# Implementation and Models Validation

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WORKFORCE SCHEDULING MODEL
IMPLEMENTATION AND MODEL VALIDITY
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Workforce Scheduling Model
The chapter four of this project notes that based on the case study of ROMCO power plant and generated daily labor demand, the optimum number of maintenance staff will be determined by developing two mathematical programming models. The first model seeks to reduce the size of the workforce under stringent work conditions while the other recommends an entirely different approach or model to be utilized under various conditions and scenarios. The first model will be used for five work days while the second will be utilized to change the work shift to seven days while maintaining the productivity and performance of the workforce. In this regards, two mathematical models have been programmed and designed to assist achieve this scheduling. This section of the research seeks to fulfill varied objectives. The first objective is to specify optimum workforce schedules to limit the increasing demand for overtime during the five working days of the week and the two days of the weekend, and the second is to reduce the cost of labors’ overtime by utilizing the available work time within minimum requirements.
5.1 IMPLEMENTATION
(14, 21) Days-Off Approach
The implementation of this days-off scheduling model is to optimize the working days, overcome the workforce constraints and avoid the need for overtime. This analysis discusses the implementation of the formulated days-off model that will take into consideration the (14, 21) days-off approach for days-off scheduling (Alfares, 2002, 191). This approach is employed to solve a three-week day cycle. In this model, each employee is assigned one work stretch of 14 consecutive workdays at any given cycle. Within the same work cycle, a worker is given a break of 7 consecutive days off after the completion of his or her workday stretch. Therefore, instead of the weekends off during the three-week cycle, each employee gets only one 7-day break. The main goal of the (14, 21) days-off scheduling problem is to minimize the size of the workforce while at the same time optimizing production.
The complexity of the personnel rostering problem is minimized by decomposing the problem into sub-problems that are simpler to tackle. However, the combination of the solutions to the sub-problems does not always solve the initial problems. Nonetheless, with the primary objective, which is to overcome over time, known, the recently published days-off scheduling approaches are surveyed (Alfares, 2002, 192). Afterward, the integer programming models of the (14, 21) scheduling problem and its dual are presented. The procedure for deriving the minimum workforce size and allocating workers to the days-off patterns are produced. This days-off schedule works under the assumptions that the workers required on weekdays are more than those expected during the weekend and that each worker must have a day off within the given cycle. Aside from the constructing a days-off schedule, the shifts that are assigned to the employees during their working days are specified and thus solving the shift rostering problem while respecting the days-off schedule that was made earlier.
Selection of a Workforce Scheduling System
The selection process is contingent on a few factors. For instance, one has to check if the model can produce a single optimized schedule (Webb, N.d, 1). The data collection process will also have to be checked for sufficiency as it is a requirement for the model to produce accurate predictions and forecasts. The model implementation will incorporate years’ worth of comprehensive data for the maximization of the model’s accuracy in forecasting. Furthermore, the system’s ability to recognize critical events in the forecasting process will be one of the main elements that ought to be checked. This is because an accurate and quick recognition of critical events will significantly improve the efficiency of the scheduling system and therefore, increase profits. The model’s ability to produce quick and accurate forecasts will be crucial to the system as repeated automated tasks will be eased. Most importantly, the model should be able to account for anything out of the ordinary and therefore adjust the results of the forecasting. This flexibility will be crucial for the proper functioning of the process. This also incorporates factors such as scalability in case the size and permutations of predictions grow in number.
Process of Implementation
The primary objective of the model is to obtain the minimum size of the workforce at minimum costs of overtime. Since there are seven days in a week, the model will include seven variables. The staff requirements will then act as the constraints in the particular weekdays. The off days will be represented by ones and off days will be represented by zeros. The initial case will consider 5 days of a week starting from Sunday until Thursday. This case will schedule workers on the basis of overtime working on weekends and then returns the labor hours in a week. The second case will move from five days to seven days’ week schedule. It will have the optimum size of workers, and this scenario will entail two off days over the week. Therefore, the labor hours in a week will be obtained with the optimum number of workforce. The two outputs of the scenarios will be compared and contrasted, and the one which meets the minimum size of the workforce at minimum cost will be selected for implementation.
The Scheduling Strategy
The central goal of the days-off schedule is to ensure that the total number of workers is minimized. The secondary objective of the (14, 21) days-off model is to reduce the number of patterns to which some workers are actually allocated the days off (Alfares, 2002, 193). Therefore, the days off will first be scheduled with the maximum demand during those days considered. Mathematical programming models representing the (14, 21) days-off approach will be used to ensure a systematic days-off roster without any conflict. The off days will be cyclically be allocated to the employees. The labor demand constraint ensures that the daily labor demands are met for every day throughout the three-week cycle (Alfares, 2002, 193). The labor requirement will vary from day to day within the week while the weekly labor demand will remain constant. Additionally, the logical constraints are also necessary for strategizing the schedule.

The model is non-trivial pure integer programming (IP) problem with up to 42 constraints and 42 variables (Alfares, 2002, 194). The size and the pure-integer characteristic of this formula make it inefficient to use in deriving optimum solutions. Therefore, in order to develop this method, the IP model should be decomposed. The secondary priority of reducing the number of active days-off patterns will be ignored temporarily. Therefore, the simplified model will be:

Where W is the workforce size, that is the number of employees assigned to all 21 days-off patterns.
Given a one-week varying daily labor requirement, the minimum workforce size is determined without integer programming. The procedure entails the allocation of unit resources to dual variables in order to optimize the dual objective W (Alfares, 2002, 196). The optimum dual solution will then be used to determine days- off assignments. The principles of complementary slackness and the basic primal-dual relationship will be used to determine the solution for the original problem. Once the workforce size and the minimum number of employees required to maintain an operation are determined, the days-off schedule would be made in consideration of the aforementioned constraints. At any time during the days-off pattern, the workers will always not be less than the required minimum allowable size.
The Scheduling Procedure
Part of the implementation is to identify the various work demands and in the process design a scheduling procedure that meets or exceeds established needs. The first step of the scheduling procedure is the selection of the most difficult days. In workforce scheduling, these days refer to periods of high demands on different days. The second step is the selection of staff groups; these refer to persons that can be scheduled principally and which can be reduced depending on changes in labor demand. Also, selection of the best suited persons which follows a number of established rules; [a] persons with most free times, [b] persons that can exactly fit into a schedule, [c] persons with long work time intervals, [d] and workers with preferences on various intervals (Jürgen and Rene, 2014, 3). Part of implementation will be to ensure that the above procedure is respected and followed for a fruitful workforce scheduling. However, depending on both the hard and the soft constraints, the above procedure can be altered or changed to suit overloads and unexpected work demands.

Assumptions to Consider During Implementation
As part of the implementing the two mathematical models, a range of assumptions shall be considered for successful scheduling. There is always one worker on vacation, training or sick leave so, it is assumed that only 14 workers are available throughout the year. Labor office regulations require plants to have 8 hour working days for five days a week. Critical system failure must be repaired immediately. The workforce is available any time and can operate for any workplace. The study will be conducted on the mechanical maintenance section in which most of the workload goes under it. Each employee should have two consecutive days off per week.
5.2 MODEL VALIDITY
The primary goal of this study is to specify optimum workforce schedules to limit the increasing demand for overtime during the five working days of the week and the two days of a weekend. The second is to reduce the cost of labors’ overtime by utilizing the available work time within minimum requirements. Model validation is an instrumental step in workforce scheduling as it brings to insight deeper details about the model. Models are usually developed to analyze particular issues and may, therefore, represent various parts of the system at different degrees of abstractions. Resultantly, validation needs to be done for different sections of the system across the full spectrum of the model’s behavior. In most cases, three aspects are considered: assumptions, input parameter variables and distribution, and output values and conclusions. Nonetheless, in many practical approaches, full validation of a model is only undertaken when the initial validation of the system’s output suggests a problem (Sargent, 2009, 169). Three approaches, which include expert intuition, real system measurements, and theoretical results, can be used to check the days-off scheduling system.
Expert Intuition
The use of expert intuition to validate the (14, 21) days-off model is similar to the use of one-step analysis during model verification. An expert with respect to the system, but not the modeler will examine the model (Sargent, 2009, 170). Additionally, the examiner should not be an expert with respect to the model. An investigation into whether the output of (14, 21) days-off approach, which is a simulation model, is useful in optimizing the workforce will be assisted by one-step analysis, tracing and animation. Every possible performance measure is extracted from the model for validation purposes regardless of the goals of the performance study.
Real System Measurements
The comparison between the days-off scheduling model with a real system is the most reliable and preferred method of validation. Before the application of the model to scheduling, it should be compared with a model that is already operational. In the case of (14, 21) days-off approach, it should be analyzed with respect to other operational days-off approaches that have proved to be effective in minimizing the workforce and overcoming overtime. The assumptions, input values, output values, workloads, configuration, and system behavior, should be compared with those noted in the actual world (Sargent, 2009, 170). The application of trace-driven simulation will enable the observation of the model under exactly similar conditions as the operational system.
Theoretical Analysis
The use of a more abstract representation of the system can provide a crude validation of the model. The operational law that is if there is a constant supply of labor even when other people are on their day off should show that the model output and thus indicating that the model behaves correctly. The operational laws are also used to check the consistency within a set of result extracted from the model. If the system acts well, the outcome of the model should consistently produce the expected outcome.
Inspection
The inspection step of model validity is the systematic and strategic process of evaluating performances and productivity over the course of time. Inspection utilizes the existing data or records to rule out possible failures or loopholes (Weiss, 2017, 3). Other than checking schedule adherence, inspection analyzes the problems and challenges that might have been experienced when schedule adherence was at its lowest. There are a number of considerations when undertaking regular inspections;Agents, managers, and supervisors turning ‘’rogue’’ can impair the service-level accuracies. If oppressive and derogatory practices are identified, it is vital to establish standardized processes to put everyone on the same page.
Shrinkage is the single most barrier towards the attainment of service levels. Shrinkage occurs when service levels are desperately lower than earlier predicted. All the drivers contributing to shrinkage can be mapped and solved to prevent future errors.
Model validation should be conducted immediately there is a significant difference between the actual data and projected forecasts. Also, if the forecast is accurate, it is critical to revisit the model regularly to establish the sources of large differences.
Regular validation of the forecast model is important to ensure that the staffing plan is on target and that all the business goals and objectives are met.
WEEKLY LABOR HOUR COMPARISONS
Five-Day Week
Mon Worker 1 Worker 2 Worker 3 Worker 4
Tue 7 hours 6 hours 8 hours 9 hours
Wed 7 hours 7 hours 7 hours 8 hours
Thursday 7 hours 8 hours 7 hours 6 hours
Friday 7 hours 6 hours 7 hours 7 hours
Seven-Day Week
Worker 1 Worker 2 Worker 3 Worker 4
Mon Off 7 hours 7 hours 7 hours
Tue 7 hours 7 hours Off 8 hours
Wed Off 7 hours 7 hours 7 hours
Thur7 hours 7 hours 9 hours Off
Fri 8 hours Off 7 hours 6 hours
Sat 6 hours 7 hours Off 7 hours
Sunday 7 hours Off 5 hours Off
Overtime Hours
Worker 1 Worker 2 Worker 3 Worker 4
Sat & Sun 13 Hours 7 Hours 5 Hours 7 Hours
Target 10 Hours 10 Hours 10 Hours 10 Hours
The pivotal goal of this investigation is to specify optimum workforce schedules to limit the increasing demand for overtime during the five working days of the week and the two days of a weekend. The second is to reduce the cost of labors’ overtime by utilizing the available work time within minimum requirements. The above work hour illustrations provide varied comparisons of workers based on work weeks. There are popular assumptions made in formulating the above total hours per week. These include:
The ROM There is always one worker on vacation, training or sick leave so, it is assumed that only 14 workers are available throughout the year.
Labor office regulations require plants to have 8 hour working days for five days a week.
Critical system failure must be repaired immediately.
The workforce is available any time and can operate for any workplace.
The study will be conducted on the mechanical maintenance section in which most of the workload goes under it.
Each employee should have two consecutive days off per week.
CO has a 10-hour weekend target for individual workers.
Conclusion
The premier reason for this study is to specify optimum workforce schedules to limit the increasing demand for overtime during the five working days of the week and the two days of a weekend. The second is to reduce the cost of labors’ overtime by utilizing the available work time within minimum requirements. The primary problem established in this research is that power plant operators take excessive overtime hours. These extra hours further require that the company incurs extra costs and expenditures, this, in turn, affects the overall production costs and in the process lowers the profit margins. Other than generating errors and problems during critical operating times, inconsistencies in overtime work hours affect the scheduling leading to poor results, frictions in scheduling, and desperately low productivity levels. This research identifies that a possible solution is to formulate a mathematical model or approach that will generate optimal scheduling plans in meeting the demand for the excess overtime hours. This section of the project has covered two broad areas; model implementation and validity. Under the model implementation, the research identifies that the first step is to identify and leverage a good scheduling system. Such a system encompasses a series of traits and characteristics among them; flexibility, interface, sound engine algorithms, and cost-effective. Part of the model implementation is to establish a standardized process through which the workforce scheduling model will be utilized in a contemporary establishment, in this case, the ROMCO power plant.
The scheduling strategy is also identified as a significant phase of implementation as it involves identifying scheduling problems and provision of relevant solutions. The scheduling procedure is also outlined to guide the management in a step-to-step implementation of the proposed scheduling model. The final part of the implementation section covers the popular assumptions held as part of putting the model to use. The second section of the research identifies model validity. Model validation is identified as a critically underpinning step in bringing to insight deeper examination of the scheduling model. The research recommends three basic approaches to model validation which include back-casting, data entry, and regular inspection. Of special concern for this research was to document a sample comparative analysis of weekly labor hours. The first labor hour takes into consideration five working days while the second observes seven working days. The two models are analyzed comparatively and the number of weekly hours illustrated. Where possible, the paper relies on credible sources such as scholarly materials and published sources to create knowledge and add insight into the workforce scheduling model proposed.
Reference List
Alfares, H.K., 2002. Optimum workforce scheduling under the (14, 21) days-off timetable. Advances in Decision Sciences, 6(3), pp.191-199.
Jürgen, S and Rene, S. (2014). Modeling and Solving Workforce Scheduling Problems. The Research Gate Source. Pg. 1 – Pg. 8.
Sargent, R.G., 2009, December. Verification and validation of simulation models. In Simulation Conference (WSC), Proceedings of the 2009 Winter (pp. 162-176). IEEE.
Thompson, G. (2009). Labor Scheduling Part 3: Developing a Workforce Schedule. Cornell University School of Hotel Administration. The Scholarly Commons.
Webb, Bobb. (N.d). 10 Steps to Selecting a Workforce Scheduling System. Pipkins.Inc. pg. 1-2
Weiss, M. (2017). Validating the Forecasting Model. ICMI Contact Center Training. Retrieved from https://www.icmi.com/

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