We consider stock positioning in a pure assembly system controlled using installation base-stock policies. When component suppliers have random capacity and end-product demand is uncertain, we characterize the system's inventory dynamics. We show that components and the end product play convex complementary roles in providing customer service. We propose a decomposition approach that uses an internal service level to independently determine near-optimal stock levels for each component. Compared with the optimal, the average error of the decomposition approach is 0.66% across the tested instances. Compared with current practice, this approach has the potential to reduce the safety-stock cost by as much as 30%. Our computational analysis on two-echelon systems also illustrates several managerial insights: We observe that the cost reduction from improving supply performance is high when demand variability or the number of components or target customer service is high, or when the end product is more expensive relative to components. On average, (i) reducing the lead time of the more expensive component yielded higher benefit than reducing the lead time for the less expensive component, and (ii) the benefit of improving one of the supply parameters (service level or lead time) was higher when the value of the other parameter was already more favorable (lower lead time or higher service level, respectively). Finally, we analytically show how a multi-echelon pure assembly system may be converted into an equivalent two-echelon assembly system to which all our results apply.assembly system, installation base-stock policy, external and internal service levels, uncertainty, decomposition approach

We consider a two-echelon serial inventory system with demand and supply uncertainty, non-zero lead times for component procurement and end-product assembly, and a minimum customer service level requirement. We present two supply models which incorporate both quantity and timing uncertainty; these models correspond to current and proposed supply environments. Assuming that installation base-stock ordering policies are followed and that the demand distribution is quasi-concave, we show that the chance-constrained problem of determining optimal base-stock levels which minimize the total inventory investment (cost-weighted stock levels) subject to a service constraint is a convex programming problem. We characterize the relation between the optimal base-stock levels of the component and the end-product. We also illustrate how an optimal internal (component) service level can be computed, which permits decomposition of the two-stage serial system into two coordinated single-echelon systems. Computational experiments illustrate insights on the effects of supply uncertainty and other problem parameters on stock-positioning in a two-echelon serial system. In particular, we evaluate the benefits of switching from one supply environment to another.

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In this paper, we address the general multi-period production/inventory problem with nonstationary stochastic demand and supplier lead time under service-level constraints. A replenishment cycle policy is modeled. We propose two hybrid algorithms that blend Constraint Programming and Local Search for computing near-optimal policy parameters. Both the algorithms rely on a coordinate descent Local Search strategy, what differs is the way this strategy interacts with the Constraint Programming solver. These two heuristics are, firstly, compared for small instances against an existing optimal solution method. Secondly, they are tested and compared with each other in terms of solution quality and run time on a set of larger instances that are intractable for the exact approach. Our numerical experiments show the effectiveness of our methods.