This study develops an inventory model to solve the problems of supply uncertainty in response to demand which follows a Poisson distribution. A positive aspect of this model is the consideration of random inventory, delivery capacities and supplier's reliability. Additionally, we assume supplier capacity follows an exponential distribution. This inventory model addresses the problem of a manufacturer having an imperfect production system with single supplier and single retailer and considers the quantity of product (Q), reorder points (r) and reliability factors (n) as the decision variables. The main contribution of our study is that we consider supplier may not be able to deliver the exact amount all the time a manufacturer needed. We also consider that the demand and the time interval between successive availability and unavailability of supplier and retailer follows a probability distribution. We use a genetic algorithm to find the optimal solution and compare the results with those obtained from simulated annealing algorithm. Findings reveal the optimal value of the decision variables to maximize the average profit in each cycle. Moreover, a sensitivity analysis was carried out to increase the understanding of the developed model. The methodology used in this study will help manufacturers to have a better understanding of the situation through the joint consideration of disruption of both the supplier and retailer integrated with random capacity and reliability.