European Scientific Journal October 2015 /SPECIAL/ edition Vol.2 ISSN: 1857 – 7881 (Print) e - ISSN 1857- 7431 53 NURSE SCHEDULING PROBLEM Erjon Duka MSc, Ing. University of Durres FASTIP Albania Abstract In this paper, what i have been discussed, is analyzing penalties and cost shifts based on several elements for nurse scheduling problem (NSP). NSP’s issue is to assign nurses to different tasks based on constraints. The problem is known to be NP-hard, in other words it does not have a solution or needs years to be solved. In this work we try to solve the problem by satisfying the constraints set, and we also include the nurse’s preference and try to balance the difficulty level of all the involved nurses. We also analyze the complexity of the problem as a function of parameters such as number of nurses, number of shifts, and optimality of the function. According to the importance in practice, many scientists have developed NSP problems in a satisfactory time limit. Keywords: NSP(Nurse Scheduling Problem), IP(Integer Programming), LIP (Linear Integer Programming), NIP(Non Linear Integer Programing), SIP(Scheduling in Integer Programming) Introduction Scheduling is always defined in the following way: Scheduling concerns in allocation of limit resources to tasks over time. It is a decision making process with the goal of optimizing one or more objectives e.g.: competition time or resource utilization. Most of works focuses in scheduling the time domain. The importance of good scheduling is strongly motivated by the present development of technology [1]. In most literature materials about scheduling problem are focused in two kinds of scheduling problems. One type is allocating resources to a program in order to optimize a given performance measure and the other type is scheduling the machine or other processors to produces a minimal time or cost. If there are tasks which can be performed by several devices, scheduling is needed in other case is not important (different devices performed exclusive tasks). A scheduling problem may not be hard to formulate but solving it is entirely another matter. Most scheduling problems are NP-hard. My problem, nurse scheduling is a NP-hard problem (Non- deterministic Polynomial-Time