Component commonality: Models with product-specific service constraints

Production and Operations Management, Summer 2002 by Mirchandani, Prakash, Mishra, Ajay K

COMPONENT COMMONALITY: MODELS WITH PRODUCT-SPECIFIC SERVICE CONSTRAINTS*

Common components are used extensively for reasons including product postponement and expediting new product development. We consider a two-stage assemble-to-order system with two products having uniformly distributed demand, one common component, and product-specific components. We develop optimization models in which the cost-minimizing inventory of the components must be determined and allocated to products in order to meet product-specific service level constraints. We compare two different commonality models based on whether or not the products are prioritized. A distinctive feature of our study is the use of product-specific service levels. We compare our results with models using aggregate service levels.

(COMPONENT COMMONALITY; STANDARDIZATION; INVENTORY; SUPPLY CHAIN MANAGEMENT; ASSEMBLE-TO-ORDER)

1. Introduction

5. Conclusion

The component commonality problem is widely prevalent but analytically complex. In this paper, we obtain a better understanding of this problem by studying the two-product commonality model. The main contributions of this study include the following:

1. We show that the distribution of the requirement of a product-specific component depends on the service level and is not the same as the demand distribution of the corresponding product.

2. We formulate, solve, and derive managerial insights for commonality models with prioritized and nonprioritized product demands.

3. The previous studies assume that the products required at most one unit of each component. We include usage as a parameter, thus allowing general requirement levels of the components.

4. Our study is among the few studies that uses product-specific service level, which is a better analogue for product-dependent shortage cost than the aggregate service level. We also compare our results with those for the aggregate service level measure.

For analytical tractability, we study two products having uniformly distributed demand. However, depending on the underlying modeling assumptions, we may be able to generalize our approach for a larger number of products, or for other distributions. For example, in the nonprioritized case with two products, we can model exponential demand using an approach similar to that in Section 3. We can determine p from (24) and the expression for ASL in Bagchi and Gutierrez (1992) and then use it to develop the service equations (9) and (10). In general, we may be able to use Laplace transforms to calculate the exact distribution of the common component requirement. If the corresponding service level constraints result in a convex program, we can use the Karush-Kuhn-Tucker conditions to derive the optimal solution. Otherwise, other nonlinear programming approaches may be used to derive good solutions.

Another important extension of this study is to allow correlated product demand as in Eynan (1996) for the ASL measure. Studying a model that considers holding costs on unused components in addition to acquisition costs and service levels also promises to be worthwhile. While this paper gives us analytical insights into the commonality problem, it is necessary to also develop fast procedures that provide good solutions for the large size problems arising in practical applications. Mirchandani and Mishra (1999) solve problems of size 100 components and 100 products in satisfactory time and conduct experiments to further examine situations in which commonality is beneficial.1

* Received August 1999; revisions received June 2000, February 2001, and June 2001; accepted October 2001.

1 We thank Professor Anant Balakrishnan for his detailed comments on an earlier version of this paper that helped significantly increase the scope of this work and improve its exposition. We also thank the referees and the editor for providing useful and constructive comments that have significantly improved the paper. The first author's research was partially funded by the National Science Foundation Grant DMI-01 115434.

References

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