This book is mainly concerned with single machine bicriteria schedulingproblems . Following a theoretic framework and a literature survey, foursingle machine b icriteria scheduling problems are studied. ??The first one is a single machine scheduling problem to minimize the totalweigh ted earliness subject to minimal number of tardy jobs. First, severalpropertiesof the problem are discussed in analyzing the problem. Then, aheuristic algori thm of time complexity O(n2) and an efficient branch andbound algorit hm a re proposed. The computational experiments show that theheuristic algorithm is??effective?? in terms of quality of the solutionsin most instances while the b ranch and bound algorithm is efficient formedium sized problems. ??The second one is a single machine scheduling problem with distinct duewindowsto minimize total weighted earliness and tardiness. A mathematicalformulation i s presented and several important properties of the problemare studied. Then anoptimal timing algorithm to decide job completiontimes for a given job sequenc e is proposed. The Tabu search scheme isemployed together with the optimal timi ng algorithm to generate jobsequences and final schedules. Several experimentswere designed andcarried out to demonstrate the performance of the proposed app roach.??The third one is a single machine common due window scheduling problemin whichjob processing times are controllable with linear costs. Theobjective of the pr oblem is to find a job sequence, a processing time foreach job, and a positionof the common due window to minimize the totalcost of weighted earliness/tardin ess and processing time compression.Several properties of the problem are studi ed and a polynomial timealgorithm of time complexity ??O(n3) is developed f or solving the problem.??The last one is concerned with the computational complexity of a singlemachinescheduling problem to minimize total processing plus weighted flowcost. The com putational complexity of the problem has been open for sometwenty years. A posi tive answer to a conjecture for this problem ispresented, showing that it is NP hard at least in the ordinary sense.??Finally, some concluding remarks and future research directions relevant tothestudies are given, providing a guideline for further research.