AN EMPIRICAL STUDY OF THREE PACKING HEURISTICS FOR BINS WITH ADJUSTABLE CAPACITY – AN APPLICATION TO OPERATING ROOM SCHEDULING Karolina Glowacka, Youxu C. Tjader The Joseph M. Katz Graduate School of Business, University of Pittsburgh, Pittsburgh PA 15260, e-mail: yotst1@katz.pitt.edu , kglowacka@katz.pitt.edu , phone: 412-648-1889 ABSTRACT Using simulation, we compare three offline packing heuristics for adjustable-size bins, a problem derived from operating room scheduling, on 500 days of generated data using different cost structures. Unlike classical bin-packing studies, we found that next-fit-decreasing is the best performing method. Subject Areas: Simulation, Bin Packing, OR and Scheduling. 1. INTRODUCTION The classical bin-packing problem (CBPP) has been investigated extensively in the literature and is NP-hard [1]. In this paper we consider a modified version of the classic one-dimensional bin- packing problem. The objective of the CBPP is to fit a set of n items into the minimum number of identical bins. Since the problem was found to be NP-hard, several efficient heuristics and approximation algorithms have been developed to deal with it. In this paper we focus on variations of three offline heuristics: First Fit Decreasing (FFD), Next Fit Decreasing (NFD), and Best Fit Decreasing (BFD). In the offline versions, we know all the items in advance, that is, we know the number of items to be packed together with their capacity requirements. In the online versions, items arrive in some order and must be assigned to a bin as soon as they arrive [2]. One of the applications of the modified bin-packing problem, which we present in this paper, is operating room (OR) scheduling. ORs can be represented as bins and surgeries to be performed as items that need to be packed. We define a base capacity of a bin by the number of regular working hours C R . However, we can extend any bin’s capacity by adding overtime at an additional cost. Naturally, the amount of overtime we add depends on its cost, so we need to ask: is the cost of added overtime greater than the cost of opening another bin? This leads to the modified bin-packing problem [3]. Our analysis shows that, of the three examined heuristics, Next Fit Decreasing is the preferred method for this particular application. In this study we use simulation to evaluate the performance of each heuristic. Experimental methods, such as simulation, can be used to provide insights on the performance of a particular algorithm in practice. Worst-case and average-case analyses provide us with asymptotic results and usually can only be applied to simple algorithms. Simulation, on the other hand, can describe and replicate very complex processes and, at the same time, gives the researcher complete control over the experimental environment [4], allowing us to explore many possible what-if scenarios. This gives us an opportunity to examine the behavior of an algorithm for a very particular problem instance. Good descriptions of experimental methods for bin-packing can be found in [5] and [4]. 4261