In this study, the continuous review order-quantity-re-order point (Q, R) model is analysed with cycle cost considerations. First, we formulate the maximum cycle cost of a given (Q, R) policy using a distribution-free approach. Then, two approaches are introduced to minimize the maximum cycle cost: (i) adjusting R of a given (Q, R) policy and (ii) designing a new (Q, R) policy. Optimum inventory control decisions are characterized for each approach. A set of numerical studies is presented to compare the outcomes of both approaches to three long-term cost minimization approaches, namely the cost minimizing (Q, R) policy, the distribution-free minmax (Q, R) policy, and the distribution-free (Q, R) policy based on the maximum entropy principle. Our numerical results demonstrate the viability of the two approaches introduced and discuss implications of penalty costs and lead time demand's coefficient of variation. Later, we formulate a bi-objective model with the objectives of expected cost and maximum cycle cost minimizations and propose a bi-directional method to approximate the set of Pareto efficient solutions. Numerical examples are presented to illustrate the algorithm and demonstrate the Pareto front.