Shift scheduling problem (SSP) is a complex NP-hard integer programming problem, especially when many shifts and large number of workers of various ranks and multi-skills are involved. Shift scheduling also needs to comply with certain labour regulations and organisation’s rules and policies. Various models for SSP have been developed and solved. However, studies on SSP for workers of power stations or utility providers are still lacking. This paper presents the study on shift scheduling of workers at the largest power station in Malaysia. The objectives of this study are to identify main criteria and conditions of SSP at the power station, to formulate a Binary Integer Goal Programming (BGP) model for SSP that optimises workers’ day-off preference and to determine the optimal schedule for workers based on the model. The scheduling focuses on three processes which are demand modelling, shift scheduling and day-off scheduling. The study involves scheduling 43 workers in a selected department of the power station for 28 days where workers work in three shifts (morning, evening and night shifts) and have standby and rest days. The SSP-BGP model considers workers’ day-off preference as its main feature and introduces objective function that maximises the overachievement and minimises under-achievement of the day-off preference. It addresses conflicting multi-objectives in determining the optimal schedule using the goal programming approach. The model also put forward new hard and soft constraints, which reflect the nature of shifts’ requirements for these workers when determining the optimal schedule. The required data have been obtained from the power station and validation and verification of the model has been acquired with the cooperation from its personnel. The SSP-BGP model was solved using MATLAB in reasonable time. It significantly reduces the time to obtain a monthly schedule as compared to current manually done scheduling. Based on the 28-day schedule obtained, the day-off preference’s satisfaction of workers has increased by 37.21% that is from 43.02% based on the existing prepared schedule to 80.23% according to the schedule produced based on the SSP-BGP model. The model has shown good performance by not only generating optimal schedule based on the required number and composition of workers for shifts but also providing positive impacts on workers through day-off preferences’ satisfaction and the possibility of working with different groups.

Solving shift scheduling problem with days-off preference for power station workers using binary integer goal programming model

Gunumuzde bircok saglik kurulusu calistirdigi her bir personelin istek ve onerilerini dikkate alarak daha iyi bir calisma ortami saglamak istemektedir. Bu istek ve onerileri saglarken de verilen hizmetin aksatilmadan yapilmasi gerekmektedir. Bu calismada da bir hastanede calisan hemsirelerin ozel izin istekleri dikkate alinarak aylik calisma planlarinin en iyi sekilde yapilmasi icin bir hedef programlama modeli gelistirilmistir. Gelistirilen modelde hemsirelerin calisma gunleri mumkun oldugu kadar dengeli bir sekilde dagitilmaya calisilmistir. Olusturulan matematiksel model ILOG Cplex Optimization programi ile cozulmustur.

/pdf/ozel-kisitli-hemsire-cizelgeleme-problemi-hedef-programlama-2s5abw9b48.pdf

Özel kisitli hemşi̇re çi̇zelgeleme problemi̇: hedef programlama yaklaşimi

In studies of parking policy, the role of parking pricing has been addressed. Most researches have focused on the determination of a proper price for city parking spaces that are open to the public and it is now evident that price is used by authorities as a tool to manage transport demand. However, studies of parking pricing that pertain to privately-owned parking resources are few and in particular, the problem of setting a proper price for physical market parking has rarely been studied, such as a mall’s ‘dual-pricing portfolio’ decision for the simultaneous determination of a parking fee and the consumer spending required for free parking (i.e., the ‘threshold’). This is a common problem for most malls, but the different agents involved (e.g., the visitors, the mall, the marketplace and the parking lot departments) usually have diverse goals, so the decision must take account of a multiplicity of criteria and subtle relationships. In order to systematically support this type of inter-departmental decision process, a decision model that includes an analytical decision-aid process and the relevant programming models is established. A numerical example verifies the proposed model by taking the data for a mall in Taiwan and the implications, in terms of management, are given. This systematic computational model can be generalized to any type of commercial market that requires a (new) parking pricing policy.

The optimal dual-pricing policy of mall parking service

Nurse scheduling problem (NSP) is a complex optimization problem of determining schedule for nurses by considering some constraints such as legal regulations, nurses' preferences, hospital policies and requirements. It is a difficult and time consuming task to deal with large problems with many constraints. In addition to this, in real world application, a person who prepared this schedule (e.g. head nurse), may be unable to state exact aspiration levels to the goals cause of system's uncertainties. So in this study, a multi objective integer programming model for NSP is proposed and then based on this model, Chang' binary fuzzy goal programming approach [1] is applied our problem. Finally a case study which is applied to a hospital in Konya, Turkey is presented to demonstrate the efficiency of the model.

Nurse scheduling using binary fuzzy goal programming

This paper presents a novel heuristic solution to the well-known Nurse Scheduling Problem (NSP). The NSP has several constraints to satisfy: some are mandatory and specified by the hospital administration, these are known as hard constraints, while other constraints are set by the nurses themselves according to their schedule preferences, these are known as soft constraints. Our solution is based on the practice of shift-swapping performed by nurses who receive an unsatisfactory schedule. The constraints are arranged in order of importance. Our technique works on two levels; first we generate a schedule that satisfies all the hard constraints and guarantees fairness. The second level is to attempt to satisfy as many of the soft constraints as possible, by shift-swapping while maintaining the hard constraints. The technique was implemented as a simulation and demonstrated a satisfactory outcome.

/pdf/a-bi-level-heuristic-solution-for-the-nurse-scheduling-3ejaxbp5dl.pdf

A Bi-level heuristic solution for the nurse scheduling problem based on shift-swapping

The cyclic scheduling for staffs in hospitals has been widely studied but none in the literature is about the nurse scheduling problem in the outpatient departments. Considering fairness and relevant constraints in scheduling outpatient nurses, this study formulates the nurse assignment problem as a binary goal programming model. An optimized and “fair” weekly schedule satisfying the stated hospital’s policies and the outpatient nurses’ preferences is solved. A “fair” schedule is in the sense that the number of due shifts and the shift patterns are assigned as same as possible for all the full-time nurses during the weekdays. A sensitivity analysis on the number of full-time nurses is also performed to answer the question about the best utilization in scheduling nurses. This study replaces the manual-made schedule with a computerized one and provides hospital managers insights in identifying the best human-resource portfolio in outpatient nurse scheduling.

Solving an outpatient nurse scheduling problem by binary goal programming

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Solving an outpatient nurse scheduling problem by binary goal programming