Base stock versus WIP cap in single-stage make-to-stock production–inventory systems

A single-stage production-inventory system produces parts in a make-to-stock mode, and unsatisfied demand is backordered. The system operates under a so-called base stock with WIP cap replenishment policy, which works as follows. Whenever the Work-In-Process (WIP) plus finished goods inventory falls below a specified level, called base stock, a replenishment order for the production of a new part is issued. If the WIP inventory is below a different specified level, called WIP cap, the order goes through and a new part is released for production; otherwise, the order is put on hold until the WIP inventory drops below the WIP cap. First, it is shown that the optimal base stock that minimizes the long-run, average, inventory holding cost for a given minimum customer service level, is a non-increasing function of the WIP cap that reaches a minimum value, called minimum optimal base stock, at a finite WIP cap value, called critical WIP cap. Then, it is shown that the optimal WIP cap is less than or equal to the critical WIP cap and therefore the optima! base stock is greater than or equal to the minimum optimal base stock. More interestingly, however, it is conjectured that the optimal WIP cap is in fact exactly equal to the critical WIP cap and therefore the optimal base stock is exactly equal to the minimum optimal base stock. The minimum optimal base stock is none other than the optimal base slock of the same system operating under a classical base stock policy (with no WIP cap). Finally, the optimal parameters of a system operating under a base stock with WIP cap policy are related to the optimal parameter of the same system operating under a make-to-stock CONWIP policy.