# Soft Computing Techniques for Boolean Function and Reliability-Based Approach of Blood Bank Supply Chain Management with Distribution Center Using Vector-Evaluated Genetic Algorithm

SRM Institute of Science and Technology

Anupam Swami

Navin Ahlawat, Dhowmya Bhatt and Tripti Pandey

SRM Institute of Science and Technology

## Role of “Mathematics” in Blood Bank Supply Chain Inventory Models

“Mathematics” has been linked to camp control until the end of time. “Mathematics” is used in the majority areas of everyday existence. Companies make use of “mathematics” in the areas of “accounting, inventory, marketing, revenue forecasting, and financial analysis.” “Mathematics” translates to “patience, discipline, and problemsolving.” Since “mathematics” is not a recognized science, other than the basis of almost all other subjects, mathematical rules have a very stable purpose. There have been cases in which management decisions have been considered very successful, but when they have been tested on the basis of “mathematics,” they have been quite flawed. These save the organizations from jumping into the incorrect car and wasting time and money. Therefore, it is very important that every decision made is accurately measured by mathematical tests. Only then can we ensure that the decision is valid. If a decision is based on the theoretical foundations of an organization and the recognition of mathematical aspects, it should gain the confidence of organization. Some people may think that the solutions provided by mathematical tools are also unsatisfactory because they consider a very ideal set of circumstances which one does not encounter in real life. However, under these situations, it can be argued that assumptions are considered too ideal, although sensitivity analysis provides a way to predict model behavior when circumstances change under ideal conditions.

If compassion psychoanalysis also indicates that the explanation is relatively unwavering, then the clarification can be considered quite accurate and feasible. With the onslaught of nonautomated inventory calculation techniques, we comprise the added improvement of moving away on or after unchanging and unbending assumption. Computerized techniques allow us to choose an acceptable solution instead of finding the optimal solution. Using computerized techniques, we can move away from reality and use satisfactory values for all parameters of the organization. In this way, “mathematics” evolved faster into the reality of noncomputer computing technologies. In view of the rapid progress in all fields of science, day- by-day theories and methods are evolving very fast. The theory related to this is rapidly upgraded. The state of “mathematics” in current affairs is that of the adviser who sets the guiding principle for others. The tools and techniques of this science are evolving little by little, which provide an improved performance space for further hypothetical and practical study expansion. Scientists and researchers want to learn more about the complexity of this science so that newly discovered terrains can serve as a guide for the whole human being. Since the emergence of those who strive to improve the quality of life, “mathematics” has been a very stable and loyal friend.

## Blood Collection and Processing

A blood bank is an institution that “collects,” “tests,” “processes,” and “stores the blood” and its mechanism for future use. The blood bank's main functions are to make arrangement and demonstrate the collection of blood and its system. The main goals of a blood bank are to ensure that there is sufficient blood for patients required for blood transfer and to make sure the waste of blood products is minimized. The blood supply to a particular blood bank comes from expeditions and blood camps. “Donors who come to the bank and donate blood are other sources of supply.” Many large blood banks collect their blood from blood banks’ shares and donations. Blood is collected and stored in plastic bags that contain anticoagulant solutions. “Blood is collected by donation and stored in plastic bags, often called whole blood (WB).”

A blood bank can also break the blood collected in camps. A single empty bag is used to store WB, whereas a third empty bag is used to collect blood that must be separated into the apparatus. The triple blood bag is a system consisting of a main blood bag and several connected satellite bags to assemble the system. To separate the different mechanisms, a triple/quad blood bag is centrifuged in a high-speed centrifuge. Due to centrifugation, several layers in the main bag diverge according to their density. The lightest component, plasma, is precipitated in the upper layer, followed by platelets in the center and red blood cells (the heavier ones) at the bottom. This mechanism can be emptied from the main bag to their respective satellite bags, when the layers are separated. Since white blood cells in the patient's body can cause many complications, some modern blood bags are equipped with leukocyte reduction filters. These filters eliminate most leukocytes that otherwise differentiate with red blood cells. Individual blood bags are very popular in quadruple pocket blood banks with capacities of 350 and 350 mL, as well as 450 and 500 mL. The main advantage of dividing the WB into plasma is that only the necessary plasma can be provided to the patient.

## Genetic Algorithm

A genetic algorithm was developed by Holl and colleagues in the 1960s and 1970s. Genetic algorithms are based on the theory of evolution, which explains the origin of species. In nature, vulnerable and unsuitable species in their environments are at risk of extinction through general selection. In the language of genetic algorithms, a solution vector x € X is called an individual or chromosome. Chromosomes have individual units called genes. One or more properties of each gene wheel chromosome. The first implementation of the genetic algorithm by Holl and colleagues assumes that genes are binary numbers. Later implementations introduced different types of genes. Typically, the chromosomal solution space contains a singular solution x. For this, a mapping system between solution space and chromosomes is required. This assignment is called coding. In fact, genetic algorithms work to code a problem, not the problem itself, but a collection of chromosomes, a population. Population is usually randomly initiated. During the research, the population includes both inclusive facilities and installation solutions, which means that they dominate the same solution.

Holland also provided a convergence record (schema set) for the global optimum, which has chromosomal binary vectors. Genetic algorithms use two operators to generate new solutions from existing solutions: crossover and mutation. The crossing operator is the most important operator of the genetic algorithm. At the crossroads, two chromosomes, called parents, are usually combined into new chromosomes, called lineages. The parents are chosen from existing chromosomes in the population, in which fitness is preferred, so that the offspring get good genes, which will make the parents fit. As a result of repeated application of the crossing operator, the population contains a large number of chromosomal genes, which ultimately leads to a globally satisfactory solution for marble industries. The mutation operator introduces random changes in chromosome properties. Mutations are usually applied at the level of the gene. In specific genetic algorithm implementations, the mutation rate (the probability of changing the properties of a gene) is very small and depends on the length of the chromosome. Therefore, the mutated chromosome is not very different from the original one. Mutations play an important role in genetic algorithms.

## Literature Review

Yadav and Swami [1, 2] presented an integrated supply chain model for the degradation of basic products with an adapted linear demand and in a climate of disruption and inflation and a constraint varying in time for a model and the portion size of the female stock. Yadav et al. [3-6] introduced a supply chain warehouse for the expiration of two stocks and inflation and proposals for an inventory model for the deterioration of two stocks and goods with varying costs and deterioration and discussed the analysis of green supply chain inventory management for warehouse storage and environmental collaboration using a genetic algorithm and sustainability performance using a genetic algorithm. Yadav and Kumar [7] demonstrated the management of the supply chain of electronic components for storage in collaboration with the environment and neural networks. Yadav et al. [8-10] examined the effect of inflation on a two-stock commodity stock, which was exacerbated by changing needs and shortages and discussed a model of inventory, which was inflationary for the deterioration of goods in two-inventory systems and proposed an obscure store nonmerchandise model before temporarily deteriorating the goods with a conditional late payment permit. Yadav [11] analyzed supply chain management in optimizing warehouses with logistics using the genetic algorithm. Yadav et al. [12, 13] explained the inventory model for two bearings with optimized soft IT functionality. Yadav [14] explained the modeling and analysis of the supply chain inventory model with two- stage economic transfer problems using the genetic algorithm.

## Blood Supply Chain

The delivery of a blood collection center is almost identical to the other logistics. The blood is exported to blood storage facilities through a procedure of manufacture and wrapping at a blood center. A shipping technique is strong-minded by the individuality of the individual blood collection sites. Figure 2.1 shows a supply chain process of the blood collection chain.

FIGURE 2.1 Blood supply chain.

Blood banks are divided into recommendation types and universal types. A blood bank can buy blood from blood centers and the medical clinic of the blood bank. However, a receipt must be distributed in the form of prescription blood. Blood storage devices communicate blood collection point policy to the blood center or clinic according to the sharing strategy. These last procedures differ according to the types of blood collection sites. In exacting, the distributor should inform the government of the provision and buy and make use of therapeutic blood collection sites. The blood distribution center manages the patient’s chemical blood collection sites, such as injections or mixtures. In blood collection stores, prescriptions or generic blood collection points are sold in accordance with the regulations. This process allows blood to be donated to the last hospital in the blood bank.

## “Boolean Function Approach for Reliability” of Blood Banks

In this chapter, the author considers blood banks. The entire organizations consist of six main parts. The first part of the scheme is blood collection sites and is represented by Dr The second part of the system is the blood center and is represented by D2, D„ and D4. The third part of the system is processing blood storage facilities and homogenizing the blood and is represented by D5. The fourth part of the system is the blood delivery center and is represented by D6. The fifth part of the system is the blood bank’s physician clinic. This means that the blood is poured into coated paper cartons or plastic bottles. It is sealed and is represented by D7. The last part of the scheme is the delivery to a hospital of banked blood. This means that blood cans or bottles are kept in defensive delivery containers and kept cool. They are delivered in cooled trailers to warehouses and then sent to individual hospitals, where they are housed in cases of cooling performance and are represented by Dl().

## Formulation of the Model

By using Boolean algebra, the condition of efficiency of the successful operations of these blood banks in terms of logic matrix is expressed as under:

By using laws of algebra of logics, equation (2.1) may be written as: where

Using orthogonalization algorithm, equation (2.3) may be written as:

Using all these values in equation (2.8), one can obtain:

Using this result in equation (2.2), we have:

Since RHS of equation (2.12) is the disjunction, the reliability of considered blood banks is given by:

The appearance for M.T.T.F in this case is given by:

## Simulation

A simulation blood collection site is to compare and verify the list management of the blood storage facilities in the supply chain. A virtual system comprises ten blood centers, bulk, ten blood distribution centers, and 55 blood collection sites stores. Table 2.1 shows 55 blood collection sites parameters for simulation.

The simulation of the supply chain was approved out with each organization method over 700 near days. We obtained results by calculating the sum of the 5000 executions of the simulations. To evaluate each method of managing blood stocks, we contrast sale prices, sale account, order number, delivery cost, share price, and net profit. Equation 2.10 describes the calculation of distribution costs, share price, and net income (Table 2.2).

TABLE 2.1

Product Parameter Blood Bank Supply Chain

 Product Max BIC Minimum Required BIC Initial Bl Price Demand (%) BBC1 8.0 2.0 13 216 45 BBC2 7.9 2.1 21 222 55 BBC3 7.8 2.9 31 223 65 BBC4 7.6 2.8 41 224 17 BBC5 7.9 2.7 51 225 47 BBC6 7.7 2.6 61 226 53 BBC7 7.6 2.5 71 227 57 BBC8 6.5 2.1 81 228 96 BBC9 6.6 2.2 23 221 87 BBC10 6.1 2.7 12 242 75

TABLE 2.2

Simulation Result Blood Bank Supply Chain

 Product Blood Sale Price Blood Sale Account Blood Order Count Blood Delivery Cost Blood Stock Price Blood Net Profit VOQBB 931 742 735 119 776 225 TOQBB 932 741 732 119 923 229 DOQBB 933 741 736 118 840 228 VEGA 938 741 731 119 665 226 Total average 934 741 737 119 851 224

## Conclusion

This chapter studies the effectual method of managing a list of blood storage facilities in the supply chain of blood collection centers. We study the supply chain of blood collection site and take out modeling and simulations. We have a residential supply chain network optimization model to run the “delivery, testing, processing, and distribution of a perishable product based on human blood.” The unique aid in this chapter includes the operational model of blood chain management, w'hich presents the extraordinary features of capturing the feasibility of this product that saves lives from side to side w'ith the use of curve multipliers. It includes the costs of squander disposal/disposal. It assesses the costs of bottlenecks and surplus at demand points and quantifies supply-side supply risk. A list policy is an important factor in determining the order time and quantity. It is also important to manage the optimal benefits of the supply chain. Therefore, to increase profits, a trade-off between consumption and control has to be reduced. This letter proposes list strategies using the vector-evaluated genetic algorithm (VEGA). The proposed VEGA calculates the optimal order from the existing stock at the expected standard time. We compare blood bank order quantity (VOQBB). blood bank order (TOQBB) volume, blood bank disposal order (DOQBB) quantity, bank order quantity of bank of blood (EQEBB), and the VEGA. The results of the simulations show' the effectiveness of the orders related to the remaining orders and the order quantity specified. The algorithm for the VEGA fulfills both conditions. The supply chain of the blood collection site is a useful method for managing list rules for blood storage facilities. The limitations of this study are as follows. It is difficult to think of the number of blood distribution centers and blood. Apart from this, we did not reflect the features of the demand.

## References

• 1. Hsieh, T.P., Dye, C.Y. and Ouyang, L.Y. (2008): Determining optimal lot size for a two- warehouse system with deterioration and shortages using net present value. European Journal of Operational Research, 191 (1). 180-190.
• 2. Benkherouf, L. (1997): A deterministic order level inventory model for deteriorating items with two storage facilities. International Journal of Production Economics, 48 (2), 167-175.
• 3. Yadav, A.S. and Swami, A. (2018): A partial backlogging production-inventory lot-size model with time-varying holding cost and Weibull deterioration. International Journal Procurement Management, 11 (5), 639-649.
• 4. Yadav. A.S. and Swami, A. (2018): Integrated supply chain model for deteriorating items with linear stock dependent demand under imprecise and inflationary environment. International Journal Procurement Management, 11 (6), 684.
• 5. Bhunia, A.K. and Maiti, M. (1998): A two-warehouse inventory model for deteriorating items with a linear trend in demand and shortages. Journal of the Operational Research Society, 49 (3), 287-292.
• 6. Goswami, A. and Chaudhuri, K.S. (1992): An economic order quantity model for items with two levels of storage for a linear trend in demand. Journal of the Operational Research Society, 43, 157-167.
• 7. Lee, C.C. (2006): Two-warehouse inventory model with deterioration under FIFO dispatching policy. European Journal of Operational Research, 174 (2), 861-873.
• 8. Sahooa, L., Bhuniab, A.K. and Kapur, P.K (2012): Genetic algorithm based multiobjective reliability optimization in interval environment. Computers & Industrial Engineering, 62. 152-160.
• 9. Yadav, A.S. and Swami, A. (2019): A volume flexible two-warehouse model with fluctuating demand and holding cost under inflation. International Journal Procurement Management, 12(4), 441.
• 10. Yadav, A.S. and Swami, A. (2019): An inventory model for non-instantaneous deteriorating items with variable holding cost under two-storage. International Journal Procurement Management, 12 (6), 690.
• 11. Yang, H.L. (2004): Two warehouse inventory models for deteriorating items with shortages under inflation. European Journal of Operational Research, 157, 344-356.
• 12. Zhou, Y.W. and Yang, S.L. (2005): A two-warehouse inventory model for items with stock-level-dependent demand rate. International Journal of Production Economics, 95 (2), 215-228.
• 13. Yadav, A.S.. Taygi, B.. Sharma, S. and Swami, A. (2017): Effect of inflation on a two- warehouse inventory model for deteriorating items with time varying demand and shortages. International Journal Procurement Management, 10 (6), 761.
• 14. Yadav, A.S. (2017): Modeling and analysis of supply chain inventory model with two- warehouses and economic load dispatch problem using genetic algorithm. International Journal of Engineering & Technology (IJET), 9 (1), 33-44.