| A supply chain generally involves many firms. In that event, there are potential benefits to the firms from forming an alliance to maximize overall profit. The question arises how to allocate the resulting profit among the owners. One principle is that the resulting profit allocated to each collection of owners should be as least as high as if those owners operated together as an independent group. Our research focuses on determining the set of all profit-allocations with this property, called the core. Our study of cooperative concave programs shows that the optimal dual solutions produce allocations in the core. Also the optimal dual solution provides incentive-compatible prices that allow each firm to operate independently and yet support the maximum-profit operation of the alliance. This approach can be implemented easily in practice. Cooperative multi-period stochastic concave programs in which the resource vectors are random variables with finitely many values are also studied. The optimal dual solutions produce allocations that are in the sequential core, i.e., they fully allocate all actual profits in each period and are in the core of the cooperative program that remains in each period.; We also study optimal flexible supply policy to allow a buyer to respond rapidly to changing market conditions. Flexibility is provided through dynamic revision of lead-times and prior order quantities with associated costs and appropriate limits on the magnitude of such changes. We characterize the buyer's minimum-expected-cost ordering, order-revision, and options policies for both the finite- and infinite-horizon problems. For the case in which only limited downward (resp., upward) revision of cumulative orders is allowed, we show that the minimum cost is additive in the state variables in the period. This makes the optimal flexible policy easy to compute. We also extend these results to serial supply chains. |
