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a new kind of production-inventory system

 

Introduction

Realizing the competitive advantages of being flexible, responsive as well as efficient, and enabled by advanced technologies, more and more manufacturing companies are reengineering their product design and delivery processes to move toward mass customization (Pine, 1993). This requires modularizing the production process so that the product can be quickly assembled from standardized components and modules in different configurations, based on what customers individually request. As a result, a new kind of production-inventory system has emerged and is becoming

increasingly popular. This is the Assemble-To-Order (ATO) system: inventories are kept only at the component level, and the final products are assembled only after customer orders are received.

This new system, in turn, presents challenging operational and system design issues to managers. As each customer order typically involves several components in different amounts, the stockout of any component will cause a delay in fulfilling the order. So, the optimal stock level of one component should be determined in conjunction with those of other components to ensure their simultaneous availability. Standard single-item inventory planning tools, while suitable for the mass-production make-to-stock environment, are no longer applicable. New planning tools are needed to strike the optimal inventory-service tradeoff in ATO systems. The current paper presents an effort towards this goal.

More specifically, we consider an ATO system supporting multiple types of demand, which arrive at the system following compound Poisson processes. The component inventories are resupplied from outside suppliers after random replenishment leadtimes. For a given component, the leadtimes are independent, identically distributed (i.i.d.) random variables. The leadtimes for different components are also independent but may have different distributions. Since the form of the optimal inventory-control policy for this system is unknown, base-stock policies are widely adopted in practice. For this reason, we assume the inventory of each component is controlled by a base-stock policy. The system performance measure we focus on is the expected backorder for each product. Our objective is to minimize a weighted average of backorders over all product types, subject to a budget constraint on the component inventory. Through Little's law (Wolff, 1989), this objective relates directly to the response time performance in fulfilling customer orders.

The optimization problem under study is quite complex. First, its objective function is nonseparable and non-differentiable. Second, its evaluation involves joint probabilities, which can be computationally challenging. To deal with the second difficulty, we develop upper and lower bounds on the backorders that involve marginal distributions only and use these bounds and approximations derived from them as surrogate objective functions in the optimization problem. This approach is similar in spirit to that in Song and Yao (2002) for the single-product ATO system. However, even with the simpler surrogate objective functions the first difficulty remains. Moreover, the bounds for the multiproduct model here are more involved than in the single-product case and exhibit different structures, so the ideas used to develop the algorithms in Song and Yao do not apply.