Optimal Control of Supply Chains in More General Situations
This chapter considers the optimal control problem for supply chains in more general situations by relaxing some assumptions made in Chap. 2. The extension is done in four directions, that is, (1) changeable order size once issued, (2) number of outstanding orders, (3) lead-time probability distribution, and (4) number of entities in the supply chain. We will provide mathematical formulations for these generalized supply chains and use numerical examples to illustrate the main structural properties of the optimal policy such as monotonicity and asymptotic behaviors. For the multistage serial supply chain systems, it is shown that the optimal policies can be characterized by a set of monotonic switching manifolds when the maximum order size is of one unit. Finally, we discuss a few relevant issues and note the literature related to optimal control of stochastic production/inventory systems in various contexts, including deterministic lead times and random demands, stochastic lead times and outstanding order, multiple replenishment channels and order information, and ordering capacity and storage capacity.