Optimal liquidation timing for surplus inventory

Surplus inventory ties up funds that could be recovered and reinvested. We study liquidation of one lot using expected discounted surplus at disposal relative to immediate liquidation proceeds reinvested to that date. With exponential sale waiting times, known constant sale intensity and fixed receipts, integration and differentiation give a closed-form optimal deadline when the reinvestment growth rate exceeds the discount rate. Two intensity thresholds distinguish whether initial waiting is worthwhile and whether indefinite waiting has positive surplus. A positive finite deadline requires the marginal benefit of extending the deadline to start positive and reach zero at a finite age. Declining regular-sale receipts relative to liquidation recovery or declining predictive sale intensity can also produce such deadlines when the discount and reinvestment growth rates are equal. For comparison, maximizing wealth at a common terminal date under constant known intensity and fixed receipts makes either immediate liquidation or waiting for regular sale until that date optimal, with liquidation then if still unsold. An equipment scenario gives a 2.32-year deadline and maximum surplus of 5.75 percent of net regular-sale receipt; indefinite waiting gives zero surplus. In a Gamma model of intensity uncertainty, treating the initial mean as known overstates both the deadline and expected surplus. The examples illustrate model implications rather than measured policy benefits.