The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in ... more The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N , where each object j, j = 1 ,..., n, is associated with a profit p j and a weight w j . The set
In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (... more In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximizing the value of the pieces cut. The TDC problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. The
In this paper we propose two exact algorithms for solving both two-staged and three staged uncons... more In this paper we propose two exact algorithms for solving both two-staged and three staged unconstrained (un)weighted cutting problems. The two-staged problem is solved by applying a dynamic programming procedure originally developed by Gilmore and Gomory [Gilmore and Gomory, Operations Research, vol. 13, pp. 94–119, 1965]. The three-staged problem is solved by using a top-down approach combined with a dynamic
The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in ... more The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N, where each object j, j = 1,...,n, is associated with a profit pj and a weight wj. The set of objects N is composed of
We study both weighted and unweighted unconstrained two-dimensional guillotine cutting problems. ... more We study both weighted and unweighted unconstrained two-dimensional guillotine cutting problems. We develop a hybrid approach which combines two heuristics from the literature. The first one (DH) uses a tree-search procedure introducing two strategies: Depth-first search and Hill-climbing. The second one (KD) is based on a series of one-dimensional Knapsack problems using Dynamic programming techniques. The DH /KD algorithm starts
Gilmore and Gomory's algorithm is one of the better actually known exact algorit... more Gilmore and Gomory's algorithm is one of the better actually known exact algorithms for solving unconstrained guillotine two-dimensional cutting problems. Herz's algorithm is more effective, but only for the unweighted case. We propose a new exact algorithm adequate for both weighted and unweighted cases, which is more powerful than both algorithms. The algorithm uses dynamic programming procedures and one-dimensional knapsack
... Viswanathan and Bagchi's exact algorithm for solving constrained two dimensional cutting... more ... Viswanathan and Bagchi's exact algorithm for solving constrained two dimensional cutting stock problems. This algorithm is one of the bestknown exact algorithms. ... These bounds are developed using onedimensional bounded knapsack problems and dynamic programming ...
The strip cutting/packing problem consists of cutting a large strip with a fixed-width and unlimi... more The strip cutting/packing problem consists of cutting a large strip with a fixed-width and unlimited length into smaller subrectangles, without violating the demand values imposed on each subrectangle. Computer science, industrial engineering, logistics, manufacturing, management, production processes are among obvious fields of applications. In this paper we propose exact approaches for solving optimally the strip cutting/packing problem. The proposed algorithms
... Mhand Hifi Corresponding Author Contact Information , E-mail The Corresponding Author , a , b... more ... Mhand Hifi Corresponding Author Contact Information , E-mail The Corresponding Author , a , b , c , Hedi M'Halla b and Slim Sadfi a , b. ... Each object type j,j=1, ,n, has a size or weight, w j , a profit, p j , and a maximum demand d j . If d j is greater than or equal to c/w j , then the ...
The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in ... more The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N , where each object j, j = 1 ,..., n, is associated with a profit p j and a weight w j . The set
In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (... more In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximizing the value of the pieces cut. The TDC problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. The
In this paper we propose two exact algorithms for solving both two-staged and three staged uncons... more In this paper we propose two exact algorithms for solving both two-staged and three staged unconstrained (un)weighted cutting problems. The two-staged problem is solved by applying a dynamic programming procedure originally developed by Gilmore and Gomory [Gilmore and Gomory, Operations Research, vol. 13, pp. 94–119, 1965]. The three-staged problem is solved by using a top-down approach combined with a dynamic
The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in ... more The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N, where each object j, j = 1,...,n, is associated with a profit pj and a weight wj. The set of objects N is composed of
We study both weighted and unweighted unconstrained two-dimensional guillotine cutting problems. ... more We study both weighted and unweighted unconstrained two-dimensional guillotine cutting problems. We develop a hybrid approach which combines two heuristics from the literature. The first one (DH) uses a tree-search procedure introducing two strategies: Depth-first search and Hill-climbing. The second one (KD) is based on a series of one-dimensional Knapsack problems using Dynamic programming techniques. The DH /KD algorithm starts
Gilmore and Gomory's algorithm is one of the better actually known exact algorit... more Gilmore and Gomory's algorithm is one of the better actually known exact algorithms for solving unconstrained guillotine two-dimensional cutting problems. Herz's algorithm is more effective, but only for the unweighted case. We propose a new exact algorithm adequate for both weighted and unweighted cases, which is more powerful than both algorithms. The algorithm uses dynamic programming procedures and one-dimensional knapsack
... Viswanathan and Bagchi's exact algorithm for solving constrained two dimensional cutting... more ... Viswanathan and Bagchi's exact algorithm for solving constrained two dimensional cutting stock problems. This algorithm is one of the bestknown exact algorithms. ... These bounds are developed using onedimensional bounded knapsack problems and dynamic programming ...
The strip cutting/packing problem consists of cutting a large strip with a fixed-width and unlimi... more The strip cutting/packing problem consists of cutting a large strip with a fixed-width and unlimited length into smaller subrectangles, without violating the demand values imposed on each subrectangle. Computer science, industrial engineering, logistics, manufacturing, management, production processes are among obvious fields of applications. In this paper we propose exact approaches for solving optimally the strip cutting/packing problem. The proposed algorithms
... Mhand Hifi Corresponding Author Contact Information , E-mail The Corresponding Author , a , b... more ... Mhand Hifi Corresponding Author Contact Information , E-mail The Corresponding Author , a , b , c , Hedi M'Halla b and Slim Sadfi a , b. ... Each object type j,j=1, ,n, has a size or weight, w j , a profit, p j , and a maximum demand d j . If d j is greater than or equal to c/w j , then the ...
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