Optimal inventory management strategies for pharmaceutical company and hospital supply chain in a fuzzy-stochastic environment

Pharmaceutical plays a crucial role in the healthcare industries due to the significant costs of the products and their storage and control requirements. It can be expensive to purchase and distribute. An effective management of pharmaceutical is required to ensure the 100% product availability at the right time, at the right cost, in good condition to right customers. Uthayakumar and Priyan (2013) proposed an integrated inventory model for pharmaceutical products in a two-echelon supply chain consisting of a pharmaceutical company and a hospital. They offered strategic decision-making to achieve the target customer service level of the hospital at minimum supply chain cost. In this paper we extend their model to reflect the following three facts: (i) fuzzify the hospital's expiry rate (dbi) and holding cost (hbi), and the pharmaceutical company's production rate (Pi), screening rate (rsi), holding cost (hwi) and selling price (sdi) for the ith product as the triangular fuzzy numbers in the total cost, (ii) hospital's quantity received does not necessarily match with the ordered quantity due to various reasons, i.e., the received quantity is uncertain, but it is a random variable following a normal distribution, and (iii) the lead time L consists of m mutually independent components. We then used the signed distance method to defuzzify the fuzzy total cost of the system and Uthayakumar and Priyan's (2013) Lagrangian multiplier approach to determine the optimal solution of the proposed model. Numerical example is given to highlight the differences between crisp and the fuzzy cases.