بهینه سازی در سطح خدمات موجودی در درون مشکل طراحی شبکه توزیع

We propose a sequential heuristic approach to optimize inventory service levels in a two-stage supply chain. The proposed approach deals with service level and inventory decisions, simultaneously with network design decisions, and incorporating unfulfilled demand costs in a previous inventory-location model. A two-step formulation is considered, where the first step optimizes service level and the second step addresses location and inventory decisions. Each algorithm iteration solves an inventory-location model for a fixed service level, and then the service level is updated in order to reach an equilibrium condition between operating system and unfulfilled demand costs. The algorithm converged in three iterations for a set of sample instances, obtaining the same outcome in comparison with a more intuitive, exact, but more time-consuming search procedure.

This paper introduces an approach to optimize inventory service level of a distribution system in conjunction with network configuration decisions (i.e., warehouse setting and customer assignment). This approach is based on a sequential or iterative marginal equilibrium for unfulfilled demand and operating system costs. The method solves a known inventory-location problem with a fixed service level, and updates this level iteratively until proposed equilibrium condition is reached. As an intermediate result, proposed methodology assures an optimal service level for a fixed, known network configuration, where operational and unfulfilled demand costs are minimized. This fact is quite relevant when the objective consists of optimizing a service level in a predetermined network configuration. Returning to the main objective of this research, the proposed approach reached equilibrium solutions in only three iterations for small numerical samples, where an inventory-location model with fixed service level was solved on each step. These results were compared to a simple service-level search procedure which solved the inventory-location model 30 times, for different service-level values. Both approaches yielded the same outcomes, although proposed iterative approach resulted in less computational efforts. Future research should consider a more detailed analysis of integer nature of network configuration variables. Moreover, underlying discontinuity of the system cost functions should also be studied. These issues are particularly relevant in terms of algorithm convergence. Further analysis with different service levels for each warehouse, and for different items, can be achieved without significant additional complexity. Service level or probability for other type of constraints, traditionally modeled with Chance Constrained Programming, can be optimized based on proposed iterative equilibrium conditions. Examples of these constraints are vehicle capacity in routing problems (Miranda and Garrido, 2004c; Miranda et al., 2009; Novaes et al., 2000) and inventory capacity in location models (Miranda and Garrido, 2006a and Miranda and Garrido, 2008; Miranda et al., 2009). Exact optimization approach and a comparison with results provided by present methodology it would be relevant. In addition, a more detailed formulation of warehouse safety stock and cycle inventory costs might be necessary. Finally, simultaneously optimization of order quantity and service level remains as a necessary future research.