We consider assemble-to-order inventory systems with identical component lead times. We use a stochastic program (SP) to develop an inventory strategy that allows preferential component allocation for minimizing total inventory cost. We prove that the solution of a relaxation of this SP provides a lower bound on total inventory cost for all feasible policies. We demonstrate and test our approach on the W system, which involves three components used to produce two products. (There are two unique parts and a common part. Each product uses the common part and its own unique part.) For the W system, we develop efficient solution procedures for the SP as well as the relaxed SP. We define a simple priority allocation policy that mimics the second-stage SP recourse solution and set base-stock levels according to the first-stage SP solution. We show that our policy achieves the lower bound and is, thus, optimal in two situations: when a certain symmetry condition in the cost parameters holds and when the SP solution satisfies a "balanced capacity" condition. For other cases, numerical results demonstrate that our policy works well and outperforms alternative approaches in many circumstances.

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We study an inventory management mechanism that uses two stochastic programs (SPs), the customary one‐period assemble‐to‐order (ATO) model and its relaxation, to conceive control policies for dynamic ATO systems. We introduce a class of ATO systems, those that possess what we call a “chained BOM.” We prove that having a chained BOM is a sufficient condition for both SPs to be L♮ convex in the first‐stage decision variables. We show by examples the necessity of the condition. For ATO systems with a chained BOM, our result implies that the optimal integer solutions of the SPs can be found efficiently, and thus expedites the calculation of control parameters. The M system is a representative chained BOM system with two components and three products. We show that in this special case, the SPs can be solved as a one‐stage optimization problem. The allocation policy can also be reduced to simple, intuitive instructions, of which there are four distinct sets, one for each of four different parameter regions. We highlight the need for component reservation in one of these four regions. Our numerical studies demonstrate that achieving asymptotic optimality represents a significant advantage of the SP‐based approach over alternative approaches. Our numerical comparisons also show that outside of the asymptotic regime, the SP‐based approach has a commanding lead over the alternative policies. Our findings indicate that the SP‐based approach is a promising inventory management strategy that warrants further development for more general systems and practical implementations.

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We tackle the challenge of applying automated negotiation to self-interested agents with local but linked combinatorial optimization problems. Using a distributed production scheduling problem, we propose two negotiation strategies for making concessions in a joint search space of agreements. In the first strategy, building on Lai and Sycara (Group Decis Negot 18 (2): [169][170][171][172][173][174][175][176][177][178][179][180][181][182][183][184][185][186][187] 2009), an agent concedes on local utility in order to achieve an agreement. In the second strategy, an agent concedes on the distance in an attribute space while maximizing its local utility. Lastly, we introduce a Pareto improvement phase to bring the final agreement closer to the Pareto frontier. Experimental results show that the new attribute-space negotiation strategy outperforms its utility-based counterpart on the quality of the agreements and the Pareto improvement phase is effective in approaching the Pareto frontier. This article presents the first study of applying automated negotiation to self-interested agents each with a local, but linked, combinatorial optimization problem.