UC Berkeley

Many modern consumer electronics firms design their own products but outsource the production to contract manufacturers. Some of these products are also multi-generational, with short product life cycles and updated versions released on a regular schedule. Therefore, firms must eventually make an end-of-production decision for each product generation. We consider a new version of the last time buy problem—traditionally, a procurement quantity problem for the last possible purchase of a product—facing such a consumer electronics firm. In our problem setting, the contract manufacturer requires the firm to make sequential capacity reservations to retain the option to procure new units, a contract feature that commonly arises when the contract manufacturer has a high opportunity cost of capacity. The presence of the sequential capacity reservation requirement also creates the need to decide the timing of the last time buy, prior to which orders can be placed in each period. We formulate the problem as a dynamic program and identify properties of the optimal policy that are different and more complex than under the usual simpler assumption that capacity reservations (or analogously, production setups) do not need to be for sequential periods.

The dynamic program to find the optimal strategy for any problem instance is computationally intensive. From a numerical study, we observed that most optimal strategies have up to two order-up-to levels, a low-to-moderate value---appropriate for satisfying this period's demand---to be used with low starting inventory levels, and a higher order-up-to level---appropriate for serving as the last time buy---to be used with starting inventory levels above a threshold. We developed a heuristic solution procedure based on these insights that performs near optimally (with an average optimality gap of 0.03% for our set of problem instances) and takes very little computing time.

We also consider a variant of our original problem in which the firm must commit to the timing of the last time buy at the beginning of the problem horizon. From a numerical study, we found that the value of the option to dynamically extend the capacity reservation, as in our original problem variant, is quite small due to the effects of the sequential capacity reservation requirement. We also consider an extension with an option to buy back units from the firm's customers after the last time buy has been made, which is especially applicable when all remaining demand is for warranty replacement units and the buy-back units can be refurbished to satisfy warranty claims. We consider both the case in which the customer response to the buy-back offer is deterministic and the case in which it is stochastic. From a numerical study, we find that the introduction of the buy-back offer has the potential to greatly reduce the firm's expected costs, and this is true whether the customer response to the buy-back offer is deterministic or stochastic. Furthermore, our results suggest that, in a sequential capacity reservation setting, the buy-back option is more valuable than the flexibility afforded by a period-to-period capacity reservation contract.