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Sharia insurance is a type of insurance where the participants make a fixed contribution to a common pool in order to protect themselves against specific financial losses under an Islamic (Sharia) principle. The mudharabah model is one of the insurer's business models under an Islamic law that is frequently used in industry to manage the participant's fund in an exchange for a certain percentage of sharing investment profits. The purpose of this paper is to discuss the mathematical model and management of premium funds in a sharia life insurance based on a modified-mudharabah scheme. In this scheme, we add a fixed proportion of underwriting surplus as an extra compensation to the operator. In this study, we sampled participants aged 25, 45, and 65 years old by using the data from the 2019 Indonesian Mortality Table. Afterwards, we compared the operator's profit with regards to participants' age, gender, and compensation. Based on the numerical simulation, we noticed that as the participants' age increased, the operator's total profit decreased. Following that, we also noted that male participant policies generated lower profit than those for female. The difference in the operator's total profit in each gender group was wider during the last years of policy contract. Furthermore, we observed that there was a constant effect on the operator's profit when the amount of death benefit changed. [ABSTRACT FROM AUTHOR]

Many industries have adopted Automatic Guided Vehicles (AGV) into production lines such as automobile factories, food processing, woodworking, and other factories. Therefore, the problem of tracking the trajectory of the AGV system needs to be solved to meet the needs of the industry. The accuracy of a system model is strongly influenced by the completeness of the state in the dynamic system. So that, an estimator is needed to meet the state requirements that cannot be measured. We derive the mathematical model of Automatic Guided Vehicle (AGV) with some assumptions, so we can obtain the non-linear AGV trajectory model. Then, we discrete the non-linear model at first before estimating it with Ensemble Kalman Filter (EnKF) algorithm. In the simulation only two states out of five are observable, so we use observations on literal velocity and yaw rate of AGV system. We use RMSE to validate the accuracy of the EnKF algorithm. The simulation results show that the non-linear AGV model that has been derived can be estimated well with the EnKF algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model based on the influence of unmonitored asymptomatic individuals, vaccinations and individuals returning home to the spread of COVID 19. The concept used is that individual populations moves in 3 regions with each region having 1 interface or 1 connecting route. Individual movement is expressed by a weight function which in modeling use the Kernel density function in the normal group. The mathematical model obtained is in the form of a System of Integro-Partial Differential Equations consisting of 3 regional sub-models and an entire regional system model. Leipzig constant analysis was carried out in order to obtain model validation that was suitable for the phenomenon that occurred. [ABSTRACT FROM AUTHOR]

In this paper, the spread of the Covid-19 in.Indonesia is described by the SIRD epidemiological mathematical model. The mathematical model used in this paper is Susceptible, Infected, Recovered, Death (SIRD). The modified extended Kalman filter algorithm is applied to predict the spread of Covid-19 in.the future. We modified the algorithm by generating real data based on the previous estimation results. The real data generated from the generation is used at the correction stage to obtain prediction results in a fairly long period. Simulations were carried out with three types of mobility restrictions, namely mobility 100%, mobility 75%, and mobility 50%. Based on the simulation results, it can be concluded that mobility restrictions in Indonesia, which starts on September 4, 2020, can reduce the number of infected and death individuals and can increase the number of individuals who recover from Covid-19. [ABSTRACT FROM AUTHOR]

Inventory control problem becomes one of the most crucial parts in a company. Basically, the problem is to determine the optimal time and quantity of replenishment. But, there are many factors affected the decision such as demand uncertainty, lifetime of the product, deterioration, unit sales price and discount offered by the supplier. In this paper, we consider a mathematical model for inventory control problem. We consider a multi-item problem with inventory and price-dependent demand and all-units discount offered by the supplier. In dealing with multi-item problem, there are two replenishment policies to consider, individual order and joint order policy. Numerical examples are given with different inventory and price-dependent demand functions for each item and compare the individual and joint order policy. We found that in our numerical example, joint replenishment policy gives lower total inventory cost compared to the individual order policy. [ABSTRACT FROM AUTHOR]

Good and properly organized inventory management is essentially needed for a company in order to ensure that its production process runs smoothly. There are many factors to be considered since they can distract the inventory management such as demand behavior, the life time of goods, uncertain replenishment time, the political and economic situation, and unexpected natural disaster. There are certain risks involved with bulk replenishment such as the higher holding cost and the possibility of damage to the stored goods. On the other hand, if we order too little, the risks lie in the possibility that the production process will stop, resulting in lost sales due to the unavailability of goods. One strategy to overcome this unavailability of goods is backorder, where the customers will wait until the next replenishment to obtain their goods. This paper develops a mathematical model for inventory-dependent demand with the backorder policy applied. The decisions variables in our model are the optimal order quantity and the number of backorders, which minimize the total inventory cost. We also performed a sensitivity analysis of the optimal solution and found that the decreasing rate of the inventory is affected by the autonomous demand (α) and the increasing demand factor (β). Inventory will deplete faster as α and β increase. The number of backorders is affected by the high demand when inventory reaches zero and backorders entail a certain cost. When demand is higher and the backorder cost is relatively cheap, the number of backorders becomes higher. [ABSTRACT FROM AUTHOR]

The subprime mortgage crisis was a multinational financial crisis that occurred in 2008. The subprime mortgage is a program by the United States government to provide housing loans for borrowers with unreliable credit histories. The impact of the crisis highly influences the development of the financial market around the world, including Indonesia. The main focus of the research is to construct a simple mathematical model for mortgage financing, especially housing, which is based on Islamic laws. Rarely did previous studies discussed this matter, especially in Indonesia. The construction of the model depends on the contract (aqad) made. The contracts that will be discussed in this study are the murabahah and musharakah mutanaqisah (MMQ) contracts. In the MMQ contract, the ujroh (rental cost) is going to be determined by depreciation using the straight-line method. Based on simulation using the example of a real contract, the obtained rates of return achieved by the simulation with simple murabahah model is 17.84%, murabahah with an annuity of an installment is 11.4%, Islamic bank housing mortgage simulation application 12.19%, and MMQ is 6.87%. This result shows that the calculation involved in the contract should be observed carefully. [ABSTRACT FROM AUTHOR]

Elementary cellular automata (ECA) rule 184 can be used as mathematical models of traffic flows. The slow-to-start model is obtained from the ECA rule 184 model by taking time lag for restart into consideration and is represented by 3-state 3-neighbor cellular automata (CA). In the present paper, we propose a traffic model where vehicles following the slow-to-start rule and those not following the slow-to-start rule are mixed. This model, called the mixed slow-to-start model, is represented by 4-state 3-neighbor CA. Further, we introduce the vector representation of CA with the slow-to-start rule and with the mixed slow-to-start rule, and then get their corresponding fuzzy CA. These fuzzy CA provide continuous-valued traffic models with the slow-to-start effect. Comparing the fundamental diagrams of the the slow-to-start model, the mixed slow-to-start model, and their fuzzy counterparts, we investigate the influence of the density and the mixing ratio of vehicles on traffic jams. [ABSTRACT FROM AUTHOR]