INTRODUCTION:

After a certain time period, perishable products like pharmaceuticals, dairy, cosmetics, packed food, fruits, vegetables, etc. not retain their newness. Customers always demand fresh products over aged one. Perishable products based research is the very important and main topic for day-to-day life requirements. Fresh products attract the customer's demand and the aging of products is the decreasing factor for demand. Mostly pharmaceutical and cosmetic inventory systems consider the constant deterioration which is not in a proper way because the healthcare products' deterioration starts after a specific period of their era. The inventory management system is the set of policies and control the inventory level and obtain the optimal level which should be maintained, how long order should be and when the stock level should be refilled.

Therefore in pharmaceutical and cosmetic products based company usually keeps inventories like as raw material, spare and accessories, sample, promotional materials, packed materials, work in process, finished goods and stock of stationary.

This research work on inventory systems for pharmaceutical and cosmetic products survey-based study consists of three main parts. In the first part, we discuss the general introduction and a survey on Economic Order Quantity (EOQ) and Economic Production Quantity (EPQ) inventory model with its historical development form starting to present scenario. We discuss the fundamental mathematical model with constraints from the data and give some references to the practitioners, managers and new researchers to provide a bridge of the fissure between the inventory policy and practice. In the second part, we analyze the fuzzy-based EOQ and EPQ inventory system to investigate the result of crisp and fuzzy environment. Here we discuss the several extensions to the basic model with consideration of triangular fuzzy numbers. Finally in the third part we mentioned the some important method which is used to solve the fuzzy-based inventory system. Usually, the health care products are used according to their life time and their demand based on their freshness and availability. In the healthcare products, the quality is the first one key and second one its price, third one its freshness time period and many more. Due to temperature, environment, humidity, storage problems the Pharmaceutical and cosmetic products especially perishable products such as packed food, fish, eggs, vegetable and cosmetic, creams, oil etc. not maintain their fresh level of a long time. Planning and scheduling of Pharmaceutical and cosmetic products based companies is a very critical activity. In the present scenario, the demand management of any industry under the parameters of life time inventory product are very challenging to handle for smooth running business organization.

For any company the maintenance of inventory level, production efficiencies, service of manufacturing business, sales or whole selling or retailing business is very essential. The scientific method of determine the policies of maintaining the demand and supply of products and able to provide the right products at right time, in right numbers, in right price, and right place. For inventory model, the trend model is Economic Order Quantity (EOQ). The research work done by firstly regarding Economic Order Quantity (EOQ) for inventory system¹. The pharmaceutical and cosmetic products are perishables, so it is a key issue to be managed carefully the sales and production time. Therefore the pharma and cosmetic industry maintain the balance between the market demand, inventory level, and production quantity. The inventory management system as a key sector for industries². They discussed the inventory theory with its types and costs with fixed and probabilistic constraints. A lot of research work examined the inventory system with various inventory cost coefficient and constraints^3-12. The study of inflation and production based system assumed the exponential demand of the products under the variable deterioration rate¹³. For optimality, we want to indicate that the optimization techniques in the decision policy and the objective function^14-19. Some important research work related inventory system can be found in the mathematical model with time varying demand for the perishable products²⁰. The analyses and discussion of the literature review based on supply chain management with its types, method, applications in the decision making system²¹. The analytic solution to an inventory system and examined the inventory policy for perishable products with the optimal result²². Some of these techniques are computefor the optimal ordering policy for inventory system and their optimal objective function²³. The perishable products based inventory management system in which demand is considered as inventory level investigated²⁴. The research work done for a non-instantaneous inventory system for perishable products under the variable form of inventory cost coefficients²⁵. The mathematical system with variable sales revenue cost which is changing due to sessional products²⁶. They consideration in the research study with perishable products and variable demand rate for the product with maximum life time policy. The finest approach assumed for a sales revenue based system with time varying storage cost²⁷.

In realistic conditions, a good mangers always plan to minimize the total spending cost for the inventory system is called total inventory cost. For perishable products, it is very difficult to manage the exact quantity of products in case of price, demand and costs so these parameters are changing according to session, place, environment and temperature etc. So, in the uncertain condition, assumed the fuzzy parameters for demand, deterioration, inventory cost coefficients to obtain the optimal ordering quantity and optimal function for smooth running of any system. The fuzzy theory based inventory model provides the improved result and relevant in uncertain conditions in case of crisp inventory model. According to this phenomena, the researcher attracts to peruse their research work in fuzzy theory. In today’s world, the demand forms for the perishable product are generally very difficult to predict. Therefore the uncertainty of product demand leads to less profit for any business organization as a result may be in loss. Fuzzy theory-based inventory models with imprecise information have added significant focus in the last 50 years due to their enormous application in science, management, and engineering. Many researchers have studied and examined the fuzzy-based inventory model with vague information. A combination of fuzzy, rough, neural, neuro, and evaluation computation all are under the soft computing techniques^28-30. A comprehensive review and mathematical model on the fuzzy-based method for inventory control are discussed and have drawn more and more attention in fuzzy theory^31-34. In such cases one capacity also assume using the fuzzy approaches for inventory system^35-39.

Most of the inventory studies considered that the product demand rate was either constant or price sensitive but it’s maybe dependent on time, inventory level, production dependence, advertisement or multivariable etc. The important contribution in the development of fuzzy inventory model with the various inventory fuzzy coefficients and types of inventory costs with its effectiveness comparison to crisp environment^40-41. Anovel inventory model with fuzzy constraints are examined in an uncertainty environment^42-43. They used triangular fuzzy numbers for inventory cost coefficients and solved the inventory system in both environment crisp as well as fuzzy with signed distance method. Also investigated their comparison to demonstrate the fuzzy approach is provide the relevant and approximate result near to exact solution. The systematic solution of a fuzzy goal constraints developed an improved solution for fuzzy system⁴⁴. They consider the decision making concepts in fuzzy environment and the maximization decision is compressed the functional equation. The fuzzy approach for solving fuzzy inventory system and determine the optimal objective function and order quantity with inventory policy is investigated⁴⁵. Regardless of the specific product, many researcher discussed and illustrated the fuzzy approach for the inventory system. The inventory management system using Yager’s ranking method under the fuzzy demand as a trapezoidal fuzzy numbers to obtain the optimal function.

In the fuzzy environment, the inventory system with centroid method was investigated in which assumed the fuzzy lead time and the fuzzy demand⁴⁶. A fuzzy theory based inventory system with the help of trapezoidal fuzzy numbers and solution obtained by Kuhn-Tucker and Graded mean integration⁴⁷. A concept of fuzzy related to inventory system are presented⁴⁸. They can be used for fuzzy objective function with fuzzy constraints and solved with two method signed distance and centroid method and compare the both result of obtained optimal cost and optimal order quantity as a resultant. Another research work based category is obtaining the optimal ordering quantity. A decision on optimal ordering quantity to coordinate the inventory system with inventory policy^49-50. In this study, as usually seen in the real-life example, investigated a coordinate’s inventory model based on fuzziness and randomness condonation with the probabilistic mean values of constraints⁵¹. As stated by due to their nature, the uncertainty products survey about the soft computing techniques with inventory theory⁵².

In the last decade, many researchers have studied and work done in the field of healthcare inventory and supply chain management. Healthcare inventory and supply chain management systems work generally based on demand and supply based. Mostly fuzzy-based inventory control techniques are applied in the EOQ or Economic order quantity model. In this regard, the fuzzy approaches, introduced and examined the mathematical modelling for the optimal policy of supply chain model under the inspection error⁵³. In recent years, many researchers have investigated the inventory system with fuzzy environment^54-56. Later, the Pareto distribution demand as a flexible source for the inventory model under the stochastic deterioration rate⁵⁷.

The concept of fuzzy theory was firstly proposed, which is an extension of classical set theory⁵⁸. In this regard, a fuzzy-based mathematical model for optimal ordering and objective function in which inventory cost coefficients are predicated as fuzzy values⁵⁹. In this research work, a review on fuzzy inventory system for pharmaceutical and cosmetic products (perishable products) is suggested. Depending on the products types, the perishable products decay in several situations and behaviours according to product types and available storage facilities in a way of rate of decay and the starting point^60-63.

FUZZY METHODS:

For inventory management system, the fuzzy sets and numbers have an important place for solving uncertain parameters based problems. Fuzzy method is suitable method for solving inventory system using fuzzy constraints which is also provide the better result in comparison to crisp method. For solving fuzzy model, we assume the ordering cost, holding cost and deteriorating costs are in fuzzy form. When the demand, deterioration and inventory cost coefficients are uncertain when fuzzy theory applied and used fuzzy-based methods such as signed distance, graded mean integration method, bees colony optimization, differential evaluation, genetic method, centroid method, function principal, robust ranking method, Kuhn-Tucker conditions, Yager’s ranking method, Lagrange multipliers, particle swarm optimization method, etc. Signed distance method is very popular and commonly used method and easily solved the uncertainty real life problem.

CONCLUSION:

The present work investigated the latest review on the existing literature and numerous types of inventory system with fuzzy approach. Inventory management plays an important role in the manufacturing plants with complex ecological systems to maintain the efficient and smooth system of the output i.e., a bridge between demand, production, transportation, storage, and supply. In the present work, we focus on the fuzzy inventory model for a review on the perishable products like dairy, health, cosmetic, dry-food, fruits, vegetables, oil, fish, eggs, etc. The pharma company chooses the optimal order policy and optimal profit function for the perishable products. The numerous research gaps can exist which may be extended in the future studied.

CONFLICT OF INTEREST:

The authors have no conflicts of interest regarding this investigation.

REFERENCES:

1. Harris, F. Operations and cost, A W Shaw Co. Chicago, 1915.

2. Hadley, G., Whitin T. M. Analysis of Inventory System, Prentice-Hall, Englewood clipps, NJ, 1963.

3. Singh, S. R. and Malik, A. K. Inventory system for decaying items with variable holding cost and two shops, International Journal of Mathematical Sciences. 2010; 9(3-4): 489-511.

4. Singh, S. R., Malik, A. K. An Inventory Model with Stock-Dependent Demand with Two Storages Capacity for Non-Instantaneous Deteriorating Items. International Journal of Mathematical Sciences and Applications. 2011; 1(3): 1255-1259.

5. Singh, S. R., Malik, A. K., and Gupta, S. K. Two Warehouses Inventory Model for Non-Instantaneous Deteriorating Items with Stock-Dependent Demand. International Transactions in Applied Sciences. 2011; 3(4): 911-920.

6. Singh, Y., Arya, K., Malik, A. K. Inventory control with soft computing techniques. International Journal of Innovative Technology and Exploring Engineering. 2014; 3(8): 80-82.

7. Vashisth, V., Tomar, A., Chandra, S., Malik, A. K. A trade credit inventory model with multivariate demand for non-instantaneous decaying products. Indian Journal of Science and Technology. 2016; 9(15): 1-6.

8. Vashisth, V., Tomar, A., Soni, R., Malik, A. K. An inventory model for maximum life time products under the Price and Stock Dependent Demand Rate. International Journal of Computer Applications. 2015; 132(15): 32-36.

9. Malik, A. K., Chakraborty, D., Bansal, K. K., Kumar, S. Inventory Model with Quadratic Demand under the Two Warehouse Management System. International Journal of Engineering and Technology. 2017; 9(3): 2299-2303.

10. Malik, A. K., Shekhar, C., Vashisth, V., Chaudhary, A. K., Singh, S. R. Sensitivity analysis of an inventory model with non-instantaneous and time-varying deteriorating Items. In AIP Conference Proceedings. 2016; 1715(1): 020059.

11. Malik, A.K. and Sharma, A. An Inventory Model for Deteriorating Items with Multi-Variate Demand and Partial Backlogging Under Inflation, International Journal of Mathematical Sciences. 2011; 10(3-4): 315-321.

12. Sharma, A., Gupta, K. K., Malik, A. K. Non-Instantaneous Deterioration Inventory Model with inflation and stock-dependent demand. International Journal of Computer Applications. 2013; 67(25): 6-9.

13. Singh, S. R. and Malik, A. K. Effect of inflation on two warehouse production inventory systems with exponential demand and variable deterioration. International Journal of Mathematical and Applications. 2008; 2(1-2): 141-149.

14. Yadav, S.R. and Malik, A.K. Operations Research, Oxford University Press, New Delhi, 2014.

15. Satish Kumar, Yashveer Singh, A. K. Malik. An Inventory Model for both Variable Holding and Sales Revenue Cost. Asian J. Management. 2017; 8(4):1111-1114.

16. A K Malik, Dipak Chakraborty, Satish Kumar. Quadratic Demand based Inventory Model with Shortages and Two Storage Capacities System. Research J. Engineering and Tech. 2017; 8(3): 213-218.

17. G. Santhi, K. Karthikeyan. EOQ Pharmaceutical Inventory Model for Perishable Products with Pre and Post Discounted Selling Price and Time Dependent Cubic Demand. Research J. Pharm. and Tech. 2018; 11(1): 111-116.

18. Manoj Kumar Sharma, V. K. Srivastava. An Optimal Ordering Pharmaceutical Inventory Model for Time Varying Deteriorating Items with Ramp Type Demand, Research J. Pharm. and Tech. 2018; 11(12): 5247-5252.

19. R.D. Patel, D.M. Patel. Two warehouse inventory model for deteriorating items with linear trend in demand and time varying holding cost under inflationary conditions and permissible delay in payments. Research J. Science and Tech. 5(1): Jan.-Mar.2013 page 113-119.

20. Malik, A. K., Singh, S. R., Gupta, C. B. An inventory model for deteriorating items under FIFO dispatching policy with two warehouse and time dependent demand. Ganita Sandesh, 2008; 22(1), 47-62.

21. Malik, A.K., Singh, A., Jit, S., Garg. C.P. Supply Chain Management: An Overview. International Journal of Logistics and Supply Chain Management. 2010; 2(2): 97-101.

22. Gupta, K. K., Sharma, A., Singh, P. R., Malik, A. K. Optimal ordering policy for stock-dependent demand inventory model with non-instantaneous deteriorating items. International Journal of Soft Computing and Engineering. 2013; 3(1): 279-281.

23. Kumar, S., Chakraborty, D., Malik, A. K. A Two Warehouse Inventory Model with Stock-Dependent Demand and variable deterioration rate. International Journal of Future Revolution in Computer Science and Communication Engineering. 2017; 3(9): 20-24.

24. Kumar, S., Malik, A. K., Sharma, A., Yadav, S. K., Singh, Y. An inventory model with linear holding cost and stock-dependent demand for non-instantaneous deteriorating items. In AIP Conference Proceedings. 2016; 1715(1): 020058.

25. Malik, A. K., Vedi, P., and Kumar, S. An inventory model with time varying demand for non-instantaneous deteriorating items with maximum life time. International Journal of Applied Engineering Research. 2018; 13(9): 7162-7167.

26. Kumar, S., Soni, R., Malik, A. K. Variable demand rate and sales revenue cost inventory model for non-instantaneous decaying items with maximum life time. International Journal of Engineering and Science Research. 2019; 9(2): 52-57.

27. Malik, A. K., Mathur, P., Kumar, S. Analysis of an inventory model with both the time dependent holding and sales revenue cost. In IOP Conference Series: Materials Science and Engineering. 2019: 594(1): 012043.

28. Halim, K.A., Giri, B.C. and Chaudhuri, K.S. Lot sizing in an unreliable manufacturing system with fuzzy demand and repair time. International Journal of Industrial and Systems Engineering. 2010; 5: 485-500.

29. Hollah, O.M., Fergany, H.A. Periodic review inventory model for Gumbel deteriorating items when demand follows Pareto distribution. J Egypt Math Soc. 2019; 27: 10, https://doi.org/10.1186/s42787-019-0007-z.

30. Hsieh, C.H. Optimization of fuzzy production inventory models. Information Sciences, 2002; 146: 29-40.

31. H. J. Zimmermann. “Description and optimization of fuzzy systems,” International Journal of General Systems. 1976; 2(4): 209–215.

32. H. J. Zimmermann. Fuzzy Set Theory and Its Applications. Kluwer-Nijho, Hinghum, Netherlands, 1985.

33. Jaggi K. et al. Fuzzy inventory model for deteriorating items with time-varying demand and shortages. American Journal of Operational Research. 2013; 2(6): 81-92.

34. K. S. Park. Fuzzy set theoretic interpretation of economic order quantity, IIIE Transactions on Systems, Man and Cybernetics. 1987; 17: 1082-1084.

35. C. Kao and W. K. Hsu. Lot size-reorder point inventory model with fuzzy demands, Computers and Mathematics with Applications. 2002; 43: 1291-1302.

36. Malik, A. K. and Singh, Y. An inventory model for deteriorating items with soft computing techniques and variable demand. International Journal of Soft Computing and Engineering. 2011; 1(5): 317-321.

37. Yao J.S. and Lee H.M. Fuzzy inventory with or without backorder for fuzzy order quantity with trapezoidal fuzzy number. Fuzzy Sets and Systems. 1999; 105: 311-337.

38. Yong He, Shou-Yang Wang, K.K. Lai (2010). An optimal production inventory model for deteriorating items with multiple-market demand. European Journal of Operational Research. 2010; 203(3): 593-600.

39. Yung, K. L., W. Ip and D. Wang. Soft Computing Based Procurement Planning of Time-variable Demand in Manufacturing System. International Journal of Automation and Computing. 2007; 4(1): 80-87.

40. Guiffrida, A.L. Fuzzy inventory models in: Inventory Management: Non Classical Views, (Chapter 8). M.Y. Jaber (Ed.), CRC Press, FL, Boca Raton. 2010: 173-190.

41. Vujosevic, M. and Petrovic, D. EOQ formula when inventory cost is fuzzy. International Journal of Production Economics. 1996, 45: 499-504.

42. Malik, A. K. and Singh, Y. A fuzzy mixture two warehouse inventory model with linear demand. International Journal of Application or Innovation in Engineering and Management. 2013; 2(2): 180-186.

43. Sujit Kumar De. Solving an EOQ model under fuzzy reasoning. Applied Soft Computing. 2021; 9: 106892, https://doi.org/10.1016/j.asoc.2020.106892.

44. Bellman, R. E. and Zadeh, L. A. Decision-making in a fuzzy environment. Management Science. 1970; 17: 141-164.

45. B. Liu, K. Iwamura. A note on chance constrained programming with fuzzy coefficients. Fuzzy sets and Systems. 1998; 100: 229-233.

46. Chang, H., C., Yao, J., S., and Quyang, L.Y. Fuzzy mixture inventory model involving fuzzy random variable, lead-time and fuzzy total demand. European Journal of Operational Research. 2006; 69: 65-80.

47. C. C. Chou. Fuzzy economic order quantity inventory model. International Journal of Innovative Computing, Information and Control. 2009; 5(9): 2585-2592.

48. J. S. Yao and J. Chiang. Inventory without back order with fuzzy total cost and fuzzy storing cost deffuziﬁed by centroid and singed distance. European Journal of Operational Research. 2003; 148: 401-409.

49. Malik, A. K., Singh, Y., Gupta, S. K. A fuzzy based two warehouses inventory model for deteriorating items. International Journal of Soft Computing and Engineering. 2012; 2(2), 188-192.

50. Singh, S. R. and Malik, A. K. Two warehouses model with inflation induced demand under the credit period. International Journal of Applied Mathematical Analysis and Applications. 2009; 4(1): 59-70.

51. Dutta, P., Chakraborty, D., and Roy, A.R. Continuous review inventory model in mixed fuzzy and stochastic environment. Applied Mathematics and Computation. 2007; 188: 970-980.

52. Singh, Y., Malik, A. K., Kumar, S., An inflation induced stock-dependent demand inventory model with permissible delay in payment. International Journal of Computer Applications. 2014; 96(25): 14-18.

53. Priyan S. and Manivannan P. Optimal inventory modelling of supply chain system involving quality inspection errors and fuzzy effective rate. Opsearch. 2017; 54: 21-43.

54. Daniel Cardoso de Salles, Armando Celestino Gonalves Neto and Lino Guimaraes Marujo. Using fuzzy logic to implement decision policies in system dynamics models. Expert Systems with Applications. 2016; 55: 172-183.

55. Sarkar, B., and Mahapatra, A.S. Periodic review fuzzy inventory model with variable lead time and fuzzy demand. International Transactions in Operational Research. 2017; 24: 11971227.

56. Shekarian, E., Kazemi, N., Abdul-Rashid, S.H., and Olugu, E.U. Fuzzy inventory models: A comprehensive review. Applied Soft Computing. 2017; 55: 588-621.

57. H. C. Chang, J. S. Yao and L. Y. Ouyang. Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number. Mathematical and Computer Modeling, 2004; 29: 387-404.

58. Zadeh. Fuzzy sets, Information and Control, 1965; 8(3): 338–353.

59. Malik, A.K. and Garg, H. An Improved Fuzzy Inventory Model Under Two Warehouses. Journal of Artificial Intelligence and Systems. 2021; 3, 115–129. https://doi.org/10.33969/AIS.2021.31008.

60. Viкtoriia Mishchenko, Viktoriya Nazarkina, Olena Vynnyk, Vitaly Chernukha, Yuliia Kurylenko, Svetlana Breusova. An Analysis of Approaches regarding the Regulation of Parapharmaceutical products sales through the network marketing system in Ukraine. Research J. Pharm. and Tech. 2020; 13(3): 1204-1210. doi: 10.5958/0974-360X.2020.00222.X

61. Elias Sakkal, Yaser Bitar, Saleh Trefi. Quality control of the active Pharmaceutical ingredients of some Pharmaceutical products prior the termination of their shelf life. Research J. Pharm. and Tech. 2019; 12(12): 6111-6118. doi: 10.5958/0974-360X.2019.01062.X

62. Yashpal Singh Chauhan, Ravi Nex, Ghanshyam Sevak, Mahendra Singh Rathore. Stability Testing of Pharmaceutical Products. Research Journal of Pharmaceutical Dosage Forms and Technology. 2021; 13(4):317-8. doi: 10.52711/0975-4377.2021.00052.

63. Shoaib Ahmad. Patents for Pharmaceutical Products and Technology: An Updated Review. Res. J. Pharm. Dosage Form. and Tech. 2017; 9(3):98-100. doi: 10.5958/0975-4377.2017.00017.9

Received on 06.03.2022 Modified on 13.10.2022

Research J. Pharm. and Tech 2023; 16(7):3494-3498.

DOI: 10.52711/0974-360X.2023.00577