LINGO Software Research Articles

A novel relationship-oriented clustering approach for extracting relational patterns from the traffic tangled data

ABSTRACT Many models have been proposed in the literature of traffic engineering to investigate the relations between the prominent traffic variables such as velocity, density, and flow. However, in a specific period and environment, the traffic variables do not follow the same pattern discovered by a model and the observations might have various behavioral patterns. This means that a wide range of tangled data must be investigated and the aforementioned diverse patterns should be extracted so that the future values of the traffic variables can be predicted. This paper proposes a new approach based on which the relations between the traffic variables in the tangled data are detected. To show the practical value of this study, different procedures of the proposed approach are carried out for the traffic data of a highway in Iran. To detect the existing patterns of the collected data, an optimization regression-based model is developed based on which the traffic observations are segregated. The objective of this model is minimization of the Mean Squared Error () metric. The proposed approach fits multiple lines to the tangled data instead of a single one; therefore, the observations are segregated and diverse relations between the traffic variables will be revealed. The developed model is a mixed-integer non-linear mathematical formulation belonging to the class of NP-hard problems. Thus, two powerful meta-heuristics including the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used to solve the model and find the coefficients of the fitting lines. For a small number of observations, the outputs of the GA and PSO have been tested in terms of validity by comparing them to the optimal values provided by the LINGO software. The GA and PSO could reach the optimal values in 77% and 64% of their runs, respectively. The validity of the results have also been confirmed by conducting one sample t-tests. The coefficient of determination has been utilized to evaluate the goodness of the fitting lines acquired by the GA and PSO. The outputs show that the values of all fitting lines are above 0.80; therefore, it can be concluded that the GA and PSO have been successful in delivering high-quality fitting lines. Having acquired high-quality fitting lines, it was proven that the proposed approach has been sufficiently efficient and effective in detecting various behavioral patterns existing in the traffic tangled data.

Vaccine production optimization model based on Monte Carlo algorithm

COVID-19 is ravaging the world. Due to the large scale of vaccine production, the production of vaccines with good quality and quantity is the key to epidemic prevention and control. The problem of vaccine production planning is essentially the same as the problem of assembly line production. Based on the production sequence of a company's vaccine, this paper conducted a normal test on the test data by USING SPSS software and found that it obeys the normal distribution. The shortest processing time and production sequence were obtained by using LINGO software. By using LINGO software, it was found that the processing time was the shortest, 184.778 minutes, in the order of YM4 -- YM5 -- YM10 -- YM7 -- YM8 -- YM1 -- YM2 -- YM3 -- YM9 -- YM6. Based on the above conclusion, monte Carlo experiment was conducted with MATLAB software to find out the maximum probability corresponding to 95% of the production time in the problem, and the result was 1.324%. To mean the lower limit of the 90% confidence interval of each flight reservation production time for each type of vaccine, ignore the machine production of waiting time and each vaccine production after the influence on other types of vaccine production, statistics each vaccine needed to consume the longest flight reservation, the total elapsed time, again will each vaccine consume the longest flight reservation of accumulative sum total production time, The number of production days is 186.189 days under the premise that the reliability is 90%.

Multi-objective optimization for multi-type transportation problem in intuitionistic fuzzy environment

Multi-objective optimization is an emerging field concerning optimization problems associated with more than one objective function, each of them has to be optimized simultaneously. Multi-objective optimization is widely used in logistics and supply chains to reduce the cost and time involved in transportation. With the increase in Global Supply Chains, many organizations are facing the challenges of delivering products to their customers at a fast pace, low cost, and high reliability. There are numerous factors that may affect the goal of an organization to optimize the cost, time, and effort during the transportation of their products to the end customers. For instance, in the existing transportation problems, the type of vehicles used for the movement of the products is not focused. Transportation of the goods is considered to utilize any type of vehicle irrespective of the nature of the goods. However, in real-life scenarios, there are certain constraints in the vehicle used to transport the finished goods or raw materials from a source to a destination. Vehicles such as tanker trucks, top open trucks, closed trucks, etc. need to be booked based on the nature of goods to be transported. Also, the cost and time of transportation are uncertain in nature. In this paper, we formulate the Multi-Objective Solid Transportation Problem (MOSTP) by considering the above issue. The uncertain parameters of the problem are considered as Pentagonal Intuitionistic Fuzzy Numbers (PIFN). Magnitude method is used for defuzzification. An algorithm to find the solution of formulated Intuitionistic Fuzzy Multi-Objective Solid Transportation problem (IFMOSTP) is provided. The proposed model is illustrated by a numerical example which is solved with the help of LINGO software.

A multi-objective decision-making model for renewable energy planning: The case of Turkey

The rapid increase in the world population along with the rising trend of global economic growth triggers serious problems related to energy consumption. In this regard, a comprehensive analysis of the current and potential energy situation in the light of demographic trends, main economic indicators, technical conditions, social and environmental concerns has become a significant issue for developing well-planned global and regional energy strategies. In this study, a multi-objective decision-making model is constructed for renewable energy planning to determine the most appropriate resource diversity for Turkey by focusing on five renewable energy sources, namely solar, wind, geothermal, hydroelectric, and biomass. There are four objective functions presented in the proposed multi-objective model including maximization of the technical score of regions, maximization of the job creation, maximization of the environmental score, and minimization of the cost. As a solution methodology, a two-phase fuzzy goal programming approach is performed. The proposed model is solved using LINGO software as a comprehensive solver for model optimization. The appropriateness of the proposed method is analyzed by comparing it with other multi-objective methods. Results reveal that the majority of the energy demand should be met via solar and hydroelectric energies for the satisfaction of the indicated objectives.

An Internet of Things Embedded Sustainable Supply Chain Management of B2B E-Commerce

Adopting digital technologies in a business can help with sustainable supply chain management. These technologies can make e-commerce development faster and empower the emergence of B2B e-commerce businesses. In this study, our focus was to develop a framework for an Internet of things (IoT) embedded sustainable supply chain to deliver textile items using a B2B e-commerce business model. We formulated a mixed-integer non-linear programming (MINLP) model to minimize the total supply chain cost, including the B2B orders’ packaging, handling, and transportation, with carbon emission taxation. Furthermore, the purchasing cost of the RFID tags and IoT facilities that were provided on the transport vehicles was high. The proposed model was solved by using the global solver in the LINGO software package and finding the optimized value of the total supply chain network cost. We tested the proposed model in different case scenarios, i.e., small- to significant-sized problems. Then, a sensitivity analysis was performed to observe the variations in the overall cost of the supply chain network when there were changes in the main parameters of the proposed model. The results of the models showed that models can be helpful for efficient logistics planning and supply chain design.

Mathematical Model & Feasibility Study for Construction an Invested Refinery of 100,000 (bbl / Day) in AL-Nasiriya Governorate

A mathematical Model and feasibility study of construction an invested Refinery with 100,000 (Bbl/day) in AL-Nasiriya governorate was performed. The project is composed of three Units, Atmospheric Column Distillation Unit (CDU), Catalytic Reformer Unit (CRU) and Residue Fluidized Catalytic Cracking Unit (RFCC) that produce different products. Based on the Platts prices of petroleum products which was provided by State Organization for Marketing of Oil (SOMO) for May of this year and by standard specifications and technical information of Petroleum Research and Development Center (PRDC), Material balance for feed and products as well as optimization process using LINGO software for these three Units were calculated in order to determine influential financial parameters: (NPV), (IRR), (PI) and Payback period of the project. Different calculation scenarios were prepared taking into account discount of crude oil and products prices, inflation indicator of Capital expenditure (CAPEX) and operation expenditure (OPEX) in addition to extending the life of the project and increase in the cost of capital as well. These scenarios are illustrated as followings: -
 1- The refinery was considered non-feasible in case of the crude feed price is taken (65$) and the products prices still constant. Discounted of oil feed was taken gradually by 10% and the products prices stay constant turns the project to be feasible at (50%) discounted oil price which gives positive financial parameters as can be seen in scenario (1), (2) but no longer feasible when increasing inflation by (3%) and (5%) as shown in scenario (3) and (4).
 2- The price of crude oil feed was taken constant (65$) and the products prices were gradually increased by (10%) till (50%) with constant other parameters gives negative financial parameters means non feasibility as can be seen in scenario (5).
 3- Increasing products prices by 10% and discount crude oil price by 10% together makes the project feasible at (25%) for both as shown in scenario (6). Conversely, when inflation was taken into account for OPEX and cost of capital, the project shifted to be feasible at (40%) for both crude oil and products as seen in scenario (7, 8, 9). The crude oil feed price and products was increased gradually by (10%) and decreased by the same percent. Both scenarios give negative financial parameters as shown in (10) and (11).
 4- Extending life of project from (4) to (6) years and let other parameters constant including CAPEX to study the impact on the financial parameters. It is noticed that the refinery gives negative income compared to previous period of project in scenarios (12), (13). The cost of capital was increased from 2,100 million to 3000 million with no change in the other parameters gives negative income as seen in scenario (14) and (15). On the other hand, cost of capital and life of project were changed together makes the project worse income due to decline in the financial parameters as illustrated in scenario (14) and (16).

A Robust Fuzzy Decision Making on Global Warming

Background: In this article we develop a global warming indicator model under fuzzy system. It is the light of sun that environmental pollution is responsible for the cause and immediate effect of global warming. Limited amount of oxygen in the air, continuous decrease of fresh water volume, more especially the amount of drinking water and the rise of temperature in the globe are the major symptoms (variants) of global warming. Thus, to capture the facts we need to develop a mathematical model which has not yet been developed by the earlier researchers. Introduction: An efficient literature survey has been done over the three major parameters of the environment namely oxygen, fresh water and surface temperature exclusively. In fact we have accumulated 150 years-data structure for these major components and have analyzed them under fuzzy system so as to develop an efficient global warming indicator model. Method: First of all, we gave few definitions on fuzzy set. Utilizing the data set we have constructed appropriate membership functions of the three major components of the environment. Then applying goal programming problem, we have constructed a fuzzy global warming indicator (GWI) model subject to some goal constraints with respective priority vectors (Scenario 1 and Scenario 2). An extension has also been included for multi-valued goal programming problem and numerical illustrations have been done with the help of LINGO software. Result: Numerical study reveals that the GWI takes maximum and minimum values in a decreasing manner as time increases. It is seen that for scenario 1, the global environmental system will attain its stability after 30 years by degrading 31% of GWI with respect to present base line. For scenario 2, after the same time the global environmental system will attain its stability quite slowly by degrading 28% of GWI with respect to present base line. Conclusion: Here we have studied a mathematical model of global warming first time using fuzzy system. No other mathematical models have been existed in the literature. Thus, the basic novelty lies in a robust decision-making approach which shows the expected time of extinction of major species in this world. However, extensive study on data analytics over major environmental components can tell the stability of the global warming indicator and hence the future fate of the globe also.

Shift Scheduling with the Goal Programming Approach in Fast-Food Restaurant: McDonald’s in Kelantan

A major fast-food restaurant chain, such as McDonald's, must perform well to maintain its credibility with customers and dominance over other competitors. A fair and balanced shift schedule of workers must be generated to ensure that the workers provide the best service and production for the restaurant. Consequently, this study proposed a fair and efficient workforce schedule at a McDonald's restaurant in Kelantan, Malaysia. Furthermore, the goal programming method and the LINGO software are used in this study to develop the best schedule for the workers over a 28-day period. Five hard constraints and three soft constraints are identified. The primary goal of this study, which demanded the same total workload for each worker, was met. However, the other two goals are not fully achieved but have little impact on the workers due to the 18-hour operation and rotation of schedules among workers. Finally, the generated schedule pattern has been shown to provide a better schedule in terms of having the same total number of shifts for each worker and giving each worker the same total number of off days.

A study on pollution sensitive sponge iron based production transportation model under fuzzy environment

Over the last few years, sponge iron-based production transportation and pollution problems for major sponge iron producing countries are triggering a critical issue. The excess of marginal pollution from production industries and their disintegration takes drives towards the change of policymaking. The sustainable development of any country signifies the reduction of biohazards, which in turn improves the health index and livelihood status of people across the world. Keeping this in mind, a cost depreciation problem for the bi-layer integrated supply chain model has been built up. We consider the functional dependencies among all considerable decision variables like production rate, consumption rate which leads to the pollution rate of different countries exclusively. In this study, we have shown how production and rail freight transport relates to pollution. To draw several graphs and numerical computations we use MATLAB software and LINGO software via solution algorithm respectively. The comparative study has been presented using general fuzzy as well as cloudy fuzzy systems. Lastly, we have justified our proposed model using sensitivity analysis along with graphical interpretation.

Coordination and Optimization of Long-Distance Passenger Departure Timetable Connected to High-Speed Railway Station: Considering the Heterogeneity of Transfer Passengers Demand

Optimizing the departure timetable of long-distance passenger transport connected to high-speed railway stations can not only improve the attractiveness of long-distance passenger transport, reduce the loss of passengers, but also alleviate the pressure of passenger flow accumulation caused by uneven arrival of high-speed railways. Considering the demand heterogeneity of high-speed railway outbound transfer passengers and analyzing the characteristics of transfer travel time, a multiobjective optimization model with unequal interval departures is established. The model takes the minimum total cost and the highest transport capacity as the goal, with the constraints of the departure interval, the waiting time of the stranded passengers, the amount of passenger loss, etc., to optimize the adjustment of the departure interval and the number of departures for long-distance passenger transport and to answer it with the help of Matlab and Lingo software. The calculation results show that the optimized timetable strengthens the synchronous connection with the arrival of small peaks of passenger flow and improves the matching degree of transportation capacity and passenger flow demand. The total passenger transfer time after optimization is reduced by 10.53 h, and the transfer time per capita is reduced by 189.54 s.

Perancangan Model Penjadwalan Teknisi pada Perawatan BD Check Pesawat Airbus dengan Memperhitungkan Beban Kerja

<p><strong>PT GMF AeroAsia is engaged in the maintenance, repair, and overhaul (MRO) of aircraft. It is known that GMF is the largest domestic MRO company at 30% while 70% is owned by foreign MRO companies. Based on the company's vision to make the company a world-class MRO, it is necessary to develop a business scheme in terms of capability, quantity, and quality. However, the scheduling of technicians in carrying out aircraft maintenance is currently unable to meet the demand every hour due to the uncertain flight schedule of the aircraft every day so that the workload of each technician exceeds the normal workload. The calculation of the workload using the full-time equivalent method showed that the workload of technicians was overloaded so that an additional number of technicians was needed, as well as analyzing the causes and consequences of the excessive workload of technicians using the fishbone diagram method and modeling the formulation of the technician scheduling problem that works in maintenance before departure check Airbus aircraft in the form of integer linear programming with decision variables such as the number of technicians, the number of shifts and the number of working days, then the constraint function is the constraints to be achieved in modeling, and the objective function is to minimize the number of technicians employed. Furthermore, the model is implemented using the LINGO 19.0 software so that it is found that the model can produce an optimal technician schedule in scheduling.</strong></p><p><strong><em>Keywords</em></strong> - <em>Fishbone Diagram, Full Time Equivalent, Integer Linear Programming, Lingo Software, Matchematical Modeling, Scheduling, Workload</em><em></em></p>

Water-energy-ecosystem nexus modeling using multi-objective, non-linear programming in a regulated river: Exploring tradeoffs among environmental flows, cascaded small hydropower, and inter-basin water diversion projects

Small hydropower (SHP) possesses significant economic, technical, and environmental advantages, and accounts for a large proportion of hydropower development in China. However, the concentrated, cascaded, and diversion-type development of SHP has resulted in long-distance dewatering of river sections, and inter-basin water transfers have led to severe exploitation of water resources and damage to river ecosystems. In this paper, the Datong River Basin, a secondary sub-basin of the Yellow River Basin in China, was selected as the illustrative case, which includes 22 hydropower projects (HPPs) and three inter-basin water diversion projects (WDPs). A nexus system model was established that used weighted multi-objective programming to consider three main objectives: the water resources utilization (local water withdrawal and inter-basin water transfer), energy production (by cascaded HPPs), and riverine environmental conservation. The Tennant method was used to estimate the environmental flows (e-flows) at the cross-sections immediately downstream of the dam/sluice gate and immediately downstream of the hydropower plant of diversion-type HPPs. The decreased percentage of regulated flow in comparison with runoff and the guaranteed rate of e-flow at the control cross-section were introduced to assess the degree of environmental impact to the river. Using a historical series of runoff data during 1956–2016 as the model input (i.e., implicit stochastic method), the Multi-start solver of nonlinear programming of LINGO software was used to conduct optimizations and analyses for multiple scenarios (with/without e-flow, with consideration of various levels of e-flow, and with/without water resources utilization). The sectoral linkages relating to the water-energy-ecosystem (WEE) nexus were quantitatively identified. The possible influences of different boundary conditions (i.e., initial/final reservoir storage, inter-basin water diversion capacity, and climate change) on the WEE nexus were further explored. The present study aims to provide an exemplar for the optimal operation and scientific management of a complicated water resources system in a regulated river with cascaded SHP and inter-basin WDPs.

Solving a single period inventory model with fuzzy inequality

The purpose of this paper is to present a fuzzy chance-constrained single period inventory model (FCCSPIM) in which the fuzziness appears in the space constraint and objective function is crisp. Here the partial order relation exists in between a random variable and a real number. That means the probability of the event is discussed under vague data. Our approach for the solution process uses mostly fuzzy Zimmermann technique to convert the FCCSPIM into a proper deterministic equivalent. Then the resulting nonlinear deterministic model is solved by using LINGO software. The result indicate that the fuzzy programming approach is effective for the inventory problem. The applications of an optimisation model under uncertainty are used to solve day to day problems. Many methods were developed by using tools of mathematics, probability theory and stochastic process. Here, one new approach of fuzzy programming technique is introduced to obtain a deterministic form.

A State-of-the-art Model of Location, Inventory, and Pricing Problem in the Closed-loop Supply Chain Network

The main objective of designing the supply chain is to increase profitability. For this reason, a state-of-the-art model of a three-echelon closed-loop supply chain is proposed that consists of the manufacturer, retailer, and collection centers. For the first time, a new separate and autonomous channel is considered in this model for the sale of Reman products aiming at increasing the manufacturer's profitability. In this model, location, inventory, and pricing of the product are also taken into consideration. Lingo software is utilized to solve nonlinear objective functions at a small scale, and metaheuristic genetic algorithms and particle swarm optimization were utilized to solve at a large scale. The research results depict that the state-of-the-art model design of the closed-loop supply chain network is credible and the optimal location of supply chain components, optimal response of product flow, and product price are determined in a proper manner. As a result, the profitability of the whole closed-loop supply chain network increased. Sensitivity analysis of mathematical model depicts that this model shows higher sensitivity to retailer replacement factor, price and purchasing power of collection centers. Also, the genetic algorithm shows better performance on a large scale in terms of response quality. On the other hand, the time required by particle swarm optimization to reach a response is far better than the genetic algorithm. Ultimately, practical suggestions for the managers are presented considering the state-of-the-art model design of a closed-loop supply chain network.

Solving Stochastic Fuzzy Transportation Problem with Mixed Constraints Using the Weibull Distribution

The development in the industries has necessitated the growth of transportation methods. Due to the variation in the transportation systems, many problems seem to arise in the present times. One such problem is the stochastic fuzzy transportation problem (SFTP). The SFTP is a chance‐constrained programming (CCP) problem with probabilistic constraints where supply and demand are randomness, and the objective function is in fuzzy nature. In this paper, we have developed three models for the SFTP, where the constraints are mixed type following Weibull distribution (WD). The aim of the research work is to optimize the transportation cost in FTP under probabilistic mixed constraints. In order to achieve this, the cost coefficient of the fuzzy objective function is converted to alpha cut representation, and the probabilistic mixed constraints are converted to deterministic form by using the WD. The proposed models are illustrated by providing a numerical example, and the problem is solved using Lingo software. It is worth pointing out that these models are constructed from different points of view. The decision‐maker’s (DM’s) preference has the final say in the usage of the models. A sensitivity analysis (SA) is performed to explore the sensitivity of the parameters in the proposed model.

Designing Sustainable Recovery Network of End‐of‐Life Product during the COVID‐19 Pandemic: A Real and Applied Case Study

One of the most important aspects of supply chain management (SCM) is the recovery network (RN), which covers all activities associated with return products (such as collection, recovery, repair, recycling, and waste disposal). Our goal in this paper is to provide a new mathematical model of sustainable end‐of‐life management (SEOLM) during the COVID‐19 pandemic for readers. The suggested recovery network model (RNM) can explain the trade‐offs between economic (minimizing total costs), environmental (minimizing bad environmental impacts), and social (minimizing bad social impacts) aspects during the pandemic and the great lockdown. A new RN can be designed with a sustainable and hygienic design when taking environmental, economic, and social considerations into account. It proposes guidelines for managers and scholars on how to address recovery network design (RND) challenges during the pandemic through a mathematical article with a sustainable approach. The scalarization approach of a multi‐objective mixed‐integer programming (MOMIP) problem in this paper is the weighted sum method. The validation of the presented model and the related Pareto frontier has been illustrated by a case study and numerical example. To perform the optimization process, Lingo software is used.

OPTIMASI BIAYA PENGIRIMAN TELUR AYAM MENGGUNAKAN PENDEKATAN MODEL TRANSPORTASI NWC DAN SOFTWARE LINGO

Distribution of goods from producers to the hands of consumers becomes one aspect in running a business that must be planned and taken into account in order to meet the needs of the market. Delivery of goods results in costs incurred and is one of the obstacles that are often faced. Problems in the distribution of goods include the amount of inventory, the amount of consumer demand, the distance traveled and the costs that come out during the delivery process. This study describes taking into account optimal postage with transportation methods to generate maximum efficiency costs. The problem faced in this case using the North West Corner (NWC) method, then the results of the data obtained were tested optimized using LINGO software. Before the research was conducted, the cost of postage incurred by the company is Rp.278.000. The results of the research obtained after applying the NWC is Rp.255.000 and LINGO software method is Rp.240.000. The purpose of this research is to get optimal costs on the distribution of chicken eggs to increase cost savings at Ayam Sehat.com Shop in Cimahi. Using the NWC method in this case can result in smaller distribution costs than before, then this NWC method can be applied to the Ayam Sehat.com shop

Passenger-to-Car Assignment Optimization Model for High-Speed Railway with Risk of COVID-19 Transmission Consideration

Narrow and closed spaces like high-speed train cabins are at great risk for airborne infectious disease transmission. With the threat of COVID-19 as well as other potential contagious diseases, it is necessary to protect passengers from infection. Except for the traditional preventions such as increasing ventilation or wearing masks, this paper proposes a novel measurement that optimizes passenger-to-car assignment schemes to reduce the infection risk for high-speed railway passengers. First, we estimated the probability of an infected person boarding the train at any station. Once infectors occur, the non-steady-state Wells–Riley equation is used to model the airborne transmission intercar cabin. The expected number of susceptible passengers infected on the train can be calculated, which is the so-called overall infection risk. The model to minimize overall infection risk, as a pure integer quadratic programming problem, is solved by LINGO software and tested on several scenarios compared with the classical sequential and discrete assignment strategies used in China. The results show that the proposed model can reduce 67.6% and 56.8% of the infection risk in the base case compared to the sequential and discrete assignment, respectively. In other scenarios, the reduction lies mostly between 10% and 90%. The optimized assignment scheme suggests that the cotravel itinerary among passengers from high-risk and low-risk areas should be reduced, as well as passengers with long- and short-distance trips. Sensitivity analysis shows that our model works better when the incidence is higher at downstream or low-flow stations. Increasing the number of cars and car service capacity can also improve the optimization effect. Moreover, the model is applicable to other epidemics since it is insensitive to the Wells–Riley equation parameters. The results can provide a guideline for railway operators during the post-COVID-19 and other epidemic periods.

Solution of an Economic Production Quantity model using the generalized Hukuhara derivative approach

In this study, an economic production quantity (EPQ) model with deterioration is developed where the production rate is stock dependent and the demand rate is unit selling price and stock dependent. The low unit selling price and more stocks correspond high demand but more stock corresponds to slow production because of the avoidance of unnecessary stocks. First of all, we develop the production model by solving some ordinary differential equations having deterministic profit function under some specific assumptions. Later, we develop the fuzzy model by solving the fuzzy differential equations using Generalized Hukuhara derivative. In fact, the differential equation of the model has been split into two parts namely gH(L-R) and gH(R-L) on the basis of left(L) and right(R) α- cuts of fuzzy numbers for which the problem itself is transformed into multi-objective EPQ problem. A new formula of aggregation of several objective values obtained at different aspiration levels has been discussed to defuzzify the fuzzy multi-objective problems. We solve the crisp and fuzzy models using LINGO software. Numerical and graphical illustrations confirm that the model under Generalized Hukuhara derivative of (R-L) type contributes more profit which is one of the basic novelties of the proposed approach.

Nurse Scheduling Optimation with Various Assignment Pattern at ABC Hospital Using Goal Programming Method

In fulfilling health services in hospitals, the availability of human resources (HR) which includes doctors, nurses, midwives, and so on, plays a very important role. In terms of amount and dominant existence in the hospital in providing health services to patients is a nurse. The role of hospital management in maintaining the availability of nurses is to plan a good schedule. Without a good resource scheduling plan, the services will not be optimal and the costs will hard to control. This research aims to optimize the nurse scheduling. Existing schedule did not pay attention to specific time that have different load to another. Management feels that a lot of idle time is experienced by some nurses. Therefore, from the data that occurred in the past there will be observations that every 4 hours will occur how many services performed and how many nurses needed. Furthermore, by using Goal Programming method, several priority objectives are made, such as how to minimize the deviation of nurses needed in one shift or slot. Then how to minimize the excess target number of nurses who work in one week. And then minimize the excess number of nurses who work on the night shift. The suggested mathematical model has been implemented using Lingo Software. Work patterns have been suggested to improve schedules quality based on different load of services that occur in specific time. The suggested approach can be used for any similar staff scheduling problem in the next research.