;

	I :== ['Seattle','San Diego'];

	(* markets *)

	J IS_A set OF symbol_constant;

	J :== ['New York','Chicago','Topeka'];

	(* plant capacities *)

	A[I] IS_A mass_rate_constant;

	A['Seattle'] :== 350 {kg/d};

	A['San Diego'] :== 600 {kg/d};

	(* market demands *)

	B[J] IS_A mass_rate_constant;

	B['New York'] :== 325 {kg/d};

	B['Chicago'] :== 300 {kg/d};

	B['Topeka'] :== 275 {kg/d};

	(* distances *)

	D[I][J] IS_A distance_constant;

	D['Seattle']['New York'] :== 2500 {mi}; (* thousands of miles *)

	D['Seattle']['Chicago'] :== 1700 {mi};

	D['Seattle']['Topeka'] :== 1800 {mi};

	D['San Diego']['New York'] :== 2500 {mi};

	D['San Diego']['Chicago'] :== 1800 {mi};

	D['San Diego']['Topeka'] :== 1400 {mi};

	(* freight costs *)

	F IS_A cost_per_mass_per_distance_constant;

	F :== 90 {USD/kg} / 1000 {mi};

	C[I][J] IS_A cost_per_mass_constant; (* shipping cost per mass, for each route *)

 	FOR i IN I CREATE

		FOR j IN J CREATE

			C[i][j] :== F * D[i][j] ;

		END FOR;

	END FOR;

	(* variables *)

	X[I][J] IS_A mass_rate;

	Z IS_A cost_per_time;

	(* equations *) 

	COST: Z = SUM[SUM[C[i][j]*X[i][j] | i IN I] | j IN J];

	supplyslack[I] IS_A mass_rate;

	FOR i IN I CREATE

		SUPPLY[i]: SUM[X[i][j] | j IN J] = A[i] + supplyslack[i];

	END FOR;

	demandslack[J] IS_A mass_rate;

	FOR j IN J CREATE

		DEMAND[j]: SUM[X[i][j] | i IN I] = B[j] + demandslack[j];

	END FOR;

	MINEXPR: MINIMIZE Z;

METHODS

	METHOD on_load;

		Z := 0 {USD/d};

	END on_load;

	METHOD self_test;

		ASSERT abs(Z - 153.675 {USD/d}) < 0.001 {USD/d};

		ASSERT abs(X['Seattle']['New York'] - 50 {kg/d}) < 0.1 {kg/d};

		ASSERT abs(X['Seattle']['Chicago'] - 300 {kg/d}) < 0.1 {kg/d};

		ASSERT abs(X['Seattle']['Topeka'] - 0 {kg/d}) < 0.1 {kg/d};

	END self_test;

END markets;