Maximizing the reward in the relocation problem with generalized due dates

The relocation problem, based on a public housing project in Boston, USA, is a generalized resource-constrained scheduling problem in which the amount of resources (new housing units) returned by a completed job (building) is not necessarily the same as the amount of resources (original housing units) it started out with for processing. In this paper we consider a variant where several generalized due dates are specified to define the number of new housing units that should be built in the entire duration of the project. Generalized due dates are different from conventional due dates in that they are job independent and common to all jobs. In the present study each generalized due date is given to specify an expected percentage of completion of the project. Given an initial number of temporary housing units, the goal is to find a feasible reconstruction sequence that maximizes the total reward over all generalized due dates. This paper investigates the time complexity of the problem. Two upper bounds and a dominance property are proposed for the design of branch-and-bound algorithms. Computational experiments are carried out to assess the efficiency of the proposed properties. The results show that the proposed properties can significantly reduce the time required for producing an optimal schedule.

[1]  Bertrand M. T. Lin,et al.  Minimizing the weighted number of tardy jobs and maximum tardiness in relocation problem with due date constraints , 1999, Eur. J. Oper. Res..

[2]  Edward H. Kaplan.  Relocation Models for Public Housing Redevelopment Programs , 1986 .

[3]  Chelliah Sriskandarajah.  A Note on the Generalized Due Dates Scheduling Problems , 1988 .

[4]  Peter Brucker,et al.  A branch and bound algorithm for the resource-constrained project scheduling problem , 1998, Eur. J. Oper. Res..

[5]  Walter Ukovich,et al.  Economic lot scheduling on multiple production lines with resource constraints , 2003 .

[6]  Bertrand M. T. Lin,et al.  Generating the best K sequences in relocation problems , 1993 .

[7]  Amihood Amir,et al.  A fast feasibility test for relocation problems , 1988 .

[8]  Bertrand M. T. Lin,et al.  On relocation problems with multiple identical working crews , 2006, Discret. Optim..

[9]  Jean-Charles Billaut,et al.  A project scheduling problem with labour constraints and time-dependent activities requirements , 2008 .

[10]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[11]  Mohamed Haouari,et al.  A bi-objective model for robust resource-constrained project scheduling , 2005 .

[12]  Bertrand M. T. Lin,et al.  Johnson's rule, composite jobs and the relocation problem , 2009, Eur. J. Oper. Res..

[13]  Jan Karel Lenstra,et al.  Scheduling subject to resource constraints: classification and complexity , 1983, Discret. Appl. Math..

[14]  Marc E. Posner,et al.  Generating Experimental Data for Computational Testing with Machine Scheduling Applications , 2001, Oper. Res..

[15]  Daniel Oron,et al.  A note on the SPT heuristic for solving scheduling problems with generalized due dates , 2004, Comput. Oper. Res..

[16]  V. Maniezzo,et al.  An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation , 1998 .

[17]  Jinxing Xie,et al.  Polynomial algorithms for single machine scheduling problems with financial constraints , 1997, Oper. Res. Lett..

[18]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[19]  Nicholas G. Hall.  Scheduling Problems With Generalized Due Dates , 1986 .

[20]  Dorota Kuchta,et al.  A note on the paper by M. A. Al-Fawzan and M. Haouari about a bi-objective problem for robust resource-constrained project scheduling , 2007 .

[21]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[22]  Shian-Shyong Tseng,et al.  Relocation problems of maximizing new capacities under a common due date , 1992 .

[23]  Chelliah Sriskandarajah,et al.  On the Complexity of Generalized Due Date Scheduling Problems , 1991 .

[24]  Bertrand M. T. Lin,et al.  Minimizing the total weighted completion time in the relocation problem , 2010, J. Sched..

[25]  Oded Berman,et al.  OR Hits the Heights: Relocation Planning at the Orient Heights Housing Project , 1988 .

[26]  Edward H. Kaplan,et al.  Relocation problems are hard , 1988 .