Abstract
Reliability is one of the important factors in production inventory system as well as in the demand of the products. During a production process, the products which are more perfect with higher reliability increase the demand of the product whereas credit facility is also one of the popular business strategies. Combining these two concepts in together, we have described and analyzed mathematically a production inventory model with a partial credit facility and the reliability effect on the production system in which the customers' demand is dependent on the price of the products and deterioration rate is considered to be constant. In this proposed model, trade credit policy on both the manufacturer and customers is introduced by taking into account all the possible situations on the basis of allowed credit periods. Under these situations, taking all possible cases for the manufacturer credit period as well as customers' credit period, seven non-linear optimization problems for the proposed model are obtained. Since the corresponding optimization problems associated to this model are highly non-linear, we have found closed form optimal solution of the corresponding each of these objective functions by using Taylor's series approximation technique. The convexity of the objective function of each non-linear problem is also investigated graphically. Finally, to validate the proposed model a set of seven numerical examples have been simultaneously solved and a sensitivity analysis is executed to notice the behavior of the parameters on the optimal solution. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.