A Simulation and Optimization Approach to Scheduling Chemotherapy Appointments

Transcription

1 A Simulation and Optimization Approach to Scheduling Chemotherapy Appointments Michelle Alvarado, Tanisha Cotton, Lewis Ntaimo Texas A&M University College Station, Texas ABSTRACT Although there is no guaranteed cure for cancer, chemotherapy is a commonly used treatment method. Cancer costs in the U.S. exceeded $124 billion in 2010 and are expected to increase 27% by 2020 while the demand for oncology services is projected to increase by 48% between 2005 and Therefore, it is increasingly important for chemotherapy appointments to be scheduled efficiently. Oncologists prescribe a unique treatment regimen, or series of chemotherapy appointments, to each cancer patient based on the individual s health. These appointments must be scheduled as close to the prescribed dates as possible in order to maximize the treatment s benefit to the patient. A scheduling decision allocates a specific date, time, and set of clinic resources to each appointment based on the treatment regimen. The scheduling process is challenging because patients often experience adverse reactions to the chemotherapy drugs that cause uncertainty in appointment durations and the demand for nursing resources. Stochastic programming, a branch of optimization that incorporates uncertainty through stochastic parameters, is one tool to address this scheduling problem. However, optimization models alone cannot accurately model the oncology clinic s complex problem setting. On the other hand, simulation models are excellent tools to imitate the reality of the oncology clinic and serve as a useful evaluation tool, but simulation alone may not adequately capture the problem s decision-making aspects. Therefore, we propose a simulation and optimization methodology that uses an optimization model and a simulation model to schedule each appointment in a patient s treatment regimen. The simulation and optimization methodology allows for evaluating resource requirements and scheduling strategies to determine the best scheduling and staffing policies for a clinic. We evaluate this methodology using patient data from a Texas oncology clinic. The simulation and optimization methodology is also discussed for the military land move problem. ABOUT THE AUTHORS Michelle Alvarado is a Ph.D. student in Industrial and Systems Engineering (ISEN) at Texas A&M University (TAMU), College Station, Texas, USA. She obtained her B.S. in industrial engineering in 2008 from the University of Alabama and her M.E. in industrial engineering in 2010 from TAMU. Michelle's research interests include riskaverse stochastic programming and simulation with applications in chemotherapy scheduling and wildfire response planning. Michelle was the 2012 Rear Admiral Fred Lewis Postgraduate I/ITSEC Doctoral Candidate Scholarship winner. She serves as the 2013 president of INFORMS-SC at TAMU and will graduate in May Tanisha Cotton is a 2013 graduate of the ISEN Department at TAMU. In 2005 she completed the Atlanta University Center Dual Degree Engineering Program with a B.S. degree in mathematics from Spelman College and industrial engineering from the Georgia Institute of Technology. She earned her M.E. in industrial engineering in 2008 from TAMU. Dr. Cotton's research interests are in stochastic programming, discrete event simulation, and systems modeling of healthcare and homeland security applications. Dr. Cotton is a former Graduate Diversity Fellow, Graduate Assistance in Areas of National Need Fellow, and an Alfred P. Sloan Scholar. Lewis Ntaimo is an associate professor of ISEN at TAMU. He received his Ph.D. in systems and industrial engineering from the University of Arizona (2004), M.S. in mining and geological engineering (2000) and B.S. in mining engineering (1998), both from the University of Arizona. Dr. Ntaimo's research interests include stochastic programming, systems modeling and engineering processes, and discrete event modeling and simulation. Applications of interest include healthcare, wildfire planning, wind energy, and air traffic flow management Paper No Page 1 of 11

2 A Simulation and Optimization Approach to Scheduling Chemotherapy Appointments Michelle Alvarado, Tanisha Cotton, Lewis Ntaimo Texas A&M University College Station, Texas INTRODUCTION Operational managers make important scheduling decisions on a daily basis. Regardless of the industry (e.g., healthcare, military, etc.), the problems faced often share similar characteristics. This paper looks at scheduling decisions that involve a complex problem setting and a high level of interaction between various entities. The decisions are based on multiple and sometimes competing objectives subject to several constraints or limitations on the scheduling decisions. Finally, some of the problem parameters (e.g., task time) may be uncertain, which complicates the problem as the managers must consider several outcomes or scenarios in the decision-making process. When all of these characteristics are combined, finding an optimal solution to the scheduling problem can be an extremely challenging task for the decision-makers. A simulation model is one tool that can assist the operational managers when making decisions. Simulation models are representations of reality. One strength is that they incorporate important factors including uncertainty. Simulation models are also useful for evaluating decision policies for practicality and performance (Perez-Roman, 2010), but they do not provide optimal solutions to the decision problem when there are many possible scenarios to consider. Therefore, a simulation model would be useful for modeling a complex problem setting (e.g., clinic or traffic network) and serve as a useful evaluation tool even though it does not include a decision-making component. Stochastic programming, a framework for modeling optimization problems that involve uncertainty, is another valuable decision-making tool. Stochastic integer programming (SIP) is a methodology for solving integer programs with data uncertainty. SIP optimization models have been used extensively in practice for decisionmaking, but there are certain limitations to the types of problems that can be solved. SIP optimization models use a large number of decision variables and constraints to characterize uncertainty and the trade-off is that they become very large and difficult to solve. Although progress has been made to solve large-scale SIP optimization models more efficiently, current decomposition algorithms are not always sufficient to solve these complex problems within a time frame that is acceptable to decision-makers who rely on them. Simplifying assumptions are used to make the problem more tractable. However, this also compromises how well the model represents the real setting. As a direct result, the decisions obtained may be optimal for the optimization model but not for the real-world problem setting. Simulation and Optimization When used in isolation from one another, the limitations of optimization and simulation models inhibit them from adequately addressing the complexity of scheduling problems with uncertainty. However, the complementary strengths and weaknesses of optimization and simulation models provide an opportunity for combining the two to solve scheduling problems with complex problem settings (Cheung, 2005; Ko, 2006). This research develops a new approach that integrates a simulation model with a SIP optimization model for scheduling decisions involving uncertainty. This new simulation and optimization approach allows decision-makers to evaluate scheduling objectives, evaluate resource requirements, and test implementation strategies to determine the best scheduling policies Paper No Page 2 of 11

3 BACKGROUND Healthcare Application - Chemotherapy Scheduling Problem Cancer is a potentially fatal disease characterized by uncontrolled growth of abnormal cells. There is no cure for cancer, but chemotherapy is a common treatment. Chemotherapy treatments are often administered orally or intravenously at outpatient oncology clinics. Cancer costs in the U.S. exceeded $124 billion in 2010 and are expected to increase 27% by 2020 (Mariotto, 2011) while the demand for oncology services is projected to increase by 48% between 2005 and 2020 (Turkcan, 2012). The rising costs and demand motivate the need for efficient chemotherapy appointment schedules. This sub-section describes the details of the chemotherapy scheduling problem, which will be relevant to the example illustration of the simulation and optimization methodology presented in this paper. Oncologists prescribe a unique treatment regimen, or series of chemotherapy appointments, to each cancer patient based on the patient s current state of health. A treatment regimen consists of the suggested duration, acuity level, and drug name for each appointment (see Table 1). Treatment regimens depend on the patient's type of cancer, stage of the cancer growth, and current health. Therefore treatment regimens are unique to each individual patient. Figure 1 gives the chemotherapy scheduling process. The treatment regimen prescribed by the oncologist is sent to a scheduler to determine the appointment schedule and allocate clinic resources for each appointment in the treatment regimen. All appointments in the treatment regimen should be scheduled simultaneously in order to guarantee the availability of subsequent appointments. To be most effective, these appointments should be scheduled as close to the prescribed dates as possible. Delay from the prescribed treatment date is referred to as the type I delay. Delays patients experience in the waiting room before being called back for treatment is referred to as the type II delay. The scheduler uses a model or algorithm to make a chemotherapy scheduling decision, which allocates a specific date, time, and set of clinic resources (e.g., chair and nurse) to each appointment in the patient's treatment regimen. Then the scheduler sends the appointment schedule to the patient and the resource schedules, for the chairs and nurses, to the oncology clinic. Table 1. Example of a Patient s Treatment Regimen Figure 1. Chemotherapy Scheduling Process Chemotherapy treatments are well-known for having nauseating side-affects that weaken the immune system and severely deteriorate a patient s state of health. The side-affects can occur suddenly, so depending on the type and intensity of the treatment, nurses must pay close attention during chemotherapy administration to monitor the patient s condition and reactions to these sideaffects. It is possible for each nurse to simultaneously monitor the chemotherapy treatments of up to four patients at the same time. However, it is crucial that the nurses are not overutilized since they must be available to assist patients experiencing an adverse reaction to the chemotherapy drugs. To account for this, the concept of acuity levels is used. An acuity level is a relative measure of the nurse s attention required by a patient during an appointment. Acuity levels are assigned a value of 1, 2, or 3, where an acuity level of 3 represents the maximum attention required by the patient from the nurse. Each nurse can 2013 Paper No Page 3 of 11

4 monitor 1-4 patients provided that the sum of the acuity levels for each patients is less than or equal to 4. Figure 2 provides an example of limitations associated with scheduling a patient appointment using acuity levels. Making a chemotherapy scheduling decision is a challenging problem when there is uncertainty in appointment durations and acuity levels. As patients experience adverse reactions to the chemotherapy drugs, the appointment duration will be extended and the patient may require more individual attention from the nurses. Complications arising during the set-up of the IV (e.g., hard-stick and clogged port-a-catheter) can also cause extended treatment times. Figure 2. Acuity Level and Appointment Start Limitations Chemotherapy scheduling decisions are also challenging because of the complex nature of the appointment flow in the oncology clinic as shown in Figure 3. When a patient arrives for a chemotherapy appointment, the patient first checks-in with a receptionist and then waits in the waiting room for an available nurse and chair. The delay patients experience in the waiting room before being called back for treatment is referred to as the type II delay. Once both a chair and a nurse are available, the assigned nurse escorts the patient to the assigned chair, orders the patient's chemotherapy drug from the pharmacy, and checks the patient's vital signs. While waiting for the drug to be read in the pharmacy, the nurse starts the patient's IV. When the chemotherapy drug is ready at the pharmacy, the patient's identity is verified and the drug infusion begins. This process takes around 15 minutes (one time slot), and the nurse is fully dedicated to a single patient during this time. Therefore, nurses can only start one patient during a single time slot. Afterwards, the nurse is free to continue monitoring all patients as the infusion can take anywhere from hours. Stopping an infusion and discharging a patient generally takes a few minutes. It can be difficult to capture all the intricate details of the appointment process in the scheduling decisions. Only recently have optimization models been used for chemotherapy scheduling. However, none of these optimization models have incorporated uncertainty in appointment durations and acuity levels. Butler, Karwan, & Sweigart. (1992) and Kropp, Carlson, & Jucker (1978) have both previously used a simulation and optimization methodology in healthcare. However, Butler et al. (1992) applied their methodology to facilities strategic hospital planning not daily operations and scheduling. Kropp et al. (1978) did use a recursive optimizationsimulation approach for staffing and facilities plan in a general healthcare setting, but their model did not include uncertainty in the optimization model or Figure 3. Oncology Clinic Patient Appointment Flow consider the problem characteristics specific to oncology clinic management. SIMULATION AND OPTIMIZATION METHODOLOGY The simulation and optimization methodology we consider is a communication between an optimization model and a simulation model to schedule and evaluate a real system (e.g., oncology clinic or road network) with uncertain parameters. Figure 4 provides the general framework for our simulation and optimization methodology. The simulation model consists of an experimental frame and a simulated system. The experimental frame (EF) captures how the modeler's objectives impact the model construction, experimentation, and evaluation. Also, the EF allows the modeler to drive the system by designing and implementing experiments. There are four main components in the EF: schedule request generator (SRG), scheduler, arrival generator (AG), and performance measures. A simulated system is a simulation of the real system. The optimization model is a mathematical representation of the scheduling problem of the real system. Both the simulation model and the optimization model are designed based 2013 Paper No Page 4 of 11

5 on the characteristics of the real system. Uncertain parameters in the real system are used to establish scenarios. Scenarios are a set of possible outcomes for the real system based on the uncertain parameters. Figure 4. Simulation and Optimization Methodology: General The SRG generates scheduling requests and sends the information in the request to the scheduler. The scheduler takes the schedule request data and calls upon the optimization model to solve the scheduling problem. Then the optimization model uses all scenarios in the formulation of the scheduling problem. Once the scheduling problem is solved, the schedule decisions are returned to the scheduler and distributed to the AG and the simulated system. A few of the decisions may impact arrival of entities to the simulated system and are processed through the AG. Other decisions (e.g., number of resources) are communicated directly from the scheduler to the simulated system. The simulated system simulates the reality of the real system using only one of the scenarios and communicates the results of specific events to the EF for computation as performance measures. Performance measures are useful in evaluation of the scheduling decisions. HEALTHCARE EXAMPLE Overview In Figure 5, the simulation and optimization methodology has been adapted to the healthcare problem of scheduling chemotherapy appointments. In the experimental frame, the appointment request generator mimics an oncologist prescribing a treatment regimen to a sick cancer patient. Appointment requests are then sent to a scheduler who utilizes a SIP optimization model to determine the patient appointment schedule and resource schedule decisions. All possible scenarios are considered in the SIP optimization model when determining the schedule decisions. Patients actually arrive to the simulated system of the oncology clinic based on their scheduled appointment time. Therefore, it is necessary to communicate the treatment regimen to the appointment arrival generator. The appointment arrival generator then generates the arrival of patients to the clinic at their respective appointment times. However, resource schedule decisions (e.g., number of nurses and chairs) are communicated directly to the simulated system of the oncology clinic. The simulated system of the oncology clinic simulates the daily operations of the clinic, including receiving patients, starting infusions, ordering drugs from the pharmacy, patient monitoring, and discharging patients. Only one of the scenarios will actually occur and be used in the simulated system of the oncology clinic. Results of specific events (e.g., infusion start times) are reported back to the experimental frame, where performance measures (e.g., delays, chair utilization, overtime, etc.) are computed. Figure 5. Simulation and Optimization Methodology: Chemotherapy Scheduling Problem 2013 Paper No Page 5 of 11

6 Simulation Model The simulation model can be implemented using any simulation software. The authors used Discrete Event System Specification (DEVS), a formal modeling and simulation framework based on dynamical systems theory that provides well defined concepts for coupling components, hierarchical and modular model construction, and an object-oriented substrate supporting repository reuse (Zeigler and Sarjoughian, 2005). DEVS allows users to specify a mathematical object called a system that is composed of a time base, inputs, states, outputs, and functions for determining the next states and outputs given current states and inputs. DEVS was chosen because of its hierarchical and modular nature, the ability to customize all components, and the ability to integrate the simulation and optimization model using the JAVA programming language. A list of the primary components in the implementation of the simulation model for the chemotherapy scheduling problem is given in Table 2. Table 2. Primary Components Used in the Simulation Model of the Chemotherapy Scheduling Problem Simulated System of the Oncology Clinic Experimental Frame Components Charge Nurse Registered Nurse Pharmacy Wait room Receptionist Appointment Request Generator Scheduler Appointment Arrival Generator Performance Measures Descriptions Oversees the clinic operations and notifies the registered nurses when their patients have arrived to the clinic Takes patient through all steps of the chemotherapy appointment (drug infusion, ordering drugs, discharging, etc.) Receives orders and prepares the chemotherapy drugs Location where the patients wait after check-in until their assigned registered nurse is available Checks the patient into the clinic upon arrival Generates appointment requests (e.g., treatment regimens for a new patient) Schedules all patient appointments in the treatment regimen by using the SIP optimization model Generates patients to arrive at the clinic at their specified appointment date and time Captures data from the simulated system for analysis of clinic operations Optimization Model The SIP optimization model should be customized to fit the specific manager s objectives in the application area. They are used to mathematically model problem constraints and objectives when there are stochastic problem parameters. SIP optimization models are decomposable into first- and second-stage decisions. First-stage decisions relate to the here and now decisions while the second-stage decisions are the recourse decisions. In the chemotherapy scheduling problem, the first-stage decisions are those that relate to the assignment of a patient appointment schedule and resource schedule since those decisions must be made in advance. In other words, we need to determine those schedules here and now. Since the primary objective of the chemotherapy scheduling problem is to start the first appointment in the treatment regimen as close to the prescribed start date as possible, the first-stage objective is to minimize the type I delay. The first-stage constraints include assignment constraints and scheduling constraints. An example of the assignment constraint is that each appointment in the treatment regimen must be assigned to exactly one nurse and one chair on one day and in one start-time slot. The scheduling constraints require that the suggested appointment duration does not overlap existing appointments or cause nurse overtime. There are two types of uncertainty considered in the SIP optimization model for the chemotherapy scheduling problem: duration and acuity level. For example, the patient may have a suggested appointment duration of 4 time slots, but in reality, the appointment could last for 3, 4, or 5 time slots. Similarly, the nursing staff may expect a patient to have very little reaction to the chemotherapy drugs at their first appointment, so the scheduler considers an assigned acuity level of 1 for the first appointment. However, the patient could react poorly to the medicine and thus demand a lot the nurse s time. In this case, there is a positive probability that the patient may actually have an 2013 Paper No Page 6 of 11

7 acuity level of 2 or 3 at the appointment. Each feasible outcome with a positive possibility is called a scenario and the SIP optimization considers all scenarios in the decision-making process. The second-stage decisions are made once a particular scenario is realized. For each scenario, this SIP optimization model s second-stage decisions are the number of patients whose appointments cause schedule conflicts and the amount of excess acuity in each time slot for each nurse. The objective of the second-stage is to minimize the scheduling conflicts across all scenarios. Figure 6 summarizes the objective function, decision variables, and uncertain parameters used in the oncology clinic scheduling SIP optimization model. For smooth implementation with the simulation model, the SIP optimization model was implemented using the JAVA programming language in CPLEX Concert Technology Data Figure 6. SIP Optimization Model for Chemotherapy Scheduling Consider an outpatient oncology clinic with two registered nurses and two chemotherapy chairs. Suppose there is a need to schedule four new patients one-at-atime. These patients need to be scheduled over a three week (15 business days) planning horizon. The clinic is open Monday-Friday from 8:00 AM-5:00 PM daily. Each day has thirty-six 15-minute time slots. There are currently five patients (patients 1-5) already scheduled and four new patients (patients 6-9) to be scheduled. Data used in this example was collected from nine patients at the Division of Hematology and Oncology at Scott and White Hospital in Temple, Texas. Treatment regimens for the four new patients are given in Table 3. Patient 6 has a prescribed start date of 1 indicating that the oncologist suggests beginning treatment on day 1 of 15, if possible. Patient 6 has three treatments in the treatment regimen shown in Table 3. The first appointment has a suggested duration of 118 minutes (ceiling (118/15) = 8 time slots) and an acuity level of 1. Names of the chemotherapy drugs to be administered at each appointment are also listed in Table 3. Table 3. Chemotherapy Scheduling Example: Scenario 1 Data for the New Patients The example has three scenarios for every patient. Scenario 1 has a 50% probability, scenario 2 has a 30% probability, and scenario 3 has a 20% probability. To derive data for scenario 2, the number of time slots in scenario 1 has been increased by one and the acuity levels in scenario 1 have increased by one (except that 3 is still the highest possible acuity level). To derive data for scenario 3, the number of time slots in scenario 1 has been 2013 Paper No Page 7 of 11

8 increased by two and the acuity levels in scenario 1 have decreased by one (except that 1 is still the lowest possible acuity level). See Table 4 for an example of the scenarios for patient 6. Table 4. Chemotherapy Scheduling Example: Scenarios for Patient 6 Results We compare the results of the chemotherapy scheduling example for the SIP optimization model to that of the current scheduling method used at Scott and White Hospital. Their current scheduling method does not include an optimization component. Instead it is likened to an as soon as possible (ASAP) method that looks for the earliest possible time that a chair is available for all appointments in the treatment regimen. The weaknesses of the ASAP method are that the uncertainty in appointment durations and acuity levels are ignored, and the assignment and availability of the nurses are not considered. We compare the two scheduling methods using the performance Table 5. Chemotherapy Scheduling Example: Results for Type I Delay (days) measures of type I delay, type II delay, chair utilization, nurse utilization, and nurse overtime. The type I delay for all new patients in the chemotherapy scheduling example is given in Table 5. The type I delay is the number of days between the oncologist s recommended start date and the patient s treatment regimen s actual start date of the. Patient 6 has a type I delay of zero days for both the ASAP and SIP methods, indicating that the patient s appointment was successfully scheduled on the recommended start date using either method. For patient 9, the ASAP method had a type I delay of eight days compared to only two days for the SIP optimization model. The ASAP and SIP methods both yielded the same average (AVG) of 3.5 days and maximum (MAX) of 8 days for the type I delay. The average and maximum type II delay among all appointments in the chemotherapy scheduling example is listed in Table 6. Type II delay is the number of minutes patients wait in the waiting room before being called by the nurse to begin the chemotherapy treatment. If the simulated system used scenario 1 as the actual outcome, then the ASAP method and the SIP optimization model have similarly low average and maximum type II delays. When the scenarios with longer appointment durations (scenarios 2 and 3) occur, the SIP optimization model has better average and maximum type II delays. Consider when scenario 3 is used in the simulated system and all appointment durations have been extended by 2 time lots (30 minutes). The SIP optimization model has an average type II delay of 7.00 minutes while the ASAP method has an average type II delay of 8.41 minutes. The SIP optimization model has a maximum type II delay of 29 minutes while the ASAP method has maximum type II delay of 32 minutes. Table 6 shows that the SIP optimization model outperformed the ASAP method in the category of type II delay for all three scenarios. Table 6. Chemotherapy Scheduling Example: Results for Type II Delay (minutes) 2013 Paper No Page 8 of 11

9 Table 7 shows the chemotherapy scheduling example results for nurse and chair utilizations and nurse overtime for the SIP optimization model when scenario 3 occurs. A utilization of zero indicates that the respective chair or nurse did not have a patient assigned (e.g., nurse 2 on day 1). Since the appointments are all extended by 30 minutes, the Table 7. Chemotherapy Scheduling Example: Results for Utilization and Overtime on SIP Scenario 3 chairs and nurses are over-utilized on several days. For example, on day 5, chair 1 had a utilization of 105% and nurse 2 had a utilization of 106% which shows that they were over-utilized (>100%) on day 5. As a result, nurse 2 had to work overtime for 33 minutes on day 5. Chair 1 had the highest chair utilization of 107% on day 2. Nurse 1 had the highest nurse utilization of 106% on day 3 and the highest overtime of 37 minutes on day 2. The highest overtime and utilization values were observed for all three scenarios for the ASAP and SIP methods. The results are summarized in Table 8. Scenario 1 did not have long appointment durations so the highest utilizations and overtime were very small for both methods. In fact, regardless of the scenario, the chair and nurse utilizations for the ASAP method and the SIP optimization model yield similar values. However, when the scenarios with longer appointment durations (scenarios 2 and 3) are simulated, the SIP optimization model has better nurse overtime. The highest nurse overtime for the ASAP method in scenario 3 is 51 minutes compared to only 37 minutes with the SIP optimization model. Table 8. Chemotherapy Scheduling Example: Results for the Highest Utilizations and Overtime In summary, the SIP optimization model and the ASAP method produced similar results for the type I delay, chair utilization, and nurse utilization in the chemotherapy scheduling example. However, the SIP optimization model performed better for type II delay and nurse overtime in the scenarios with longer appointment durations (scenarios 2 and 3). Therefore, the simulation and optimization methodology with the SIP optimization model outperformed or was as good as the current scheduling practice of the ASAP method for all scenarios in the example. Thus, the SIP optimization model is the preferred scheduling method in this example. MILITARY LAND MOVE PROBLEM The simulation and optimization methodology is useful for optimizing and evaluating scheduling decisions that involve a complex problem setting and have a high level of interaction between various entities. Suitable problems require decisions based on multiple and sometimes competing objectives subject to several constraints or limitations on the types of schedules that can be created. Finally, some of the problem parameters (e.g., task duration) may be uncertain, which complicates the problem as the managers must consider several outcomes or scenarios in the decision-making process. When all of these characteristics are combined, finding an optimal solution can be an extremely challenging task. This paper specifically focused on using this methodology for a healthcare scheduling 2013 Paper No Page 9 of 11

10 problem. However, the simulation and optimization methodology is also applicable to military scheduling decisions as well. Consider the military land move problem, which involves the movement of a large amount of military equipment from a military fort to a sea port. All military equipment must be moved from one source location to one destination, but the volume of trucks moving is so large that the trucks must be grouped into convoys. The military equipment is typically packed such that there are three types of military items that require movement: containers, vehicles, and big items (e.g., expandable bridges). There are three modes of transportation available: military truck, commercial truck, or train. Limitations exist on which type of transportation each item can use. Each convoy has a maximum size due to the shortage of support vehicles and a minimum size so that the convoy can stay together. The trucks used for transportation have capacity limitations in terms of weight and volume. Additionally, military traffic is limited to certain road networks and there are suggested maximums on the number of military vehicles per hour on a particular road segment as large convoys block civilian traffic. Scheduling decisions must factor in the affects that large convoys have on other traffic. A military land move scheduling decision determines an assignment of military items to a convoy and the departure time of each convoy. Sources of uncertainty include the travel time between the fort and the depot and the loading time at the port. Each convoy has a finite time window for arrival and loading onto the ship at the port and cannot arrive late. The objectives of the military land move problem are to minimize the waiting time at the port, to minimize the travel time on the routes, and to minimize the number of switches from one road to another. The military land move decision problem can be formulated as a SIP optimization model and the road network can be developed as simulated system. Table 9 highlights the similarities between the chemotherapy scheduling problem and the military land move problem in terms of the decisions, objectives, uncertainty, constraints, and the simulated system. Uncertainty in the military land move problem is the load/unload times of the items onto the trucks and the traffic congestion. Poor traffic conditions cause travel delays and impact the travel time and waiting time in the objective. The simulated system of the military land move problem will include an extensive road network between the initial fort location and the final port destination. The simulated system will be able to capture details such as travel speed, congestion, and fuel stops. The comparisons in Table 9 demonstrate that the simulation and optimization approach is application to problem settings other than healthcare. Table 9. Comparison of the Healthcare and Military Scheduling Problems General Healthcare: Chemotherapy Scheduling Military: Land Move Problem Problem Problem Description To efficiently schedule chemotherapy patient appointments and resources at an oncology clinic To efficiently schedule the movement of large military equipment from a fort to a port Schedule Decisions 1) Patient s appointment schedule 2) Chair and nurse schedules 1) Assignment times to convoys 2) Departure times of convoys Objective Minimize type I delay and scheduling conflicts Minimize waiting time, travel time, and number of road switches Uncertainty 1) Appointment duration 2) Acuity levels 1) Traffic congestion 2) Load/unload times Important Constraints Nurse and chair availability, acuity level limits, number of patient starts Convoy sizes, truck capacity, vehicles per hour on a road segment, loading time frame/window Simulated System Oncology clinic Road network between the fort and the port SUMMARY This work developed a simulation and optimization methodology for scheduling problems with uncertain parameters and complex problem settings. The methodology is applicable to many different scheduling problems, including the chemotherapy scheduling problem and the military land move problem. Our methodology defines the relationship between a simulation model and an optimization model when used together to solve these challenging problems. Both models are extensions of the real problem setting. The optimization model makes decisions considering 2013 Paper No Page 10 of 11

11 several scenarios and the simulation model shows the results and performance for one scenario at a time. This approach allows for testing the scheduling objectives and clinic operations before implementation in a real setting. Using a small example of the chemotherapy scheduling problem, the results showed that the simulation and optimization methodology with a SIP model improved the overall performance of the oncology clinic. The performance measures of type I delay, nurse utilization, and chair utilization showed very similar results between the SIP optimization model and the current ASAP method used to schedule chemotherapy patient appointments. However, the simulation and optimization methodology using the SIP optimization model did successfully improve the type II delay and the nurse overtime. These promising results indicate that the simulation and optimization methodology can be used to improve the performance of real systems. Next steps are to implement the approach on a larger-scale using data from a four-month period at Scott and White Hospital. There are a few challenges with using the simulation and optimization methodology. The formulation of the optimization model needs to be carefully considered as to be accurate for the needs of the decision-makers, but not too detailed as to cause slow computational performance. Ideally, the entire simulation and optimization system needs to provide optimal decisions for the management in real time. Design of the simulated system takes a large amount of time to develop and yields results specific to the problem setting. The results at one oncology clinic will not necessarily be applicable to a clinic in another location and a new simulated system may need to be developed. There are several future extensions to the chemotherapy scheduling problem. One possible extension is to consider how the clinic is managed during worst-case scenarios. The here and now first-stage decision of when a patient should arrive for an appointment cannot change; however, we can determine which second-stage decisions should be implemented to adjust the schedule throughout the day. Another extension is to expand upon the current riskneutral SIP optimization model by adding mean-risk objectives in order to evaluate risk-averse decision-making at the clinic. Finally, a third extension is to use the performance measures to improve the SIP optimization for an iterative approach between the optimization and simulation models. ACKNOWLEDGEMENTS This research was supported by the U.S. Department of Education through GAANN Award P200A and the 2012 RADM Fred Lewis Postgraduate I/ITSEC Doctoral Candidate Scholarship. Additionally we would like to thank Dr. Bill Carpentier, Theresa Kelly, Valerie Oxley, and the staff at the Hematology and Oncology Clinic at Scott and White Hospital, Temple, Texas for their assistance with the chemotherapy scheduling problem. REFERENCES Butler, T., Karwan, K., and Sweigart, J. (1992). Multi-level strategic evaluation of hospital plans and decisions. The Journal of Operational Research Society, 43(7): Cheung, W., Leung, L. C., and Tam, P. C. (2005). An intelligent decision support system for service network planning. Decision Support Systems, 39: Ko, H. J., Ko, C. S., and Kim, T. (2006). A hybrid optimization/simulation approach for a distribution network design of 3pls. Computers and Industrial Engineering, 50: Kropp, D. H., Carlson, R. C., and Jucker, J. V. (1979). Use of both optimization and simulation models to analyze complex systems. Highland, H.J., editor, Proceedings of the 1978 Winter Simulation Conference, pages , Miami Beach, FL, USA. Institute of Electrical and Electronics Engineers. Mariotto, A., Yabro, K., Shao, Y., Feuer, E., and Brown, M. (2011). Projections of the cost of cancer care in the United States: Journal of National Cancer Institute, 103(2): Perez-Roman, E. (2010). Simulation and optimization models for scheduling multi-step sequential procedures in nuclear medicine. PhD thesis, Texas A&M University. UMI Number: Turkcan, A., Zeng, B., and Lawley, M. (2012). Chemotherapy operations planning and scheduling. IIE Transactions on Healthcare Systems Engineering, 2(1): Zeigler, B. and Sarjoughian, H. (2005). Simulation with JAVA: developing component-based simulation models. steve/cw/455/bernie-devs.pdf Paper No Page 11 of 11