ADAPTIVE SCHEDULING FOR OPERATING ROOM MANAGEMENT

The perioperative process in hospitals can be modelled as a 3-stage no-wait flow shop. The utilization of OR units and the average waiting time of patients are related to makespan and total completion time, respectively. However, minimizations of makespan and total completion time are NP-hard and NP-complete. Consequently, achieving good effectiveness and efficiency is a challenge in no-wait flow shop scheduling. The average idle time (AIT) and current and future idle time (CFI) heuristics are proposed to minimize makespan and total completion time, respectively. To improve effectiveness, current idle times and future idle times are taken into consideration and the insertion and neighborhood exchanging techniques are used. To improve efficiency, an objective increment method is introduced and the number of iterations is determined to reduce the computation times. Compared with three best-known heuristics for each objective, AIT and CFI heuristics can achieve greater effectiveness in the same computational complexity based on a variety of benchmarks. Furthermore, AIT and CFI heuristics perform better on trade-off balancing compared with other two best-known heuristics. Moreover, using the CFI heuristic for operating room (OR) scheduling, the average patient flow times are decreased by 11.2% over historical ones at University of Kentucky Health Care

Minimising total flowtime in a no-wait flow shop (NWFS) using genetic algorithms

This paper considers a no-wait flow shop scheduling (NWFS) problem, where the objective is to minimise the total flowtime. We propose a genetic algorithm (GA) that is implemented in a spreadsheet environment. The GA functions as an add-in in the spreadsheet. It is demonstrated that with proposed approach any criteria can be optimised without modifying the GA routine or spreadsheet model. Furthermore, the proposed method for solving this class of problem is general purpose, as it can be easily customised by adding or removing jobs and machines. Several benchmark problems already published in the literature are used to demonstrate the problem-solving capability of the proposed approach. Benchmark problems set ranges from small (7-jobs, 7 machines) to large (100-jobs, 10-machines). The performance of the GA is compared with different meta-heuristic techniques used in earlier literature. Experimental analysis demonstrate that solutions obtained in this research offer equal quality as compared to algorithms already developed for NWFS problems

Algorithms for Scheduling Problems

This edited book presents new results in the area of algorithm development for different types of scheduling problems. In eleven chapters, algorithms for single machine problems, flow-shop and job-shop scheduling problems (including their hybrid (flexible) variants), the resource-constrained project scheduling problem, scheduling problems in complex manufacturing systems and supply chains, and workflow scheduling problems are given. The chapters address such subjects as insertion heuristics for energy-efficient scheduling, the re-scheduling of train traffic in real time, control algorithms for short-term scheduling in manufacturing systems, bi-objective optimization of tortilla production, scheduling problems with uncertain (interval) processing times, workflow scheduling for digital signal processor (DSP) clusters, and many more

Bi-criteria Scheduling in an Assembly Flow Shop with Limited Buffer Storage and Shift Production

In this research, the comparative performance of permutation and non-permutation schedules is investigated in an assembly flow shop (AFS) with shift production, where a limited buffer storage is available between two machines. Most of the traditional scheduling problems consider continuous production, i.e., production occurs for 24 hours (3 * 8-hour shifts) each day, seven days a week. However, some companies operate only one or two shifts each day, which creates a limited availability constraint on the machines. This causes a discontinuity in production between end and start of two successive production days. To mimic real-life industry practice, dynamic job release and dynamic machine availability times have been considered. Each job considered in a problem can have different weight assigned based on customers’ preferences. The setup times between jobs are assumed to be machine- and sequence-dependent. However, at the start of each production day, setup times are not sequence-dependent but depend on machine startup times such as preheating time, pressure build up, etc. The objective of the problem is to minimize the linear combination of total setup time and weighted tardiness. The minimization of total setup time represents producer’s interest whereas the minimization of weighted tardiness represents customers’ interest. Since these two objectives are not evaluated on a commensurate basis, a normalization factor is used. The problem is formulated as a mixed-integer linear programming (MILP) model, MILP-1 for permutation schedules and MILP-2 for non-permutation schedules. The MILP models for small-size problem instances are solved to optimality using CPLEX. However, the problem is shown to be NP-hard. As a result, it is not possible to find an optimal solution within a reasonable time, as the problem size increases. Hence, a meta-heuristic search algorithm based on short-term Tabu Search (TS) and Tabu Search/Path-Relinking (TS/PR) are developed. TS represents a local search algorithm, whereas TS/PR represents a hybridization of local search enhanced with population-based search algorithm. Two algorithms each, are developed for both, permutation (PN) and non-permutation (NPN) sequences. One of the algorithms is based on short term TS and the other is based on TS/PR. The developed heuristics are tested on sixteen small-size problems and their solution quality are compared with the optimal solution obtained from CPLEX. The evaluations show that the developed heuristics obtain good quality solutions within much less computational time. For PN sequence, the best algorithm obtained an average deviation of 0.49% compared with the optimal solution and for NPN sequence, the deviation is 0.13%. In addition, a slight improvement of 2.68% was obtained by adopting an NPN sequence over PN sequence for these problem instances. A statistical designed experiment is conducted to evaluate the difference in performance of the developed heuristics, and permutation and non-permutation schedules. The results show that the TS/PR algorithms outperform short-term TS, in the case of both PN and NPN sequences. The comparison between the solutions from the best PN algorithm and the best NPN algorithm shows that an average improvement of 1.64% is obtained by implementing an NPN sequence over PN sequence. The statistical analysis shows that the improvement offered by NPN sequence is statistically significant for problems with large number of product types and small number of jobs in each product. In addition, it is also shown that the NPN sequence performs better for non-continuous production as compared to continuous production. The efficiency of the algorithms was analyzed using the computational time required by the algorithms. The results show that PN algorithms require a significantly less computational time as compared to NPN algorithms. Hence, it is recommended that NPN sequences be considered only for the problems with large number of product types and small number of jobs in each product. For other problems, only PN sequence should be considered. TS/PR algorithm is recommended for both, PN and NPN sequences

Performance analysis and scheduling strategies for ambulatory surgical facilities

Ambulatory surgery is a procedure that does not require an overnight hospital stay and is cost effective and efficient. The goal of this research is to develop an ASF operational model which allows management to make key decisions. This research develops and utilizes the simulation software ARENA based model to accommodate: (a) Time related uncertainties – Three system uncertainties characterize the problem (ii) Surgery time variance (ii) Physician arrival delay and (iii) Patient arrival delay; (b) Resource Capture Complexities – Patient flows vary significantly and capture/utilize both staffing and/or physical resources at different points and varying levels; and (c) Processing Time Differences – Patient care activities and surgical operation times vary by type and have a high level of variance between patient acuity within the same surgery type. A multi-dimensional ASF non-clinical performance objective is formulated and includes: (i) Fixed Labor Costs – regular time staffing costs for two nurse groups and medical/tech assistants, (i i) Overtime Labor Costs – staffing costs beyond the regular schedule, (i i i) Patient Delay Penalty – Imputed costs of waiting time experienced patients, and (iv) Physician Delay Penalty – Imputed costs of physicians having to delay surgical procedures due to ASF causes (limited staffing, patient delays, blocked OR, etc.). Three ASF decision problems are studied: (i) Optimize Staffing Resources Levels - Variations in staffing levels though are inversely related to patient waiting times and physician delays. The decision variable is the number of staff for three resource groups, for a given physician assignment and surgery profile. The results show that the decision space is convex, but decision robustness varies by problem type. For the problems studied the optimal levels provided 9% to 28% improvements relative to the baseline staffing level. The convergence rate is highest for less than optimal levels of Nurse-A. The problem is thus amenable to a gradient based search. (ii) Physician Block Assignment - The decision variables are the block assignments and the patient arrivals by type in each block. Five block assignment heuristics are developed and evaluated. Heuristic #4 which utilizes robust activity estimates (75% likelihood) and generates an asymmetrical resource utilization schedule, is found to be statistically better or equivalent to all other heuristics for 9 out of the 10 problems and (iii) Patient Arrival Schedule – Three decision variables in the patient arrival control (a) Arrival time of first patient in a block (b) The distribution and sequence of patients for each surgery type within the assigned windows and (c) The inter arrival time between patients, which could be constant or varying. Seven scheduling heuristics were developed and tested. Two heuristics one based on Palmers Rule and the other based on the SPT (Shortest Processing Time) Rule gave very strong results

Scheduling based on earliness and tardiness criteria in assembly job shops

In this research, the following four scheduling problems have been studied: (1) single machine problem with earliness cost minimization, (2) single machine problem with the sum of the weighted earliness and weighted tardiness cost minimization, (3) assembly job shop problem with earliness cost minimization, and (4) assembly job shop problem with the sum of weighted earliness and weighted tardiness cost minimization. Four mathematical models based on these four scheduling problems were developed in an effort to obtain optimal solutions. Six heuristic algorithms have been developed to solve the problems. The performances of the heuristic algorithms were demonstrated on some sample test problems. Quality of solutions and CPU time of solutions were the factors of interest. Several properties of optimal solutions for the single machine scheduling problem with the objective of minimizing the weighted earliness penalty have been identified in the research. Algorithms I, III, V, and VI were developed based on these identified properties while the algorithms II and IV were developed based on the tabu search concept;Algorithms I and II were developed to solve the first case (1) problem. The results indicate that these two algorithms are able to produce solutions close to optimal in small size problems. The results also show that algorithm I is relatively better than algorithm II in large size problem;Algorithms III and IV were developed to solve the second case (2) problem. Both algorithms obtained a small average deviation solutions (i.e., less than 2%) from optimal in small size test problems. For all problems tested, the algorithm IV is the best algorithm for solving the earliness/tardiness problems compared to algorithm III and the Ow & Morton algorithm;Algorithm V was developed to solve the third case (3) problem. It obtained an average deviation solutions less than 1% from the optimal. Algorithm VI was developed to solve the fourth case (4) problem. Algorithm VI obtained an average deviation solutions of 2.53% from the optimal;In testing all developed heuristics the computational requirements for solving the problems are less than 2 second in all test problems

New Solution Approaches for Scheduling Problems in Production and Logistics

The current cumulative PhD thesis consists of six papers published in/submitted to scientific journals. The focus of the thesis is to develop new solution approaches for scheduling problems encountering in manufacturing as well as in logistics. The thesis is divided into two parts: “ma-chine scheduling in production” and “scheduling problems in logistics” each of them consisting three papers. To have most comprehensive overview of the topic of machine scheduling, the first part of the thesis starts with two systematic review papers, which were conducted on tertiary level (i.e., re-viewing literature reviews). Both of these papers analyze a sample of around 130 literature re-views on machine scheduling problems. The first paper use a subjective quantitative approach to evaluate the sample, while the second papers uses content analysis which is an objective quanti-tative approach to extract meaningful information from massive data. Based on the analysis, main attributes of scheduling problems in production are identified and are classified into sever-al categories. Although the focus of both these papers are set to review scheduling problems in manufacturing, the results are not restricted to machine scheduling problem and the results can be extended to the second part of the thesis. General drawbacks of literature reviews are identi-fied and several suggestions for future researches are also provided in both papers. The third paper in the first part of the thesis presents the results of 105 new heuristic algorithms developed to minimize total flow time of a set of jobs in a flowshop manufacturing environ-ment. The computational experiments confirm that the best heuristic proposed in this paper im-proves the average error of best existing algorithm by around 25 percent. The first paper in second part is focused on minimizing number of electric tow-trains responsi-ble to deliver spare parts from warehouse to the production lines. Together with minimizing number of these electric vehicles the paper is also focused to maximize the work load balance among the drivers of the vehicles. For this problem, after analyzing the complexity of the prob-lem, an opening heuristic, a mixed integer linear programing (MILP) model and a taboo-search neighborhood search approach are proposed. Several managerial insights, such as the effect of battery capacity on the number of required vehicles, are also discussed. The second paper of the second part addresses the problem of preparing unit loaded devices (ULDs) at air cargos to be loaded latter on in planes. The objective of this problem is to mini-mize number of workers required in a way that all existing flight departure times are met and number of available places for building ULDs is not violated. For this problem, first, a MILP model is proposed and then it is boosted with a couple of heuristics which enabled the model to find near optimum solutions in a matter of 10 seconds. The paper also investigates the inherent tradeoff between labor and space utilization as well as the uncertainty about the volume of cargo to be processed. The last paper of the second part proposes an integrated model to improve both ergonomic and economic performance of manual order picking process by rotating pallets in the warehouse. For the problem under consideration in this paper, we first present and MILP model and then pro-pose a neighborhood search based on simulated annealing. The results of numerical experiment indicate that selectively rotating pallets may reduce both order picking time as well as the load on order picker, which leads to a quicker and less risky order picking process