Queuing System with Inventory

In this research paper, a discussion of all operations carried by manufacturing firms significant in getting line balance. Nonetheless, to get higher job delegated to human resource and find if manufacturing proficiency growing revenue of businesses. The study will also evaluate the efficiency of catastrophe bonds for the financial management of hazards related to transport and infrastructure business (Rheinberger & Treich 2017). A detailed review on queuing inventory model with varied cases is discussed such as single server queuing systems with inventory, inventory systems with stochastic environment, with substitute flexibility and in production inventory. A transient solution for the queuing frameworks is found using a Bessel work belonging (Dharmaraja & Kumar 2015).

 Thus, the amounts of customers are determined in the system consistently. In-depth, the paper will evaluate their catastrophic threats and chances of that they spread and increase the magnitude of disasters (Pizzutilo & Venezia 2018). Measures to counter such problems are discussed vividly and decision approaches used in the research and direct budgetary view that explore various aspects of people’s views towards social threats. A regular audit on queuing models with various cases like Single Server, Queuing systems with Inventory, Queuing structure with stochastic condition, Queuing structures in profitability with and versatility, Queuing systems in progress stock, Queuing models with advantage stock. Creating limit strategy in the system work best in order to find a transient solution for the queuing strategies. The transient chances of estimating the number of customers in the system are realized in a growing order. The paper further gives detailed information about Catastrophe risk and chance that a fiasco risk can be identified as it spread in the recognized wavelength of disasters. In point of introduction, to contemplate from decision scenario, research has it that, the direct budgetary viewpoints explores workers views toward various social risks (Rheinberger, and Treich, 2017).

Introduction with Problem Statement

Over the last years, the research on queuing systems with inventory control has attracted the attention of many scholars. This system provides customers services time after the other providing them with continuous services they require. For the customer service to be complete, it requires data from the inventory thus, a customer who is served leaves the system immediately decreasing the on-hand inventory after the service is complete. The inventory is supplied with an outside supplier, this system is referred to as the queuing- inventory system. It is quietly different from the traditional as the attached inventory influences the service. The service may be interrupted when there is no inventory on hand. It is also different from traditional inventory management because the inventory is utilized at the serving rate than the customers arrival rate when customers’ are queued up for services.

 Khalili, et al. (2016) most of the multi-server queuing models Tackled in the literature assume the servers to be similar. However, the situation is not very realistic as it can prevail only when the service process very mechanically regulated. The assembly area is carried out by workers, hence; the system is human centered as its entire performance depends on human resources. Operating fuzzy queuing systems to analyze the number of income role in the projected queuing model was aimed at influence of research of queuing system. Some benefits over the conventional meeting line balancing representations. The correct measures and clarity of queuing systems theory from single margin, and varied records of queuing systems and additional the other side of the margin has strived to simple functions of the projected queuing model in a enormous diversity of industrialized circumstances around varied organizations (Khalili, Mohammadzade, & Fallahnezhad, 2016).

It is in history from the past decades, vital approaches have been used in including vested attention towards funding the projects to analyze queuing models with catastrophes. The concept of catastrophes happening without prediction has lead to declining of every client and there temporarily little support of the service facility waiting for the arrival of new customers as pre-emptied in different situations in the organization. The catastrophes could also arises from the environs of the designed structure or from other service position in the organizations (Dharmaraja, & Kumar, 2015). Catastrophes such as Quakes, storms, flooding, terroristic assaults, and avalanches cannot necessarily create or make harm spans, dams, control plants, railroads, thruways, harbors but can also cause a sensational reduction of incomes if the companies are hindered as an outcome of the event. Cat bonds have been presented and created with the point of presenting safety net providers of insurance and reinsurers a supplementary technique to direct their catastrophe risks (Pizzutilo, & Venezia, 2018). As such, fundamental idea is that a general population is trading off its own one of a kind decreased chances of possible cost cut down through disaster management thus providing a platform for decision making issues hypothetically by looking at it as how guy might construct a tradeoff between reduced use as against a lower probability of that person's own separately disastrous management (Rheinberger, and Treich, 2017). Then business scholars manage risks just like they manage perils, they also believe that development should be disaster oriented in an established measures.

Summary of the Literature

In general, literature review provides a production resources are categorized into three main categories including machinery, raw materials and operators (Karthikeyan & Sudhesh 2016). With an overview of the research done in the process of manufacturing process, much research has been done to plan resources, material and machine. Another ignored factor in the ancient the management of human resources especially when the company faces expensive equipments assembly line. Decision made in the end of human resource management are done in either long term planning which is essential to find the number of line operators, and short term (Karthikeyan & Sudhesh 2016). The study done by researchers have categorized into individual parts such as time study of operator and the right person in the right job position. As such, the time study deals with time of performing operation. Most studies have established operator’s assignments as problem is originally formulated as a mix integer programming problem thus, solved by heuristic algorithm (Adulyasak, Cordeau & Jans 2015). This minimizes the cycle time for manpower where they focus on Just in Time production systems. A mix integer is also applied as it helps in solving problems in manufacturing process in cellular systems which balances the workload among the cells to minimize the production cycle time. In the ground of using queuing model in production settings, much work is achieved as such; much research helps to record the power and accomplishment of vital inventory levels to improve the storage capability and the structural procedures. This approach with stock control has vested interest of many scholars over the span of last years. This structure initiates customers’ advantages as it carries out the true objective to meet the customers need. For the reason of its efficiency, it served customers rapidly from the structure and near to stock decay by an right now of organization culmination.                    

Analysis of Research Methodologies Found

Queuing systems with inventory derived stationary distribution of joint queue length and inventory processes in the explicit product form for various systems with inventory under continuous review and different inventory Management policies and with lost sales. In this case, demand follows distribution service times and lead times exponential distribution (Khalili, Mohammadzade & Fallahnezhad 2016). Queuing systems with the inventory under the (R, Q) policy and with lost sales in which the demands occurs according to poison process and service time are exponentially distributed. All customers arriving during stock out are lost (Kumar 2017). Assuming that the operators with varied skills existed in the industry and their aim was to minimize the cycle time with consideration of non-determined process. In solving the problems of operator assignment when time of operation was dependent on the operator. The major goals were to reduce the completion time (Khalili, et al. 2016). Dynamics such as management of human resource and using of stations and the rate of service for machinery then the effectiveness of machinery can improve. A simulation-based dynamic strategy for assignment of operator that considered problems such as set up time, work process, and interaction of operators with the machine and also considered the random conditions of production systems. This approach is presented in decision making based on data development analysis to determine the requirement number of operators in U-shape cellular manufacturing systems. Each decision made is evaluated using the simulation. Scholars in their study proposed a method for optimal assignment of human resource in the assembly line balancing with regards to the effectiveness of varied skilled operators.

 The approach provided a method of algorithm for problem solving during assigning operators to develop feasible solutions. Kumar, (2017) proposed the Fuzzy TOPSIS method was employed as a two way criteria decision making to solve operators assigning problems and they used both methods of hierarchical analysis of optimizing the weight criteria. The main focus was on the problem of optimizing assignment of multi-skilled operators in a production line and presented a mixed integer programming model. In the aim of using queuing models in production environments, much work has been done, but most of the research is about inventory control and achieving optimal inventory levels, Zade's optimizing storage capacity and the sequence of operations. This approach was presented as fuzzy queuing model with consideration of customer arrival capacity constraints, where the customer arrival rate and their service rate of were considered in the form of trapezoidal fuzzy numbers (Kumar, 2017).

The authors determined membership function using cut method and extension principle to solve linear programming method in order to determine the optimal parameters of the model. Parametric linear programming model for fuzzy queuing system were used in which service rate and arrival rate were both fuzzy (Khalili, Mohammadzade & Fallahnezhad 2016). The cut approach was used to determining the membership function and validation of the method in FM/FM/1 models, which is used in transportation management. Another article proposed a mathematical programming approach for machine interference problem in which some parameters were to show the performance of a bi-product supply chain, they consider a network including two M/M/1 queue for each type of products (Kumar, 2017). The supply is modeled with this approach thus computer measure of the system finds optimal supplier’s order size.

 The stochastic environment presented an inventory model combined with queuing theory and considered demand and lead time as stochastic parameters. Kumar, (2017) proposed the use of poison distribution for demands and exponential for production times in a single item make-to stock production systems and M/M/1 queuing system for modeling was introduced. Such approaches are great when addressed well because the inventory control of a multi-supplier strategy in a two level supply chain is applied. They are considered random as customers arrive and randomly delivered time for suppliers and represented the systems as a queuing network (Kumar, 2017). The use of queuing theory is represented in a stochastic model for the system as some assume that the lead time is negligible or it can be ignored in practice when it is short in contrast to other factors for some inventory production paper. Many researchers didn’t consider lost sales. However, considered the back orders as a rationale managerial policy.

Queuing inventory system with substitution flexibility was introduced as an application of queuing theory in inventory systems with substituting flexibility which improves profitability in many multiple product inventory systems (Karthikeyan & Sudhesh 2016). They prepared a comprehensive inventory model where an inventory system with two substitute’s products with ignorable lead time has been considered and simultaneous ordering has been examined properly. Karthikeyan & Sudhesh (2016) found that demands of customers for both products also resided as stochastic parameters and queuing theory used to contract a model of mathematics. They used a one way substitute system with two products which uses S-1, S policy. Another model was also used which consisted of two dimensional Markovia process to develop the approach where the aim was to find optimal order levels (Dharmaraja & Kumar 2015). Later on, there was an introduction of continuous level production rate with a base-stock level inventory.

The transient solution of Markova explains the heterogeneity of service which is a common feature of many real multi-server queuing situations (Dharmaraja & Kumar 2015). The services mechanism is invaluable as they schedule modules that allow customers to receive different quality of services. The role of quality and service performance is vital as they help customers’ perception and firms must dedicate much attention to them when designing and implementing their operations (Dharmaraja & Kumar 2015). As such, the queues with heterogenous servers have received a considerable attention in the literature. Many scholar use fuzzy queuing system for the performance analysis of a heterogeneous computing network. The queuing system considered in this Paper its application in call centre management. In a call centre, there is a natural tradeoff between minimizing customer wait time and family and fairly dividing the workload among agents of different skills levels. In the proposed method, is among best processes of all as the production or assembly line is modeled using fuzzy queuing models. Then, different scenarios of assigning operators to workstations are designed. Then, Khalili, Mohammadzade & Fallahnezhad (2016) suggested that fuzzy is calculated for each scenario using unconstrained fuzzy software programming method. Then, fuzzy data obtained from different scenarios are ranked using a fuzzy ranking method. The scenario with the maximum data is chosen as the best scenario of assigning operators to the workstation thus very appropriate. The decision concerning which agent should handle an arriving call when more than one agent is available thus, the routine policy considered is the paper is fastest server first.

 Centered on the observation, the transient result for the state probability of the heterogeneous multi-server Markovian queuing models for business is identified to catastrophes by outlining appropriate possibility generating function (Dharmaraja, & Kumar, 2015). Right approaches, to get the ideal some of operations delegated to the production line, authorities need to first resolve the number of machines that would be given to every worker sectors to ease the performance of the systems. The specialists can give more than two queuing systems to every worker; as such, each of these assignments allotments gives result in outlays and profits for the business. Therefore, for every case, the entire turnover purpose which contains revenue and expenses that result from the operation of that illustration evaluated properly hence allowing the average acquisition from assigning operators to the assembly line thus providing a solution to the system (Khalili, et al. 2016).

Analysis and Evaluation of the Problem

Pizzutilo & Venezia (2018) have noted that the frequency of natural and man-made disasters appears to increase over the past few decades especially during a given climatic and environmental changes. Currently, the world is experiencing the spread of geographical friction as a result of the rapidly growing population globally hence, resulting in financial loss in cases of catastrophes (Pizzutilo & Venezia 2018). As such, the risks cannot be neglected thus need attention to be managed carefully. A failure in such task creates a great loss if such events occur and dramatic difficulties in restoring the catastrophic economy. Traditionally, the insurance contracts concludes towards this end, nonetheless, the exceptional of losses relates to some catastrophic activities such as hurricane, earth quakes, terroristic activities and the this factors have driven insurance in the and reinsurance firms (Pizzutilo & Venezia 2018). Thus, the term catastrophe carries different meaning according to many people. It is therefore defined as a consequence focusing solely on the number of fatalities. In this case, all possible distributions of fatalities pertaining to one risky situation and propose an approach to rank the distribution in terms how relatively catastrophic of fatalities’ hence can help keep the expected number of risks across the situation. Catastrophic risks are characterized by low frequency but high severity of possible losses (Pizzutilo & Venezia 2018). However, it is pure risk that catastrophe does not occur. From a risk management perspective, the low frequency of occurrence means that it can be very difficult to estimate the occurrence and magnitude with high degree of accuracy and threat model usually employed for financial and operation risks. In this scenario, the term peril is any catastrophic event that the term hazard to any situation that can lead to the intensification of its outcomes. Catastrophe is generally assessed by its physical nature, social and economic severity measures to provide an estimate of the potential probability of damage (Pizzutilo & Venezia 2018). The complex problem related to the management of catastrophe risk is the estimate of the vulnerability of the potential losses. However, the vulnerability is a dynamic concept since the demographic and economic condition of the area changes drastically in relation a given period of time. Thus as for other financial and operation risks modeling catastrophe risk is the primary step in setting up the effective risk management measures. Pizzutilo & Venezia (2018) concluded that Catastrophe bonds are securities that allow the transfer to the financial market of the uncertainty surrounding the damage and losses of potential catastrophic events. Initially thought to deal with the need of insurance and reinsurance companies to reduce and manage their catastrophe exposure effectively, they have been successfully employed by nonfinancial companies operating in the transport and in the infrastructure industry as a supplemental and concurrent instrument to traditional insurance contracts (Pizzutilo & Venezia 2018).

The social choice of the empirical reviews the available evidence on attitude towards catastrophe risk (Rheinberger & Treich 2017). Such risk involves lives arising from the survey studies in which subjects evaluate risky social situations of the human lives. It is limited to factors such as it is hypothetical by necessity. A decision involves possibly many facilities which cannot be given incentives in the same way that economic experiment typically. Rheinberger & Treich (2017) highlighted some of the limitationsuc as the perspective of a social planner is influenced by most people as their decisions are vulnerable to various heuristic and biases as explored in the psychometric risk literature. It is also a subject of to consider the problem in isolation and to ignore the social cost of their decisions. In light of these limitations the whole of this survey is limited. Nonetheless, they provide a good starting point. The general picture that emerges from the summary is striking and most likely surprising as most of the studies is given evidence in flour of catastrophe accepting attitudes (Rheinberger & Treich 2017). A wide study has been done to elicit the various types of risks social choices have creating attitudes towards catastrophe risk. It is emphasis that most problems involve life and death of perspective to fewer 1000 people. Catastrophe is thus used in the technical sense of definition than in the colloquial sense of an apocalyptic threat.

Conclusion and Future Research Considerations

The paper has highlighted various ways to handle a range of queuing systems and catastrophe measures in the operation are in the organization. Various models such as how to determine optimal assignment of human resources to the assembly line was presented. IN this model assignment scenario was considered. Each of these scenarios were modeled using a queuing framework theory framework model. As such, the profit function including costs and revenue resulted from the implementation of each of these scenarios was determined considering that some of the problems were fuzzy. The sum of profits on the data which the risks of production set up is considered. Thence, these results remain valid, even if the initial data changes in the regular interval. Substantially, the solutions are presented in the research in a manner that they solve problems such as optimal assignment of human resources when they are experiencing uncertainty in the parameters. The research study also provides cases such as those which are not considered for future. The future suggestion is to close the model to the condition of real environment to consider different services rates for operators. Another suggestion is that of assuming the Markovian queuing model with the entry of the product to production line or serviced time of operation following a general distribution. It is clear that there are also some more high-tech cases of production that do not have full conformity with the conventional queuing models; thus, in these cases, it is recommended that a combination of simulation techniques and these models should be used for efficiency. Profit function for different scenarios is obtained as a fuzzy number thus it has to be applied for fuzzy prioritization techniques to select the best assignment. In this study, the use of triangular fuzzy numbers is reasonable approaches to deal with risks exist in manufacturing environment. It follows the results of the data analysis by which this method can provide additional information for the management to make decisions.

References

Adulyasak, Y., Cordeau, J. F., & Jans, R. (2015). The production routing problem: A review of formulations and solution algorithms. Computers & Operations Research, 55, 141-152.

Dharmaraja, S., & Kumar, R. (2015). Transient solution of a markovian queuing model with heterogeneous servers and catastrophes. Opsearch, 52(4), 810-826.

Karthikeyan, K., &Sudhesh, R. (2016). Recent review article on queueing inventory systems. Research Journal of Pharmacy and Technology, 9(11), 2056-2066.

Khalili, S., Mohammadzade, H., &Fallahnezhad, M. S. (2016). A new approach based on queuing theory for solving the assembly line balancing problem using fuzzy prioritization techniques. Scientia Iranica.Transaction E, Industrial Engineering, 23(1), 387-398.

Kumar, R. (2017). A transient solution to the M/M/c queuing model equation with balking and catastrophes. Croatian Operational Research Review, 8(2), 577-591.

Pizzutilo, F., & Venezia, E. (2018). Are catastrophe bonds effective financial instruments in the transport and infrastructure industries? evidence and review from international financial markets. Business and Economic Horizons, 14(2), 256-267.

Rheinberger, C. M., &Treich, N. (2017). Attitudes toward catastrophe.Environmental and Resource Economics, 67(3), 609-636.