In this paper, we propose to solve the circular packing problem (CPP) whose objective is to pack n different circles C(i) of known radius r(i) , i = 1, …, n into the smallest containing circle C. The objective is to determine the radius r of C as well as the coordinates (x(i) , y(i)) of the...

In this paper, we propose an optimal algorithm for the Multiple-choice Multidimensional Knapsack Problem MMKP. The main principle of the approach is twofold : (i) to generate an initial solution, and (ii) at different levels of the tree search to determine a new upper bound used with a...

We study the two-staged fixed orientation constrained two-dimensional two-staged cutting stock problem. We solve the problem using several approximate algorithms, that are mainly based upon a strip generation procedure (HESGA) already developed in ([13)]. We evaluate the performance of these...

This paper solves the binary single-constrained Knapsack Problem (KP) and undertakes a sensitivity analysis of its optimum solution. Given a knapsack of capacity c, and a set of n items, with each item j, j = 1,?,n, characterised by a weight wj and a profit pj, the binary single-constrained KP...

This paper solves the binary single-constrained Knapsack Problem (KP) and undertakes a sensitivity analysis of its optimum solution. Given a knapsack of capacity c, and a set of n items, with each item j, j = 1,…,n, characterised by a weight wj and a profit pj, the binary...

In this paper, we study the sensitivity of the optimum of a max-min combinatorial optimization problem, namely the Knapsack Sharing Problem (KSP), to the perturbation of the profit of an arbitrary item. We mainly establish the interval limits of each perturbed item by applying a reduction of the...