18 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / JANUARY/FEBRUARY 2001 OPTIMIZING RESOURCE UTILIZATION FOR REPETITIVE CONSTRUCTION PROJECTS By Khaled El-Rayes, 1 Member, ASCE, and Osama Moselhi, 2 Fellow, ASCE ABSTRACT: Optimizing resource utilization can lead to significant reduction in the duration and cost of re- petitive construction projects such as highways, high-rise buildings, and housing projects. This can be achieved by identifying an optimum crew size and interruption strategy for each activity in the project. Available dynamic programming formulations can be applied to provide solutions for this optimization problem; however, their application is limited, as they require planners to specify an arbitrary and an unbounded set of interruption options prior to scheduling. Such a requirement is not practical and may render the optimization problem infeasible. To circumvent the limitations of available formulations, this paper presents an automated and practical optimization model. The model utilizes dynamic programming formulation and incorporates a scheduling al- gorithm and an interruption algorithm so as to automate the generation of interruptions during scheduling. This transforms the consideration of interruption options, in optimizing resource utilization, from an unbounded and impractical problem to a bounded and feasible one. A numerical example from the literature is analyzed to illustrate the use and capabilities of the model. INTRODUCTION Repetitive construction is commonly found in high-rise buildings, housing projects, highways, pipeline networks, and bridges. The application of traditional scheduling techniques (e.g., bar charts, the critical path method, PDM, or the program evaluation and review technique) to repetitive construction projects has been criticized in the literature for their inability to maintain crew work continuity (Birrell 1980; Selinger 1980; Kavanagh 1985; Reda 1990; Russell and Wong 1993). To maintain crew work continuity during scheduling, a number of scheduling techniques have been developed for repetitive construction projects (Selinger 1980; Johnston 1981; Arditi and Albulak 1986; Chrzanowski and Johnston 1986; Russell and Caselton 1988; Al Sarraj 1990; El-Rayes and Moselhi 1998). Maintaining crew work continuity leads to maximizing the learning curve effect and minimizing the idle time of each crew (Ashley 1980; Birrell 1980). Despite the apparent ad- vantages of maintaining crew work continuity, its strict appli- cation may lead to a longer overall project duration. Selinger (1980) suggested that the violation of the crew work continuity constraint, by allowing work interruptions, might reduce the overall project duration. A number of dynamic programming formulations have been developed to optimize the scheduling of this class of projects, either focusing on minimizing project cost (Moselhi and El- Rayes 1993; Eldin and Senouci 1994) or minimizing project duration (Selinger 1980; Russell and Caselton 1988). These formulations are either one-state variable (Selinger 1980; Mo- selhi and El-Rayes 1993) or two-state variable (Russell and Caselton 1988; Eldin and Senouci 1994), aiming to determine the optimum crew formation or the optimum crew formation and the optimum interruption vector, respectively. Despite the apparent advantages of available two-state variable formula- tions in minimizing the duration of repetitive construction projects, they require construction planners to arbitrarily spec- ify, prior to scheduling, a set of interruption vectors for each 1 Asst. Prof., Dept. of Civ. and Envir. Engrg., Univ. of Illinois at Ur- bana-Champaign, Urbana, IL 61801. 2 Prof. and Chair, Dept. of Build., Civ., and Envir. Engrg., Concordia Univ., Montreal, PQ, Canada H3G 1M8. Note. Discussion open until July 1, 2001. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on September 1, 1999. This paper is part of the Journal of Construction Engineering and Management, Vol. 127, No. 1, January/February, 2001. ASCE, ISSN 0733-9634/01/0001-0018– 0027/$8.00 + $.50 per page. Paper No. 21784. crew formation in the project. As such, these formulations suf- fer from the following three main limitations: 1. It is impractical to require construction planners to iden- tify a set of possible interruption vectors for each crew formation of each activity in the project prior to sched- uling. 2. The number of feasible interruption vectors that can be considered for a repetitive activity can be unbounded if there is no upper limit on the number of crew interrup- tion days. Even if such a limit (I max ) is arbitrarily estab- lished, the number of interruption vectors that can i (NIV ) n be considered for a crew formation n associated with repetitive activity i increases exponentially with the in- crease of the number of repetitive units (J). The appli- cation of an I max value means that a crew can be inter- rupted by a value that ranges from 0 to I max days before the start of the activity in a repetitive unit j. For each repetitive unit j, this leads to a total number of possible interruptions of I max + 1, assuming that interruptions can vary from 0 to I max by an increment of one day. Accord- ingly, the total number of all possible combinations of interruption vectors that can be considered for i (NIV ) n crew formation n of activity i repeated in J repetitive units can be identified as follows: i J-1 NIV =(I + 1) (1) n max For example, an upper limit of six interruption days (I max = 6) imposed on an activity that is repeated in 15 units (J = 15) can result in approximately 680 billion possible combinations of interruption vectors [i.e., =(I max + i NIV n 1) J-1 =7 14 = 680 billion]. These 680 billion vectors need to be analyzed as a second state variable in the dynamic programming formulation for each crew formation of each activity in the project. This clearly illustrates that even imposing a reasonable value for I max (e.g., six days) still renders the optimization problem practically infea- sible. 3. The arbitrary assignment of interruption vectors prior to scheduling does not guarantee an optimum solution. This paper presents an automated and practical model for optimizing resource utilization in repetitive construction that circumvents the above three limitations. The model incorpo- rates a scheduling algorithm and an interruption algorithm.