This paper considers a class of multi-period dynamic supply contracts in which a buyer orders a product from a supplier in each period and the supplier allows the buyer to cancel a portion of an outstanding order with penalty during a planning horizon. We assume that both the buyer and the supplier have common knowledge. We first characterize the buyer's ordering and canceling policy that minimizes his expected cost during the planning horizon. We also characterize the supplier's optimal production policy under a very mild assumption on the costs of production and storage. Based on this structure, we then use simulation to show how the supplier chooses cancellation costs that minimize her expected cost during the planning horizon. Our simulation shows that both the buyer and the supplier would benefit from the contract.
This paper studies the problem of how to coordinate a one-supplier, multi-retailer supply chain by requiring retailers to adopt the unified number of annual orders proposed by the supplier. The paper presents two coordination models: one considering a small number of retailers; the other considering a large number of retailers. In the proposed models, the supplier views all retailers or some selected retailers (if more beneficial) in the supply chain as one group, then offers a price discount to entice the retailers in this group placing their orders only with the specific number of annual orders. A heuristic is developed for each model to let the supplier know which retailers will be selected to implement the common number of annual orders, and how to determine the corresponding optimal number of annual replenishments and price discount. By using a numerical study, we evaluate the benefit of the proposed coordination strategy.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.