IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 207 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 AN AHP-BASED OPTIMAL DISTRIBUTION MODEL AND ITS APPLICATION IN COVID-19 VACCINATION Arpan Garg Research Scholar; Dept. of Mathematics & Scientific Computing National Institute of Technology, Hamirpur, India arpan1996garg@gmail.com Y D Sharma Professor & Head; Dept. of Mathematics & Scientific Computing National Institute of Technology, Hamirpur, India yds@nith.ac.in Subit Kumar Jain Assistant Professor; Dept. of Mathematics & Scientific Computing National Institute of Technology, Hamirpur, India Jain.subit@nith.ac.in ABSTRACT COVID-19 is causing a large number of causalities and producing tedious healthcare management problems at a global level. During a pandemic, resource availability and optimal distribution of the resources may save lives. Due to this issue, the authors have proposed an Analytical Hierarchy Process (AHP) based optimal distribution model. The proposed distribution model advances the AHP and enhances real-time model applicability by eliminating judgmental scale errors. The model development is systematically discussed. Also, the proposed model is utilized as a state-level optimal COVID-19 vaccine distribution model with limited vaccine availability. The COVID-19 vaccine distribution model used 28 Indian states and 7 union territories as the decision elements for the vaccination problem. The state-wise preference weights were calculated using the geometric mean AHP analysis method. The optimal state-level distribution of the COVID-19 vaccine was obtained using preference weights, vaccine availability and the fact that a patient requires exactly π‘Ÿvaccine doses to complete a vaccination schedule. The optimal COVID-19 vaccine distribution along with state and union territory rank, and preference weights were compiled. The obtained results found Kerala, Maharashtra, Uttarakhand, Karnataka, and West Bengal to be the most COVID-19 affected states. In the future, the authors suggest using the proposed model to design an optimal vaccine distribution strategy at the district or country level, and to design a vaccine storage/inventory model to ensure optimal use of a vaccine storage center covering nearby territories. Keywords: COVID-19; vaccine distribution model; AHP; MCDM; risk assessment mailto:arpan1996garg@gmail.com mailto:yds@nith.ac.in mailto:Jain.subit@nith.ac.in IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 208 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 1. Introduction In early December 2019, the first active human COVID-19 (Corona virus disease) case was officially identified in Wuhan city, Hubei province, China (WHO situation report– 94). On January 30, 2020, the World Health Organization (WHO) declared COVID-19 with its exponential rate of increase and zoonotic nature, an international public health emergency (WHO situation report –11). On February 18, 2021, only 1 year and 3 months after first being identified, COVID-19 had infected around 110 million people worldwide. A sobering statistic shows that out of 87,769,856 cases, 2,441,043 or almost 3% have died. (Worldometer, 2020). Currently, this pandemic has affected 219 countries and 2 international conveyances. Many government organizations, universities, and independent institutions are investing a very large amount of money, time, and man- power in research to ensure the creation of a scientifically sound and safe treatment or vaccine for COVID-19. Vaccines can be divided into a number of different types such as live attenuated vaccines (LAV), inactivated virus vaccines, sub-unit vaccines, viral vector-based vaccines, DNA vaccines, and mRNA vaccines (Kaur & Gupta, 2020); however, they all work on the same principle of stimulating the immune response to recognize a disease-causing organism. According to the WHO (steps in vaccine development), a vaccine candidate has to clear pre-clinical studies (including studies on animals for efficiency and safety), phase-1, phase-2, phase-3, and post-marketing surveillance studies to ensure complete vaccine development. The COVID-19 pandemic has produced a number of healthcare issues including not only finding an efficient vaccine, but determining an optimal distribution strategy as well. A pandemic response using a vaccine requires a systematic solution for vaccine i) development ii) production, and iii) distribution. For the first step, according to WHO, a number of vaccine candidates from all over the world are in various clinical stages (subdivided into phase 1, Β½, 2, and 3), and some have shown promising outcomes in the human trials (WHO draft-landscape,2021). The second step of the program includes the production of a clinically sound vaccine. Since, the most advanced and cutting-edge production strategy is needed to fulfill the global requirements for COVID-19 vaccines, many alliances among various biotech companies have been formed to advance vaccine production (Lancet, 2020). The final step of the program requires an answer to the question; what is the optimal distribution plan? The Ministry of Health and Family Welfare, in India has issued operational guidelines (2020) for phase-1 vaccine roll out, and plans to sequentially vaccinate about 10 million healthcare workers, 20 million frontline workers, and around 270 million people above 50 years of age. The phase-1 roll out (2021) of the COVISHIELD (viral vector vaccine) and COVAXIN (inactivated virus vaccine) vaccines in India started in January 16, 2021. Both COVISHIELD and COVAXIN need 2-doses to complete the vaccination schedule. Since, an inactivated virus type vaccine requires booster shots to maintain immunity (Kaur & Gupta, 2020), those receiving COVAXIN will need an additional booster dose to complete the vaccination schedule. The authors observed that the production of the COVID-19 vaccine would definitely fall short of the global requirements Hence, the need for an optimal COVID-19 vaccine distribution strategy is an expected multicriteria decision-making (MCDM) problem in the near future due to the availability constraints and multiple dose requirement of the COVID-19 vaccine. IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 209 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 While searching for a solution to the state-level vaccine distribution problem, the authors found a popular MCDM problem-solving tool known as the AHP. The AHP methodology was introduced by T.L Saaty (1977, 1990, 2003) to solve real-time complex MCDM problems. The application of the existing AHP model can be defined as a five- step procedure (Rosenbloom, 1997). The easy to apply systematic AHP model has a large domain of applications, including supply chain management, construction, healthcare management, safety sciences, risk assessment and many other non-mathematical fields. Recently, we have observed the presence of various mathematical theories (Mishra et al., 2020) in COVID-19 research. The AHP has been useful in solving various healthcare policy issues including a number of management issues due to the COVID-19 pandemic. Mohammed et al. (2021) applied AHP methodology to propose a convalescent plasma transfusion intelligent framework for COVID-19 patients, and Garg et al. (2020) conducted a COVID-19 risk assessment considering the ease in lockdown restrictions and population density of various activities. Moreover, Halder et al. (2020), Improt et al. (2019), Corvinet et al.(2020),and Hezametal et al. (2021) have applied the AHP to deal with various health care management issues. The authors observed that the AHP is an efficient MCDM technique with less computational requirements than most methods that can be utilized to develop a multi- purpose distribution model resulting in significant advancements. The AHP uses Saaty’s fundamental scale (Saaty, 1990) to collect pairwise comparison responses from different respondents, and to construct a pairwise comparison matrix (PCM). Therefore, the outputs are highly dependent on the data collection and human responses. Moreover, the solution strategy for a real-time distribution problem using the AHP provides no possible way to use human responses. This methodological issue can be solved by replacing the verbal scale with a well-defined mathematical expression that helps produce an unbiased PCM for the vaccination model. Therefore, the authors have developed a more dynamic AHP-based distribution model that has some significant improvements over the existing AHP model. In the present article, the authors have proposed an AHP-based multipurpose optimal distribution model. The proposed model is used to determine an optimal distribution strategy for the COVID-19 vaccine for 28 Indian states and 7 union territories (U.Ts). It can be used for limited, but varying, vaccine availability and can be generalized for large or small territorial areas. Moreover, the authors have also identified and discussed various healthcare management applications of the proposed distribution model. The work presented in this article is divided into four sections. The first section provides a general introduction to the vaccine distribution problem and the AHP procedure. In the second section, the authors have developed an AHP-based multi- purpose distribution model. The third section includes the results and discussion, in which the proposed model is applied with the COVID-19 data to provide an optimal state-level COVID-19 vaccine distribution strategy in India. In the last section, the conclusions are discussed and the future scope of the proposed model is presented to researchers and various policy makers for the use of AHP to solve heath care management issues. 2. AHP distribution model development An ethical vaccine distribution model must be free from human bias that might favor people based on region or religion, or include possible methodological errors resulting from a human judgmental scale. However, the distribution model must be able to compile IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 210 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 the heterogeneous effects of a number of factors to the degree of importance present among the decision elements. The authors have proposed an AHP-based optimal distribution model, along with required advancements, in a systematic manner as given below: 1. Hierarchy structure: The first step in this model includes identifying a finite number of decision elements, and then defining the distribution problem into a hierarchy structure of decision elements (Saaty, 1987). 2. Decision element coefficient(𝑅𝑖 ): The decision element coefficient(𝑅𝑖 )value for the π‘–π‘‘β„Ž decision element, compiling the combined effect of various heterogeneous factors, is defined as 𝑅𝑖 = βˆ‘ 𝑀𝑗 𝑗 βˆ— π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘— where βˆ‘ 𝑀𝑗𝑗 = 1, and 𝑀𝑗 represents a justified weight assigned to the 𝑗 π‘‘β„Ž factor. The general computation formula 𝑅𝑖 is designed to include the effect of a finitely large number of important factors for the problem into the model. The proposed strategy for addressing a large number of factors, including those accountable for small but significant preference variation, may help improve the real-time applicability of the model. 3. Pairwise comparison matrix (PCM): The proposed model uses the mathematical function, 𝑓: 𝑆 β†’ 𝑅+ defined over the set 𝑆 of all possible pairs of decision element coefficients to the set 𝑅+of positive real numbers, such that 𝑓( 𝑅𝑖 , 𝑅𝑗 ) = 𝑓𝑖𝑗 = 𝑅𝑖 𝑅𝑗 ⁄ βˆ€ 𝑖 π‘Žπ‘›π‘‘ 𝑗. for pairwise comparison of decision elements to construct the required PCM [𝑓𝑖𝑗 ]𝑙×𝑙 . Mathematically, the pairwise comparison function 𝑓,with 𝑓𝑖𝑗 . π‘“π‘—π‘˜ = 𝑅𝑖 𝑅𝑗 . 𝑅𝑗 π‘…π‘˜ = 𝑅𝑖 π‘…π‘˜ = π‘“π‘–π‘˜ ensures perfect consistency (Saaty, 2003) of the PCM that eliminates any potential conflict over the selection of a particular AHP analysis method. Also, replacing the linguistic judgment scale from a well-defined mathematical function 𝑓, leads to the elimination of human bias. 4. Preference weight𝑠(𝑣𝑖 ) and ranking: The preference weight values(𝑣𝑖 ) can be calculated using the suitable AHP analysis method. However, the model provides a complete choice for selecting a suitable AHP analysis method; the authors used the geometric mean method (GMM)(Crawford & Williams, 1985) to calculate the preference weight values(𝑣𝑖 ). The presented model can be utilized as an efficient AHP-based MCDM problem solving tool and as a multipurpose optimal distribution model. Further, the model is designed to IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 211 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 calculate an optimal state-level distribution strategy for COVID-19 vaccines. The additional steps required to develop an optimal state-level distribution model are given below. 5. Optimal vaccine distribution: The optimal vaccine distribution for the π‘–π‘‘β„Ž state with total vaccine availability 𝑉, and the fact that a patient requires exactly π‘Ÿ vaccine doses along with ensuring state-wise homogeneity is defined as π‘Ÿ. ⌊ 𝑉.𝑣𝑖 π‘Ÿ βŒ‹ ; where, ⌊ βŒ‹is greatest integer function. The vaccine distribution formula uses the greatest integer function to obtain distribution optimality by avoiding state- level redundant overlapping of vaccine doses (i.e. vaccine doses left that are not sufficient for single patient treatment). 3. Results and discussion The proposed vaccine distribution model is explained as a five-step procedure. Since COVID-19 is transmitted via human contact (Chan et al., 2020), it is commonly thought that highly populated countries will suffer the worst from COVID-19. Therefore, the authors have utilized this distribution model to create an optimal vaccine distribution strategy for the world’s second most populated (1.39 billion) and seventh largest country, India) (Population of India, 2021). The proposed model was applied for all states and U.Ts, excluding Lakshadweep, to determine an optimal vaccine distribution strategy for the COVID-19 vaccine using the reported COVID-19 data as of January 15, 2021(Covid19india, 2021). For the first step, the model used 28 Indian states and 7 U.Ts as decision elements for the problem. The hierarchy structure of the state-level optimal vaccine distribution problem was defined by placing all 35 decision elements as alternatives of the study at the second hierarchy layer, and the problem to select a state or U.T receiving the largest vaccine lot was placed at the first hierarchy layer (Figure1). Figure 1 Hierarchy structure of the vaccine distribution problem IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 212 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 The authors observed that for a country like India, that covers a large territorial area and is sub-divided into a number of states and union territories (U.T) that differ from each other in size, population, density, health care facilities and medical staff availability etc., it is important to consider a measure of healthcare efficiency heterogeneity among the states/U.Ts. Since the lack of healthcare facilities and medical staff availability during the pandemic resulted in a higher number of deaths, these figures along with the number of active COVID-19 cases are considered critical factors for a vaccination model to a degree of significance to calculate the risk coefficient value relating to a state/U.T. For the second step in formulating an optimal COVID-19 vaccine distribution model, the authors calculated the state risk coefficient (𝑅𝑖 ), considering the number of active COVID-19 cases(π‘Žπ‘– ), and the number of deaths(𝑑𝑖 ) reported in the 𝑖 π‘‘β„Ž state/U.T. The model application utilized two key factors for this problem, but it can also be generalized for future studies using several other factors such as the strength of the healthcare system and front line workers, pregnant women, condition of infected people, and population of senior citizens (individuals age >= 50). The globally reported 3% death rate influenced the authors to assign a weight of 0.03 to the number of deaths and 0.97 to the other factor, i.e., Ri = 0.97 βˆ— π‘Žπ‘– + 0.03 βˆ— 𝑑𝑖 . Also, all 28 states and 7 U.Ts in India were listed from 1 to 35 in alphabetical order with the number of active COVID-19 cases(π‘Žπ‘– ), number of deaths(𝑑𝑖 ) reported as of January 15,2021 (Covid19india, 2021), and the calculated state risk coefficient (𝑅𝑖 ) in Table1. IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 213 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 Table 1 State-wise reported COVID-19 data (Covid19india, 2021) and calculated 𝐑𝐒 value S.no (𝑖) State/Union territory Active (π‘Žπ‘– ) Death (𝑑𝑖 ) State Risk coefficient (𝑅𝑖 ) S.no (𝑖) State/Union territory Active (π‘Žπ‘– ) Death (𝑑𝑖 ) State Risk coefficient (𝑅𝑖 ) 1 Andaman and Nicobar Islands 22 62 23.2 19 Madhya Pradesh 6957 3746 6860.67 2 Andhra Pradesh 2199 7139 2347.2 20 Maharashtra 52152 50336 52097.5 3 Arunachal Pradesh 64 56 63.76 21 Manipur 436 365 433.87 4 Assam 1616 1066 1599.5 22 Meghalaya 161 144 160.49 5 Bihar 3981 1449 3905.04 23 Mizoram 89 9 86.6 6 Chandigarh 266 330 267.92 24 Nagaland 104 88 103.52 7 Chhattisgar h 6923 3544 6821.63 25 Odisha 1910 1951 1911.23 8 Dadra and Nagar Haveli and Daman and Diu 11 2 10.73 26 Puducherry 294 640 304.38 9 Delhi 2795 10732 3033.11 27 Punjab 2739 5485 2821.38 10 Goa 866 753 862.61 28 Rajasthan 5608 2744 5522.08 11 Gujarat 6750 4360 6678.3 29 Sikkim 163 130 162.01 12 Haryana 2184 2979 2207.85 30 Tamil Nadu 6299 12251 6477.56 13 Himachal Pradesh 767 951 772.52 31 Telengana 4442 1574 4355.96 14 Jammu and Kashmir 1428 1920 1442.76 32 Tripura 45 387 55.26 15 Jharkhand 1289 1049 1281.8 33 Uttarakhand 9581 8558 9550.31 16 Karnataka 8790 12158 8891.04 34 Uttar Pradesh 2406 1602 2381.88 17 Kerala 67492 3416 65569.7 35 West Bengal 7223 10026 7307.09 18 Ladakh 104 128 104.72 IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 214 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 Table 2 Optimal COVID-19 vaccine distribution for 𝒓 = 𝟐, πŸ‘ 𝒂𝒏𝒅 𝑽 = 𝟏. πŸ“, 𝟐, 𝟐. πŸ“ 𝒂𝒏𝒅 πŸ’. πŸ“ (in Lakh) with state preference weight and rank S.No (𝑖) State or Union Territory Preference weight (𝑣𝑖 ) Rank Optimal vaccine distribution with π‘Ÿ = 2 and Optimal vaccine distribution with π‘Ÿ = 3 and 𝑉 = 1.5 lakh 𝑉 = 2 lakh 𝑉 = 2.5 lakh 𝑉 = 4.5 lakh 𝑉 = 1.5 lakh 𝑉 = 2 lakh 𝑉 = 2.5 lakh 𝑉 = 4.5 lakh 1 Andaman and Nicobar Islands 0.000112362 34 16 22 28 50 15 21 27 48 2 Andhra Pradesh 0.01136795 16 1704 2272 2840 5114 1704 2271 2841 5115 3 Arunachal Pradesh 0.000308802 32 46 60 76 138 45 60 75 138 4 Assam 0.007746692 19 1162 1548 1936 3486 1161 1548 1935 3486 5 Bihar 0.018912875 12 2836 3782 4728 8510 2835 3780 4728 8508 6 Chandigarh 0.001297589 26 194 258 324 582 192 258 324 582 7 Chhattisgarh 0.033038492 7 4954 6606 8258 14866 4953 6606 8259 14865 8 Dadra and Nagar Haveli and Daman and Diu 0.000051967 35 6 10 12 22 6 9 12 21 9 Delhi 0.014689947 13 2202 2936 3672 6610 2202 2937 3672 6609 10 Goa 0.004177789 22 626 834 1044 1880 624 834 1044 1878 11 Gujarat 0.032344317 8 4850 6468 8086 14554 4851 6468 8085 14553 12 Haryana 0.010693051 17 1602 2138 2672 4810 1602 2136 2673 4809 13 Himachal Pradesh 0.003741466 23 560 748 934 1682 561 747 933 1683 14 Jammu and Kashmir 0.00698757 20 1048 1396 1746 3144 1047 1395 1746 3144 15 Jharkhand 0.006208009 21 930 1240 1552 2792 930 1239 1551 2793 16 Karnataka 0.043061051 4 6458 8612 10764 19376 6459 8610 10764 19377 17 Kerala 0.317567018 1 47634 63512 79390 142904 47634 63513 79389 142905 18 Ladakh 0.00050718 29 76 100 126 228 75 99 126 228 19 Madhya Pradesh 0.033227571 6 4984 6644 8306 14952 4983 6645 8304 14952 20 Maharashtra 0.252318511 2 37846 50462 63078 113542 37845 50463 63078 113541 21 Manipur 0.002101318 24 314 420 524 944 315 420 525 945 22 Meghalaya 0.000777285 28 116 154 194 348 114 153 192 348 23 Mizoram 0.000419421 31 62 82 104 188 60 81 102 186 24 Nagaland 0.000501368 30 74 100 124 224 75 99 123 225 25 Odisha 0.009256462 18 1388 1850 2314 4164 1386 1851 2313 4164 26 Puducherry 0.001474172 25 220 294 368 662 219 294 366 663 27 Punjab 0.013664497 14 2048 2732 3416 6148 2049 2730 3414 6147 IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 215 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 28 Rajasthan 0.026744517 10 4010 5348 6686 12034 4011 5346 6684 12033 29 Sikkim 0.000784646 27 116 156 196 352 117 156 195 351 30 Tamil Nadu 0.031372094 9 4704 6274 7842 14116 4704 6273 7842 14115 31 Telengana 0.021096769 11 3164 4218 5274 9492 3162 4218 5274 9492 32 Tripura 0.000267635 33 40 52 66 120 39 51 66 120 33 Uttarakhand 0.046254025 3 6938 9250 11562 20814 6936 9249 11562 20814 34 Uttar Pradesh 0.011535912 15 1730 2306 2882 5190 1728 2307 2883 5190 35 West Bengal 0.03538967 5 5308 7076 8846 15924 5307 7077 8847 15924 For the third step, the authors performed the pair wise comparison by 𝑓𝑖𝑗 = 𝑅𝑖 𝑅𝑗 ⁄ for every possible pair (𝑖, 𝑗); 𝑖, 𝑗 =1,2…35 using the calculated 𝑅𝑖 value. The computational work was done with Microsoft Excel and Statistical Software for Social Sciences (SPSS) to formulate a 35 order PCM [𝑓𝑖𝑗 ]. For the fourth step, the GMM (Crawford & Williams, 1985) was applied over the PCM[𝑓𝑖𝑗 ] to calculate the state and U.T preference weights (𝑣𝑖 ). For the fifth step, an optimal COVID-19 vaccine distribution was calculated, for π‘Ÿ = 2 with 𝑉 = 1.5, 2, 2.5 π‘Žπ‘›π‘‘ 4.5π‘™π‘Žπ‘˜β„Ž, and for π‘Ÿ = 3 with𝑉 = 1.5, 2, 2.5 π‘Žπ‘›π‘‘ 4.5 π‘™π‘Žπ‘˜β„Ž, using the mathematical formula π‘Ÿ. ⌊ 𝑉.𝑣𝑖 π‘Ÿ βŒ‹ as mentioned in step 5. When vaccine availability fell short of the requirement, an optimal distribution model, that was capable of ensuring homogeneity among the states and U.Ts for different 𝑉and π‘Ÿ values was required. It was found that the model saved a total of 34, 40, 30, 38 and 54, 54, 46, 48 vaccine doses from overlapping for π‘Ÿ = 2 with 𝑉 = 1.5, 2, 2.5 π‘Žπ‘›π‘‘ 4.5 lakh and π‘Ÿ = 3 with 𝑉 = 1.5, 2, 2.5 π‘Žπ‘›π‘‘ 4.5 lakh availability respectively, which are able to be reassigned. The integrated model outcomes including the optimal COVID-19 vaccine distribution for π‘Ÿ = 2,3 π‘Žπ‘›π‘‘ 𝑉 = 1.5,2,2.5 π‘Žπ‘›π‘‘ 4.5 π‘™π‘Žπ‘˜β„Žvaccine availability and the state preference weight(𝑣𝑖 ) are represented in Table2. 4. Conclusions COVID-19 is one of the most lethal pandemics ever faced by humankind, and is producing a large number of tedious management problems. Because of this, the authors observed that a multipurpose distribution model that is able to compile a large number of critical factors according to the requirements of a problem under study is required to deal with this problem. In this work, the authors developed an AHP-based multi-purpose distribution model to ensure optimal drug/vaccine distribution. The proposed model used a mathematical function for pairwise comparison to construct a PCM and eliminated any possible error caused by using linguistic judgment scales. It ensures perfect consistency to avoid any conflict that results from using different AHP analysis methods. Real-time distribution optimality was achieved by mathematically embedding the fact that exactly π‘Ÿ vaccine doses are required to complete a vaccination schedule for one patient; therefore, avoiding overlapping of vaccine doses in every state or U.T. IJAHP Article: Garg, Sharma, Jain/An AHP-based optimal distribution model and its application in COVID-19 vaccination International Journal of the Analytic Hierarchy Process 216 Vol. 13 Issue 2 2021 ISSN 1936-6744 https://doi.org/10.13033/ijahp.v13i2.863 The proposed model was applied in a systematic manner based on reported COVID-19 data for 28 Indian states and 7 U.Ts to provide an optimal distribution of limited COVID- 19 vaccine doses. The state and U.T preference weight values(𝑣𝑖 )were calculated using the geometric mean AHP analysis method (Crawford & Williams, 1985) and are ranked from 1 to 35 for a greater to lesser 𝑣𝑖 value. The computational results from the proposed model along with optimal vaccine distribution that was subject to varying vaccine availability(𝑉) along with state-wise preference weights and ranks are shown in Table 2. In the future, the proposed distribution model can be used as a multipurpose MCDM tool to solve various management problems due to its methodological flexibility. The model can be applied to design optimal vaccine distribution in smaller territorial areas such as at the district level within a state/U.T by considering districts as the decision elements of the problem, or at the vaccination center level within a city by considering vaccination centers as the decision elements of the problem. The model can also be generalized from the state level to the country level. Moreover, the distribution model is flexible enough to use varying vaccine availability or vaccine production capacity, and to provide an optimal vaccine distribution in milligrams or other SI units. The authors also suggest using the proposed model to design a vaccine storage or inventory model to provide optimal use of a vaccine storage center to cover nearby territories. 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