Dual Supply Channel Disruption and Supply Chain Design

Daniel Dumke — Mon, 19 Dec 2011 16:35:00 +0000

This is the continuation of the Greece week and today I am going to have a look at a mathematical model to capture the effects of dual disruptions in a news-vendor model.

This time the three authors (Xanthopoulos, Vlachos and Iakovou) come from the Aristotle University of Thessaloniki.

Method

The authors developed a model where a retailer is able to order from two different supply channels. Figure 1 shows the supply chain schematic.
Three different types of the model are modeled separately:

unconstrained model,
fill rate constrained model,
Type I service level constraint,

The decision variables are the order quantities from channel one and two.

Figure 1: Schematics of the Supply Chain Model (Xanthopoulos et al., 2012)

Analysis and managerial insights

The models are analyzed using a numeric analysis with the parameters given in figure 2. Different values for the purchasing cost c_i, disruption probabilities for the supply channels one and two (p_i). The impact of the disruption is denoted by y_i.

Figure 2: Experimentation Data (Xanthopoulos et al., 2012)

144 parameter combinations are analyzed. Figure 2 shows the iso-profit lines for the order quantities Q₁ and Q₂ for different impact levels in the first supply channel (y₁: a) 0.9, b) 0.6, c) 0.1)

Figure 3: Effect of different Disruption Impacts on Supplier 1 (Xanthopoulos et al., 2012)

The authors conclude

It is also observed that as the impact of a disruption on the first channel increases, the optimal solution moves from a solution that mainly utilizes the first supply chain to a solution that mainly utilizes the second one.

Depending on the values of the purchase costs (c_i), the disruption probabilities (p_i), and the effect of a disruption (y_i), one of the suppliers may dominate over the other one, leading to a single supply source.

Nevertheless, for both the uncapacitated and capacitated problems for certain combinations of the values of c_i, p_i, and y_i, a dual-sourcing policy outperforms a single-sourcing one. In such cases, it is optimal to place the larger part of the total order to the dominant channel and its lesser part to the second one, so as to hedge/mitigate the disruption risks.

Moreover, for very high service levels (near 100%), large orders should be placed to both suppliers.

[In] the case in which the first supplier is the dominant supplier as well as the more reliable from the two. In such a case, no matter how high the fill rate will be, orders should be placed only to the first supplier and the second one should not be activated at all.

Conclusion

This article provides some insights into a dual supply channel disruption case. From the title and abstract of the article, I was however expecting more discussion of the results, perhaps the impact of other driving factors beside the impact, probability and ordering cost.

Reference:

Xanthopoulos, A., Vlachos, D., & Iakovou, E. (2012). Optimal newsvendor policies for dual-sourcing supply chains: A disruption risk management framework Computers & Operations Research, 39 (2), 350-357

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Diversification under Yield Randomness in Inventory Models

Daniel Dumke — Mon, 03 Oct 2011 10:20:00 +0000

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.

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.

Results

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

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.

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

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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