This study presents a stochastic planning framework for battery swapping station (BSS) networks tailored to developing countries. The mixed-integer model co-optimizes siting and operations for interconnected stations while capturing uncertainties in electric vehicle (EV) arrivals, energy prices, electrical load, and degradation cost. A 24-h scenario study on the IEEE 33-bus feeder uses a normalized probability distribution function (NPDF) and retains the 10 most-probable scenarios. Location matters: placing a single station near the source (Bus 1) yields a total network cost $11,886.61, whereas installing at Bus 33 increases the cost to $12,065.92 but raises operator profit from $8111.82 to $8753.89 via fewer discharge cycles. With one station (Bus 2), energy arbitrage injects 7.5 MW and 5.3 MW at peak hours 15–16. Splitting capacity across two stations (Buses 2 and 10) improves service: Station 10 charged 700 batteries and served 222 EVs, while Station 2 exchanged 9.975 MW with the grid. Under uncertainty, purchased power rises modestly; total network cost increases from $11,894.13 to $11,912.09, while profit grows to $8156.62. Sensitivity analyses show that higher initial charged inventory and larger interconnection capacity reduce system cost and increase profit. The framework offers actionable siting and operating guidance for equitable, cost-aware BSS deployment.