Two-Agent Advertisement Scheduling on Physical Books to Maximize the Total Profit

Most of us may have had the experience of forgetting some term from a physical book when the term appears in neither the table of contents nor the index. Unfortunately, we must search for it page by page. In one edition of the popular physical book "Harry Potter and the Sorcerer's Stone", for example, the term "dragon's blood" only appears on pages 81 and 175, so browsing through the whole book to find it. would be inevitable. In this study, a mechanism is provided to carry out an online search on physical books. To financially support this mechanism, we can put online advertisements with different offers on these physical books. An advertisement scheduling problem (ASP) is therefore formulated to maximize the total profit. To obtain the optimal schedules, we propose a branch-and-bound algorithm equipped with an upper bound. Experimental results show that the proposed upper bound performs well and completes the search in only 4% of the execution time of an ordinary branch-and-bound algorithm.