Minimizing total completion time on a single machine with step improving jobs

Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming (MIP) model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions

2-Player Nash and Nonsymmetric Bargaining Games: Algorithms and Structural Properties

The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear constraints, admits a rational solution and such a solution can be found in polynomial time using only an LP solver. If in addition, the game is succinct, i.e., the coefficients in its convex program are ``small'', then its solution can be found in strongly polynomial time. We also give a non-succinct linear game whose solution can be found in strongly polynomial time

The impact of using combinatorial optimisation for static caching of posting lists

Abstract. Caching posting lists can reduce the amount of disk I/O required to evaluate a query. Current methods use optimisation proce-dures for maximising the cache hit ratio. A recent method selects posting lists for static caching in a greedy manner and obtains higher hit rates than standard cache eviction policies such as LRU and LFU. However, a greedy method does not formally guarantee an optimal solution. We investigate whether the use of methods guaranteed, in theory, to find an approximately optimal solution would yield higher hit rates. Thus, we cast the selection of posting lists for caching as an integer linear pro-gramming problem and perform a series of experiments using heuristics from combinatorial optimisation (CCO) to find optimal solutions. Using simulated query logs we find that CCO yields comparable results to a greedy baseline using cache sizes between 200 and 1000 MB, with modest improvements for queries of length two to three

Register Allocation Via Coloring of Chordal Graphs

Abstract. We present a simple algorithm for register allocation which is competitive with the iterated register coalescing algorithm of George and Appel. We base our algorithm on the observation that 95 % of the methods in the Java 1.5 library have chordal interference graphs when compiled with the JoeQ compiler. A greedy algorithm can optimally color a chordal graph in time linear in the number of edges, and we can eas-ily add powerful heuristics for spilling and coalescing. Our experiments show that the new algorithm produces better results than iterated regis-ter coalescing for settings with few registers and comparable results for settings with many registers.

Solving the Asymmetric Travelling Salesman Problem with Time Windows by branch-and-cut

Many optimization problems have several equivalent mathematical models. It is often not apparent which of these models is most suitable for practical computation, in particular, when a certain application with a specific range of instance sizes is in focus. Our paper addresses the Asymmetric Travelling Salesman Problem with time windows (ATSP-TW) from such a point of view. The real-world application we aim at is the control of a stacker crane in a warehouse. We have implemented codes based on three alternative integer programming formulations of the ATSP-TW and more than ten heuristics. Computational results for real-world instances with up to 233 nodes are reported, showing that a new model presented in a companion paper outperforms the other two models we considered - at least for our special application - and that the heuristics provide acceptable solutions