Hedging against Disruptions with ripple Effects

Daniel Dumke — Mon, 02 Jan 2012 17:10:00 +0000

I have read several articles by Mark Daskin (also reviewed another one here). So with him on the author list of today’s paper I think one can expect a clearcut research question, some kind of mathematical model, a fitting solution method and a definite answer to the underling problem. Well, let’s have a look!

Topic and method

The goal of this research is to analyze disruptions with a regional effect (as opposed to local, single facility disruptions). An example for a regional disruption may be an earthquake, storms or floods. The results should show how to better handle disruptions which are not locally limited and exhibit contagious tendencies.

The authors approach the problem by modeling three separate sub-models, namely the Defender Problem, the Attacker Problem and the User Problem.
The basic assumptions are:

each facility has a fixed capacity,
the capacity is affected by a disruption,
a defense strategy can be defined for selected facilities, it protects the facilities against the disruption

Defender Problem:
“The objective of the defender is to minimize the impact of the disruption by optimally choosing Q facilities to protect. Constraints states that no partial protection of a facility is possible.”

Attacker Problem:
“The objective of this program is to strike the system as hard as possible by identifying the worst-case set of exactly R facilities chosen among those which are not protected (6).2 Finally, no partial interdiction is possible.”

User Problem:
“The user level problem deals with the minimum cost assignment of customer demands to facilities. The total cost is given by the cost for the service provided, plus the penalties paid for the demand which is not met.”

Correlation Matrix:
“The correlation matrix represents the interdependence among the facilities when an attack occurs or, in other words, the extent to which other facilities are affected when a target facility is disrupted.

Figure 1: Map of the 2009 earthquake in L’Aquila, Italy (Liberatore, et al. 2012; USGS)

Solution and Case

The authors develop a solution method, to optimize the given problem.
Data from the 2009 earthquake in L’Aquila, Italy was used to test the model.
Figure 1 shows a map of the area.

The dataset represents the Abruzzo region, a seismically active region of Italy, where L’Aquila is located. The set of the demand nodes, N, includes all the 305 towns and cities in the region and the associated demands, ai, correspond to the number of inhabitants as at beginning of April 2009 expressed in thousands of citizens. The set of initial facilities, F, represents the 35 hospitals of the region.

The model is solved for different parameters in two steps: first calculating the optimal defense program and second calculating the “optimal” attack, also calculating the incurred cost and correlated disruptions.

Figure 2 shows the example for two different solutions:
The buildings represent the available hospitals, stars mark the defended locations and the colored circles represent the disruption, which causes the worst effects.

Figure 2: Two solution Results (a and b). Buildings representing Hospitals, Stars protected Locations, Circles worst possible Disruption Effects (Liberatore, et al. 2012)

Conclusion

The attacker (in this case an earthquake) always looks for the place where it can hit hardest, so the focus is on the worst case scenario: How can one fortify a system so that even in the worst case it still performs at a desired level?

But keeping that in mind also leads to the conclusion that this system might not be for everyone: What if the earthquake does not hit at the worst point? Or not at all? As a rule of thumb, I would say the investments suggested by this model are magnitudes higher than those of an “optimal” (in terms of money) solution. So when do you use such a model?
I think there are two cases: Either if one is dealing with critical infrastructure, like water, food or possibly military installations and (I know its related) if one has to decide how to safe lives: As in the case study itself, where the optimal hospital location has to be found.

Reference:

Liberatore, F., Scaparra, M.P., & Daskin, M.S. (2012). Hedging against disruptions with ripple effects in location analysis Omega, 40 (1), 21-30

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Customer Service or Cost? Optimization of the Supply Chain Design

Daniel Dumke — Mon, 28 Feb 2011 14:09:00 +0000

In several articles I talked about competing objectives to the classical cost reduction goals (eg. with responsiveness or with reducing uncertainty).

Shen and Daskin (2005) explore the “Trade-offs Between Customer Service and Cost in Integrated Supply Chain Design”. The goal is to find ways to simultaneously improve customer service and reduce operating cost.

Modell

The authors model a three tier supply chain, with a supplier, distribution center, and retailer.
The following cost factors are considered: Facility Location, Inventory, divided into working inventory and safety stock, and distribution cost.
Since the goal is to find design decisions which lead to reduced cost and improved service the customer service is measured by the fraction of all demands that are within a specific distance to the distribution center. To make the cost and service requirements comparable Shen and Daskin have to introduce a weighing factor, in this case for the uncovered demand. In practice this factor represents the cost equivalent of any unmet demand, including lost sales, but also effects of negative reputation due to bad service, etc.

Solution

Shen and Daskin use an genetic algorithm to solve the network design problem. A genetic algorithm uses several concepts which follow the genetic selection metaphor. Operators in genetic algorithms are, for example: preservation of elites, mutations and expansions. Using this they reach optimal or near optimal solutions.

Management Insight

The authors gain two major insights from their experiments:

The cost difference between the cost-minimization solution and the service-maximization solution can be quite large.
Significant improvements in customer service can often be achieved at relatively little cost.

Conclusion

Shen and Daskin found the trade-off they promised in the title. At least for most parts of such a trade-off curve it is impossible to make service improvements without adding cost. Even though the insights somehow follow general intuition of increasing marginal cost for any trade-off, it stands as an important finding.
But as usual with modelling, it is important what factors you consider and which you leave out. There very likely could be positive effects on costs if the customer reaction to varying service levels had been considered.

You also already realized that the service measure used is probably not perfect as well. Most companies I talked to are using a more dimensional measure, which includes the fact that also customers out of a specific range can still be serviced.

Furthermore the authors could have used specific methods for calculating the weights of the service consideration (eg. using AHP, analyzed here).

Reference:

Shen, Z., & Daskin, M. (2005). Trade-offs Between Customer Service and Cost in Integrated Supply Chain Design Manufacturing Service Operations Management, 7 (3), 188-207 DOI: 10.1287/msom.1050.0083

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