Due　to　the　fact　that,　some　fast　food　restaurants　which　provide　take　away　service　may　refuse　some　delivery　orders　when　they　receive　requests　from　customers　so　as　to　improve　efficiency　and　cut　cost.　This　results　in　some　forms　of　penalty,　like　reputation　damage,　etc.　To　achieve　the　goal　of　minimizing　the　whole　time　of　serving　plus　the　total　penalties　of　all　rejected　requests,　we　propose　the　real-time　version　of　online　travelling　salesman　problem　(OL-TSP)　with　rejection　options　and　advanced　information.　We　proposed　lower　bounds　and　algorithms　on　the　non-negative　real　line　and　the　real　line.　These　conclusions　are　more　general　than　the　results　in　the　real-time　version　of　online　TSP　with　rejection　options.　©　2016,　Systems　Engineering　Society　of　China.　All　right　reserved.