SIAM Journal on Computing
Journal of Algorithms
A Tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints
Networks - Special Issue In Memory of Stefano Pallottino
Ant colony optimization for the two-dimensional loading vehicle routing problem
Computers and Operations Research
An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints
Transportation Science
Heuristics for the strip packing problem with unloading constraints
Computers and Operations Research
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In this paper we present approximation algorithms for the two-dimensional strip packing problem with unloading constraints. In this problem, we are given a strip S of width 1 and unbounded height, and n items of C different classes, each item a"i with height h(a"i), width w(a"i) and class c(a"i). As in the strip packing problem, we have to pack all items, minimizing the height used, but now we have the additional constraint that items of higher classes cannot block the way out of items of lower classes. For the case in which horizontal and vertical movements for removing the items are allowed, we design an algorithm whose asymptotic performance bound is 3. For the case in which only vertical movements are allowed, we design a bin packing based algorithm with an asymptotic approximation ratio of 5.745. Moreover, we also design approximation algorithms for restricted cases of both versions of the problem. These problems have practical applications in dealing with routing problems with loading/unloading constraints.