Adaptation of shift sequence based method for high number in shifts rostering problem for health care workers

LTStraipsnyje nagrinėjamas pamainų sekų metodo efektyvumas sudarant didelių ligoninių gydytojų darbo tvarkaraščius, kai yra daug (iki 15) pamainų. Nagrinėjamas pavyzdys, kai tvarkaraštis sudaromas vienam kalendoriniam mėnesiui 27-iems gydytojams. Dėl skirtingo gydytojų darbo krūvio (dalis gydytojų dirba visu etatu, dalis – puse etato, trečdalis – ketvirčiu etato) susidaro 15 skirtingų pamainų. Sudarant tvarkaraštį susiduriama su daugiau nei 20 ribojimų. Ankstesni tyrimai parodė, kad šis metodas gana efektyvus sudarant darbo tvarkaraštį, kai pamainų skaičius nedidelis (iki 4 pamainų). Sprendžiant gydytojų tvarkaraščių sudarymo uždavinį pastebėta, kad didėjant pamainų skaičiui, pailgėja tvarkaraščio sudarymo laikas. Kai yra keturios pamainos šiuo metodu tvarkaraštis gali būti parengiamas per 20 sekundžių (pasirinkus 1 iteraciją). Kai pamainų skaičius išauga iki 15, tvarkaraščio sudarymo trukmė yra 15 minučių (pasirinkus 1 iteraciją). Straipsnyje pasiūlyta modifikacija leidžia sudaryti tvarkaraštį per apytikriai 45 kartus trumpesnį laiką. Pasiūlytoje modifikacijoje pamainos skirstomos į keturias grupes: rytinės pamainos, dieninės pamainos, naktinės pamainos ir budėjimo pamainos. Pamainų sekos sudaromos naudojant ne pačias pamainas, o jų grupes. Taip sumažinamas tinkamų pamainų sekų skaičius (nuo 260 000 pamainų sekų iki 64 pamainų sekų). Remiantis gautomis pamainų sekomis sudaromas kiekvieno gydytojo darbo tvarkaraštis vietoje pamainų sekų grupės įrašant konkrečią pamainą. Jei apskaičiuojamas darbo krūvis neatitinka darbo sutartyje apibrėžto darbo krūvio, pamaina, atsižvelgiant į tai, ar gautas darbo krūvis yra mažesnis, ar didesnis už apibrėžtą darbo sutartyje, keičiama į kitą ilgesnę arba trumpesnę tai pačiai grupei priklausančią pamainą. [...].

ENPurpose is to investigate a shift sequence-based approach efficiency then problem consisting of a high number of shifts. Research objectives: Solve health care workers rostering problem using a shift sequence based method. Measure its efficiency then number of shifts increases. rostering problems are highly constrained. Constraints are classified to soft and hard constraints. Soft and hard constraints of the problem are additionally classified to: sequence constraints, schedule constraints and roster constraints. Sequence constraints are considered when constructing shift sequences. Schedule constraints are considered when constructing a schedule. Roster constraints are applied, then constructing overall solution, i.e. combining all schedules. Shift sequence based approach consists of two stages: shift sequences construction, the construction of schedules. In the shift sequences construction stage, the shift sequences are constructed for each set of health care workers of different skill, considering sequence constraints. Shifts sequences are ranked by their penalties for easier retrieval in later stage. In schedules construction stage, schedules for each health care worker are constructed iteratively, using the shift sequences produced in stage 1. Shift sequence based method is an adaptive iterative method where health care workers who received the highest schedule penalties in the last iteration are scheduled first at the current iteration. During the roster construction, and after a schedule has been generated for the current health care worker, an improvement method based on an efficient greedy local search is carried out on the partial roster.It simply swaps any pair of shifts between two health care workers in the (partial) roster, as long as the swaps satisfy hard constraints and decrease the roster penalty. Using shift sequence method for solving health care workers rostering problem is inefficient, because of large amount of shifts sequences (feasible shifts sequences are approximately 260 thousands). In order to speed up roster construction process shifts are grouped to four groups: morning shifts, day shifts, night shifts and duty shifts. There are only 64 feasible shifts sequences, in this case. After roster construction shift groups are replaced with the one of shift belonging to that group of shifts. When all shifts are added to roster, computation of workload for each schedule is performed. If computed workload is equal to the one defined in working contract, then this schedule is complete, else begin shifts revision process. During revision process those schedules are considered which do not meet work contract requirements. If computed workload is larger than the one defined in working contract, each shift is replaced with the shift, if it’s possible, with lesser duration time. If computed workload is lesser than the one defined in working contract, each shift is replaced with the shift, if it’s possible, with larger duration time. This process continues while schedule does not meet workload requirement defined in working contract or no further improvement can be made. Problem dimension: 27 health care workers, 15 shifts, over 20 soft constraints, rostering period - one calendar month. […].