1    	/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
2    	/*                                                                           */
3    	/*                  This file is part of the program and library             */
4    	/*         SCIP --- Solving Constraint Integer Programs                      */
5    	/*                                                                           */
6    	/*  Copyright (c) 2002-2023 Zuse Institute Berlin (ZIB)                      */
7    	/*                                                                           */
8    	/*  Licensed under the Apache License, Version 2.0 (the "License");          */
9    	/*  you may not use this file except in compliance with the License.         */
10   	/*  You may obtain a copy of the License at                                  */
11   	/*                                                                           */
12   	/*      http://www.apache.org/licenses/LICENSE-2.0                           */
13   	/*                                                                           */
14   	/*  Unless required by applicable law or agreed to in writing, software      */
15   	/*  distributed under the License is distributed on an "AS IS" BASIS,        */
16   	/*  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */
17   	/*  See the License for the specific language governing permissions and      */
18   	/*  limitations under the License.                                           */
19   	/*                                                                           */
20   	/*  You should have received a copy of the Apache-2.0 license                */
21   	/*  along with SCIP; see the file LICENSE. If not visit scipopt.org.         */
22   	/*                                                                           */
23   	/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
24   	
25   	/**@file   sepa_mcf.h
26   	 * @ingroup SEPARATORS
27   	 * @brief  multi-commodity-flow network cut separator
28   	 * @author Tobias Achterberg
29   	 * @author Christian Raack
30   	 *
31   	 * We try to identify a multi-commodity flow structure in the LP relaxation of the
32   	 * following type:
33   	 *
34   	 *  (1)  sum_{a in delta^+(v)} f_a^k  - sum_{a in delta^-(v)} f_a^k  <=  -d_v^k   for all v in V and k in K
35   	 *  (2)  sum_{k in K} f_a^k - c_a x_a                                <=  0        for all a in A
36   	 *
37   	 * Constraints (1) are flow conservation constraints, which say that for each commodity k and node v the
38   	 * outflow (delta^+(v)) minus the inflow (delta^-(v)) of a node v must not exceed the negative of the demand of
39   	 * node v in commodity k. To say it the other way around, inflow minus outflow must be at least equal to the demand.
40   	 * Constraints (2) are the arc capacity constraints, which say that the sum of all flow over an arc a must not
41   	 * exceed its capacity c_a x_a, with x being a binary or integer variable.
42   	 * c_a x_a does not need to be a single product of a capacity and an integer variable; we also accept general scalar
43   	 * products.
44   	 */
45   	
46   	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
47   	
48   	#ifndef __SCIP_SEPA_MCF_H__
49   	#define __SCIP_SEPA_MCF_H__
50   	
51   	#include "scip/def.h"
52   	#include "scip/type_retcode.h"
53   	#include "scip/type_scip.h"
54   	#ifdef __cplusplus
55   	extern "C" {
56   	#endif
57   	
58   	/** creates the mcf separator and includes it in SCIP
59   	 *
60   	 * @ingroup SeparatorIncludes
61   	 */
62   	SCIP_EXPORT
63   	SCIP_RETCODE SCIPincludeSepaMcf(
64   	   SCIP*                 scip                /**< SCIP data structure */
65   	   );
66   	
67   	#ifdef __cplusplus
68   	}
69   	#endif
70   	
71   	#endif
72