Supply Chains and Fuzzy Demand

Daniel Dumke — Wed, 04 May 2011 15:33:00 +0000

Risk in supply chains can be included in several different ways into the decision making process.

No Risk

A statement in many supply chain models is that some/most/all parameters of the model are fixed (e.g. fixed demand, zero probability of a hurricane).

The result is, if the real value of this parameter diverges from the assumptions, the results of the model will be flawed to a certain degree (up to completely unusable).

Distributions

Another allegedly more complete way of including risks into modeling is to assign specific probabilities or even stochastic distributions the model’s parameters. In this way using a normal distribution, would represent the uncertainty about the future values of the parameter. Nonetheless, this approach has theoretical and practical flaws as well. From a practical standpoint, the time needed for solving the resulting model (especially with realistic model sizes) increases dramatically and may even be insolvable. And from a theoretical point of view, the assigned distributions may also prove to be wrong in reality.

Fuzzy Sets

Fuzzy logic is another way of introducing risk considerations into a model. This article is about the theoretical application of this logic to a supply chain problem.

Fuzzy sets are a construct which can be used to a limited amount of uncertainty into a system’s model.

A fuzzy demand variable, as an example, could have four possible manifestations of (14, 16, 18, 19). This can be interpreted as the demand can have one of those values without further specification of the individual probabilities.

Model and Results

Wen and Iwamura (2008) developed a facility location allocation model where the demand parameter has been defined as a fuzzy variable.

Since the demand in this case is not deterministic anymore, decisions have been based on an expected value.

The authors used the Hurwicz criterion, a decision function based on the weighted average of the worst and best outcome of a given decision, as the objective function to evaluate the “best” location-allocation.

They also suggest and test an solution heuristic. A possible solution of this location problem is shown in figure 1.

Figure 1: Exemplary Results: Location of Customers (dot) and Facilities (diamond) (Wen and Iwamura, 2008)

Conclusion

One advantage of the concept of fuzzy sets is that it may be easier for an analyst or expert to specify a limited number of possible demand values than fill the parameters an appropriate distribution function.

The disadvantages lie in the further assumptions of the fuzzy sets.

The fuzzy variables are defined to be trapezoidal, ie. probabilities are assigned to the possible manifestations eg. (14, 16, 18, 19) in such way that the probability for the extreme values are lower than the center values. And this is basically the representation of a discrete distribution function.

There is no evidence for fuzzy logic as better representing the uncertainty in a real supply chain system

The data shows that the computational efficiency does not seem to be very good

Furthermore, fuzzy logic does not allow to represent extreme and unlikely events in a adequate manner. In the case of demand, there may be the possibility of extreme high or low demand which could lead to a change in the optimal locations.

Reference:

Wen, M., & Iwamura, K. (2008). Fuzzy facility location-allocation problem under the Hurwicz criterion European Journal of Operational Research, 184 (2), 627-635 DOI: 10.1016/j.ejor.2006.11.029

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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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