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4    	/*         SCIP --- Solving Constraint Integer Programs                      */
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24   	
25   	/**@file   benderscut_nogood.h
26   	 * @ingroup BENDERSCUTS
27   	 * @brief  Generates a no-good cut for solutions that are integer infeasible
28   	 * @author Stephen J. Maher
29   	 *
30   	 * The no-good cut is generated for the Benders' decomposition master problem if an integer solution is identified as
31   	 * infeasible in at least one CIP subproblems. The no-good cut is required, because the classical Benders' decomposition
32   	 * feasibility cuts (see benderscut_feas.c) will only cut off the solution \f$\bar{x}\f$ if the LP relaxation of the CIP
33   	 * is infeasible.
34   	 *
35   	 * Consider a Benders' decomposition subproblem that is a CIP and it infeasible. Let \f$S_{r}\f$ be the set of indices
36   	 * for master problem variables that are 1 in \f$\bar{x}\f$. The no-good cut is given by
37   	 *
38   	 * \f[
39   	 * 1 \leq \sum_{i \in S_{r}}(1 - x_{i}) + \sum_{i \notin S_{r}}x_{i}
40   	 * \f]
41   	 */
42   	
43   	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
44   	
45   	#ifndef __SCIP_BENDERSCUT_NOGOOD_H__
46   	#define __SCIP_BENDERSCUT_NOGOOD_H__
47   	
48   	
49   	#include "scip/def.h"
50   	#include "scip/type_benders.h"
51   	#include "scip/type_retcode.h"
52   	#include "scip/type_scip.h"
53   	
54   	#ifdef __cplusplus
55   	extern "C" {
56   	#endif
57   	
58   	/** creates the no good Benders' decomposition cut and includes it in SCIP
59   	 *
60   	 *  @ingroup BenderscutIncludes
61   	 */
62   	SCIP_EXPORT
63   	SCIP_RETCODE SCIPincludeBenderscutNogood(
64   	   SCIP*                 scip,               /**< SCIP data structure */
65   	   SCIP_BENDERS*         benders             /**< Benders' decomposition */
66   	   );
67   	
68   	#ifdef __cplusplus
69   	}
70   	#endif
71   	
72   	#endif
73