Integrating inventory and assortment planning decisions is a challenging task that requires comparing the value of demand expansion through broader choice for consumers, with the value of higher in-stock availability. We develop a stockout-based substitution model for trading off these values, in a setting with limited store capacities and inventory replenishment, two features missing in the literature. Using the closed-form solution for the single product case, we develop an accurate approximation for the multi-product case. This approximated formulation allows us to optimize inventory decisions by solving a fractional integer program with a fixed-point equation constraint. When products have equal margins, we solve the integer program exactly by bisection over a one-dimensional parameter. In contrast, when products have different margins, we propose a fractional relaxation that we can also solve by bisection, and results in near-optimal solutions. Overall, our approach provides solutions within 0.1\% of the optimal policy and finds the optimal solution in 80\% of the random instances we generate.