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Abstract
The paper proposes a production-inventory model for pharmaceutical new-products considering long-run profitability and growth of a firm. The demand rate of the new-product, when launched in a market, is dependent on revenue from sales unit, level of stock in hand and advertising/sales team constituted by general physician, pharmacist and other salesmen of the firm. An optimal control policy based on its dynamical system is solved to obtain optimal revenue and advertising effort over time. The paper investigates a stable relation among revenue, advertising effort and sales rate by examining the equilibrium property of a dynamical system. The model also estimates the cost overtime of government and nongovernment organisations.
Acknowledgements
The authors would like to express their gratitude to the reviewers for their constructive suggestions and corrections to enhance the clarity of the present paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Notes on contributors
Shib Sankar Sana
Dr Shib Sankar Sana is currently an associate professor in the Department of Mathematics at Bhangar Mahavidyalaya under the University of Calcutta. He served at the Department of Applied Mathematics, Birla Institute of Technology, Mesra, and Ranchi as an associate lecturer during 1999–2001. His main area of research is the modelling of production planning and inventory control. He has published over 95 papers in European Journal of Operational Research, International Journal of Production Economics, Computers and Mathematics with Application, Mathematical and Computer Modelling, Applied Mathematics and Computation, American Journal of Mathematical and Management Sciences, International Journal of Systems Science, Far East Journal of Applied Mathematics, Nonlinear Phenomena in Complex Systems, Advanced Modelling and Optimization, Vietnam Journal of Mathematics, Yugoslav Journal of Operational Research, International Journal of Operational Research, International Journal of Services Operations Management, International Journal of Modelling, Identification and Control, International Journal of Innovative Computing and Application, International Journal of Procurement Management, International Journal of Mathematics and Operations Research, IMA Journal of Management Mathematics, International Journal of Information and Decision Science, International Journal of Management Science and Engineering Management, Applied Mathematical Modelling, Decision Support Systems, Service Sciences, International Transaction on Operational Research, Journal of Industrial Engineering, International Journal of Applied and Mathematical Computation, Annals of Operational Research, Journal of Manufacturing Systems, CIRP Journal of Manufacturing Science and Technology, Economic Modelling, Applied Soft Computing, Expert Systems with Application, International Journal of Production Research, Cogent Business & Management, etc. He is a member of editorial board of American Journal of Industrial and Business Management, American Journal of Computational and Applied Mathematics, Universal Journal of Applied Mathematics, Journal of Modern Management and Foresight, Applied Science Segments, International Journal of Scientific Management and Development and Operations Research and Applications: An International Journal.
Shibaji Panda
Dr Shibaji Panda received his MS degree in applied mathematics at Jadavpur University, Kolkata and PhD degree in inventory and production management at Kalyani University, Kalyani, West Bengal, India. Currently, he is an associate professor in the Department of Mathematics, Bengal Institute of Technology, Kolkata, India. His main area of research is production and inventory control, supply chain management and multi-objective optimization. He has published several papers in Computers & Industrial Engineering, Transportation Research Part E: Logistics and Transportation Review, Economic Modelling, Central European Journal of Operational Research, Asia-Pacific Journal of Operational Research, International Journal of Systems Science, Yugoslav Journal of Operational Research, International Journal of Management Science and Engineering Management, International Journal of Mathematics in Operational Research, Cogent Business & Management, etc.