While just-in-time ideas have been enthusiastically embraced by manufacturing practitioners, the small replenishment batch sizes advocated are difficult to reconcile with the standard management science cost trade-off approach. In a previous paper by the authors, which analysed a multi-product manufacturing scenario under deterministic demand, this difficulty was diagnosed as being due to the standard assumption that capital for inventory is borrowed and hence boundless. When inventory is financed by investors and is thus finite, the investment level must be treated as an additional variable in the decision to adopt inventory reduction policies. For lean investments which might be chosen to maximise return on investment (ROI) rather than absolute profit, or for reasons of flexibility, JIT replenishment becomes more attractive for certain components than the standard analysis would suggest because the capital formerly invested in these components can be reinvested in the inventory of the remaining batch components to improve efficiencies. This paper treats the stochastic version of the same problem, develops a tractable solution method for the decision problem, and in addition to reinforcing the findings of the previous study, reveals several other ways in which JIT replenishment and component substitution can improve performance by limiting the cost of dealing with uncertainty. The analysis is illustrated using an actual case study of a small manufacturing enterprise seeking to reduce inventory and increase ROI.