On approximating the Incremental Knapsack Problem
نویسندگان
چکیده
منابع مشابه
Approximating the Incremental Knapsack Problem
We consider the 0–1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time period depends on its profit as well as on a time factor which reflects the importance of the period in the objective function. The problem calls for maximiz...
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Given a list of d-dimensional cuboid items with associated profits, the orthogonal knapsack problem asks for a packing of a selection with maximal profit into the unit cube. We restrict the items to hypercube shapes and derive a ( 5 4 + )-approximation for the twodimensional case. In a second step we generalize our result to a ( 2 +1 2d + )approximation for d-dimensional packing.
متن کاملApproximating the solution of a dynamic , stochastic multiple knapsack problem
We model an environment where orders arrive probabilistically over time, with their revenues and capacity requirements becoming known upon arrival. The decision is whether to accept an order, receiving a reward and reserving capacity, or reject an order, freeing capacity for possible future arrivals. We model the dynamic, stochastic multiple knapsack problem (DSMKP) with stochastic dynamic prog...
متن کاملApproximation Algorithms for the Incremental Knapsack Problem via Disjunctive Programming
In the incremental knapsack problem (IK), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of T periods and the capacity of the knapsack is Bt in period t for t = 1, . . . , T . We are also given a set S of N items to be placed in the knapsack. Item i has a value of vi and a weight of wi that is independent of the time period. At any time period...
متن کاملOn the Robust Knapsack Problem
We consider an uncertain variant of the knapsack problem that arises when the exact weight of each item is not exactly known in advance but belongs to a given interval, and the number of items whose weight differs from the nominal value is bounded by a constant. We analyze the worsening of the optimal solution value with respect to the classical problem, and exactly determine its worst-case per...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2019
ISSN: 0166-218X
DOI: 10.1016/j.dam.2019.02.016