Abstract
Consider a set of n advertisements (hereafter called “ads”) A ={A1,...,An} competing to be placed in a planning horizon which is divided into N time intervals called slots. An ad A i is specified by its size s i and frequency w i. The size s i represents the amount of space the ad occupies in a slot. Ad A i is said to be scheduled if exactly w i copies of A i are placed in the slots subject to the restriction that a slot contains at most one copy of an ad. In this paper, we consider two problems. The MINSPACE problem minimizes the maximum fullness among all slots in a feasible schedule where the fullness of a slot is the sum of the sizes of ads assigned to the slot. For the MAXSPACE problem, in addition, we are given a common maximum fullness S for all slots. The total size of the ads placed in a slot cannot exceed S. The objective is to find a feasible schedule \(A' \subseteq A\) of ads such that the total occupied slot space \(\sum {_{A_i \in A'} w_i s_i }\) is maximized. We examine the complexity status of both problems and provide heuristics with performance guarantees.
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Dawande, M., Kumar, S. & Sriskandarajah, C. Performance Bounds of Algorithms for Scheduling Advertisements on a Web Page. Journal of Scheduling 6, 373–394 (2003). https://doi.org/10.1023/A:1024060710627
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DOI: https://doi.org/10.1023/A:1024060710627