Minimizing sum of completion times on a single machine with sequence-dependent family setup times

This paper presents a branch-and-bound (B&B) algorithm for minimizing the sum of completion times in a singlemachine scheduling setting with sequence-dependent family setup times. The main feature of the B&B algorithm is a new lower bounding scheme that is based on a networkformulation of the problem. With extensive computational tests, we demonstrate that the B&B algorithm can solve problems with up to 60 jobs and 12 families, where setup and processing times are uniformly distributed in various combinations of the [1,50] and [1,100] ranges

A tabu search algorithm for scheduling a single robot in a job-shop environment

We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the travelling-salesman problem with time windows, where additionally generalized precedence constraints have to be respected. The objective is to determine a sequence of all nodes and corresponding starting times in the given time windows in such a way that all generalized precedence relations are respected and the sum of all travelling and waiting times is minimized. We present a local search algorithm for this problem where an appropriate neighborhood structure is defined using problem-specific properties. In order to make the search process more efficient, we apply some techniques which accelerate the evaluation of the solutions in the proposed neighbourhood considerably. Computational results are presented for test data arising from job-shop instances with a single transport robot

Graph search methods for non-order-preserving evaluation functions: applications to job sequencing problems

AbstractGraph search with A∗ is frequently faster than tree search. But A∗ graph search operates correctly only when the evaluation function is order-preserving. In the non-orderpreserving case, no paths can be discarded and the entire explicit graph must be stored in memory. Such situations arise in one-machine minimum penalty job sequencing problems when setup times are sequence dependent. GREC, the unlimited memory version of a memory-constrained search algorithm of the authors called MREC, has a clear advantage over A∗in that it is able to find optimal solutions to such problems. At the same time, it is as efficient as A∗ in solving graph search problems with order-preserving evaluation functions. Experimental results indicate that in the non-order-preserving case, GREC is faster than both best-first and depth-first tree search, and can solve problem instances of larger size than best-first tree search

A multistage graph-based procedure for solving a just-in-time flexible job-shop scheduling problem with machine and time-dependent processing costs

This paper deals with a new flexible job-shop scheduling problem in which the objective function to be minimised is the sum of the earliness and tardiness costs of the jobs and the costs of the operations required to perform the jobs, the latter depending on the machine and the time interval in which they are performed (as happens in many countries with the costs of electric power or those of manpower). We formalise the problem with a mathematical model and we propose a heuristic procedure that is based primarily on constructing a multistage graph and finding in it the shortest path from the source to the sink. We also describe the generation of the data-set used in an extensive computational experiment and expose and analyse the obtained results.Peer ReviewedPostprint (author's final draft

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem

In this paper, we study the job shop scheduling problem with the objective of minimizing the total weighted tardiness. We propose a hybrid shifting bottleneck - tabu search (SB-TS) algorithm by replacing the reoptimization step in the shifting bottleneck (SB) algorithm by a tabu search (TS). In terms of the shifting bottleneck heuristic, the proposed tabu search optimizes the total weighted tardiness for partial schedules in which some machines are currently assumed to have infinite capacity. In the context of tabu search, the shifting bottleneck heuristic features a long-term memory which helps to diversify the local search. We exploit this synergy to develop a state-of-the-art algorithm for the job shop total weighted tardiness problem (JS-TWT). The computational effectiveness of the algorithm is demonstrated on standard benchmark instances from the literature

Models for robust resource allocation in project scheduling.

The vast majority of resource-constrained project scheduling efforts assumes complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. In reality, however, project activities are subject to considerable uncertainty which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects the makespan of a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed robust resource allocation problem in exact and approximate formulations. The procedure relies on constraint propagation during its search. We report on computational results obtained on a set of benchmark problems.Model; Resource allocation; Scheduling;