The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the smallest number of facets of any polyhedron P such that the integer points in P coincide with X. It is an important tool ...
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ISBN:
(纸本)9783030738792;9783030738785
The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the smallest number of facets of any polyhedron P such that the integer points in P coincide with X. It is an important tool to investigate the existence of compact linear descriptions of X. In this article, we derive tight and computable upper bounds on rc g (X), a variant of rc(X) in which the polyhedra P are required to be rational, and we show that rc(X) can be computed in polynomial time if X is 2-dimensional. We also present an explicit formula for rc(X) of a specific class of sets X and present numerical experiments on the distribution of rc(X) in dimension 2.
The field of opportunistic replacement deals with the benefits of performing maintenance on equipment prior to failure in order to avoid prohibitively high costs associated with failure. Problems of a deterministic na...
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An extended variant of Location-Routing Problem namely LRP with Multi-Product and Pickup and Delivery (LRP-MPPD) is considered in this study. The proposed model deals with simultaneously selecting (locating) one or mo...
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ISBN:
(纸本)9781479903146
An extended variant of Location-Routing Problem namely LRP with Multi-Product and Pickup and Delivery (LRP-MPPD) is considered in this study. The proposed model deals with simultaneously selecting (locating) one or more facilities from a set of potential hub (locations), assigning customers to the selected hubs and defining routes of the vehicles for serving multi-product customers demand in such way that each selected hub must be visited once for delivering, though they can be visited many times for picking up. We propose a mixed integer linear programmingformulation and a heuristic approach for this problem. Since there is not any instance compatible with LRP-MPPD in the literature, we have extended known LRP instances to evaluate the performance of the proposed approach. A comparison with CPLEX shows that the proposed algorithm is a viable approach to solve small and large size LRP-MPPD instances.
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