Diversification under Yield Randomness in Inventory Models

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I haven’t really touched on the early research on risks in supply chain management. One major stream is on random yields. Parlar and Wang (1993) were one of the firsts to extend the classic Newsboy and EOQ (Economic Order Quantity) models to include uncertainty.

h5. Models

Both models calculate the optimal inventory while including different cost factors (like setup cost for ordering, inventory holding cost) and decision variables (order volume and order timing).
As an extension the Newsboy problem also includes random demand.

Parlar and Wang now extended these models by a second raw material source and making the availability random of both sources. In this case the yield of the supplier is represented by a exponential distribution with two independent expected yield and standard deviation for both suppliers.

h5. Results

An example of some numerical calculations done on the EOQ model is represented in figure 1.

Non-convex objective function of the EOQ model
Figure 1: Cost Function depending on the Quantities ordered (Parlar and Wang, 1993)


For both problems the authors find ways to calculate the optimal order decisions (figure 2, for the EOQ model). But they also admit that solving the newsboy problem required some extra effort and any addition to the model (like a third supplier) would make it even harder to solve.

optimal order quantities
Figure 2: Optimal Order Quantities for EOQ Model (Parlar and Wang, 1993)


h5. Conclusion

These are operational models and they can and should be applied for operational decisions in inventory management and purchasing. But on the other hand they are also very abstract leaving many parameters out and (according to the authors) being hard to extend.

Reference: 

Parlar, M., & Wang, D. (1993). Diversification under yield randomness in inventory models European Journal of Operational Research, 66 (1), 52-64 DOI: 10.1016/0377-2217(93)90205-2

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