robust design

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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Optimal Design of Supply Chain Networks with uncertain Demand

Daniel Dumke — Mon, 12 Dec 2011 16:02:00 +0000

This week is dedicated to the works on supply chain management from Greek supply chain researchers. Today’s article has been published in the Journal of Management Sciences (Omega) by four researchers from northern Greece and the UK.
After my last reviews which focused more on the conceptual aspects of supply chain risk and management. This paper is again more hands-on in the sense that it describes a mathematical model which integrates supply chain design and uncertain demand and therefore leads to a more robust supply chain design.

Method

The authors propose a mixed-integer linear program to solve a strategic supply chain design problem. Strategic design decisions include:

Where to locate new facilities (be they production, storage, logistics, etc.).

Significant changes to existing facilities, e.g. expansion, contraction or closure.

Sourcing decisions – what suppliers and supply base to use for each facility.

Allocation decisions – e.g., what products should be produced at each production facility; which markets should be served by which warehouses, etc.

Figure 1: Location and possible Locations of Plants and other Facilities (Georgiadis et al., 2011)

Model parameters

To be useful supply chain models usually are limited to a specific supply chain context. In this case the goal is to select an optimal design as well as some tactical / operational parameters.

Figure 1 and 2 describe the location design aspects of the model. The locations of plants and customers are fixed; for the warehouses and distribution centers a set of possible locations is given, and the optimal location has to be selected from the sets.

Figure 2: Locational Limitations to the Supply Chain Design Decisions (Georgiadis et al., 2011)

There are several more constraints implemented, which are concerned with the transportation flows, production resources, safety stocks and capacities. Inventory can be held at different locations, which is solved during the optimization of the model.

The objective is to minimize expected total cost over the planning horizon.

Uncertainty

There are two basic options to integrate uncertainty into a mathematical model:

scenario approach, which discretize the uncertain parameters into a limited number of specified scenarios, or a
probabilistic approach, using stochastic programming.

The authors select the first approach:

In this paper, we adopt a scenario planning approach for handling the uncertainty in time varying product demands. A question that needs to be addressed in this context concerns the generation of the scenarios to be considered. It is, of course, possible to assume that the demand for each product in each customer zone is an independent random parameter. However, more realistically, demands for similar products will tend to be correlated and will ultimately be controlled by a small number of major factors such as economic growth, political stability, competitor actions, and so on.
The complexity of the overall-model is then dependent on the complexity of the basic model (e.g. number of possible connections and locations) and the number of selected scenarios.

Two kind of decisions must be considered in the model: here-and-now decisions (the “really strategic ones”), those have to be selected before any more knowledge about the outcome of the uncertainty can be obtained. The wait-and-see decisions are those which can be altered during a model run. The concept is shown in figure 3.

Figure 3: Types of Decisions in a Strategic Model: ‘here-and-now’ and ‘wait-and-see’ (Georgiadis et al., 2011)

Case study

The authors then set the parameters for the model using an “European wide production and distribution network comprising of three manufacturing plants producing 14 different types of products and located in three different European countries, namely the UK, Spain and Italy” (see figure 1).
The proposed demand volume is given in four scenarios for all customer areas and products. Two cases are compared: one with low safety stock and another one with a general higher safety stock level.
The resulting optimal supply configuration for the high inventory case is shown in figure 4.

Figure 4: Optimal Solution of the Supply Chain Case in the high Safety Stock Setting (Georgiadis et al., 2011)

Conclusion

The authors keep up to their promise and delivered a quite detailed model description and its results. But still, would it be possible to reproduce their results or rebuild their model using this data only? Very unlikely.

Even though the model is detailed. There is still a lot of information missing about the specific parameters used and the interconnections in the model. One major factor in the scientific acceptance and validity of research is the reproducibility of the results. And sadly, that’s one of the reasons, why complex models are still not commonly presented in renowned journals.

In my opinion the only chance to circumvent this obstacle is not only to publish the article, but also the complete model source code and the parameters used.

In the article these omissions are necessary to stay below a certain page limit – the authors already had to distribute the result charts of their case study throughout the paper to have a chance to include the most relevant ones.

But beside these necessary exclusions, I found that some other things would have been interesting to read about.

Demand risk: For a strategic (i.e. long term) model and so many different demand centers, I think only four demand scenarios might be too few to represent reality in a sufficient way. More scenarios could have been included, since the CPU time it took to calculate one optimal solution was quite low (some hundred seconds only).
Other risks: Furthermore it would have been interesting to analyze the effects of other risks in the model, but they were omitted as well.
Overview: I was also missing a short general overview over the given scenarios.
Sensitivity analysis: Lastly, the validity of a model can be further improved by analyzing the sensitivity of the model towards parameter change. The authors did not omit this point, but they choose to test and present only two deviations from their original model parameters, which I think is too little to assess the validity of the model sufficiently.

I think my conclusion can be summarized as follows: It is definitely hard to present a complex supply chain model in a way which sustains the validity and reproducibility of the results. But, since the description of the model is quite elaborate, this paper can still be a great source and foundation for one’s own strategic supply chain model.

Reference:

Georgiadis, M.C., Tsiakis, P., Longinidis, P., & Sofioglou, M.K. (2011). Optimal design of supply chain networks under uncertain transient demand variations Omega, 39 (3), 254-272

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The Power of Flexibility for Mitigating Supply Chain Risks

Daniel Dumke — Wed, 26 Oct 2011 13:31:00 +0000

This article sheds light on the question of how much flexibility is necessary to secure the supply chain against disruption risks.
The paper reviewed today takes a closer look at three supply chain risks: supply, process and demand risks (figure 1).

Figure 1: Selected Risks for further Analysis (Tang and Tomlin, 2008)

Strategies

The authors focus on the short term agility to reduce risk and chose five strategies, which are analyzed in depth (figure 2).

Figure 2: Strategies for risk reduction using Flexibility (Tang and Tomlin, 2008)

The strategies are backed by several case studies each.
For all five strategies the authors build a different model. First stands the description of the scenario, second is the development of the model which fits the scenario and is able to deploy the strategy. The last step is the description of the results.

Supply risks

Flexibility via multiple suppliers
Multiple alternative suppliers can reduce the supply cost risks, since the company gains the flexibility to purchase from the company with the lowest prices.
The first model is based on a case by Intercon Japan and Li and Fung. One ordering company is confronted with supply cost risk. The price of the identical goods is random and can vary between $5 and $15. The authors calculate the profit for the single up to a five (optional) supplier case and conclude that profits rise with increasing number of suppliers, whereas the marginal increase declines (figure 3).

Figure 3: Profit vs. Number of Supplier to reduce Supply Cost Risks (Tang and Tomlin, 2008)

Flexibility via a flexible supply contract
Flexible supply contracts allow the ordering firm to adjust its predetermined order at short notice usually within a limited quantity range.
This model is based on a case with Canon, HP and Best Buy. Demand is random, the purchasing contracts between buyer and seller are negotiated in the beginning of a period. But the actual ordered quantity can be adjusted between u% less or more than the originally agreed quantity. Calculating the profits for increasing flexibility u% gives the results shown in figure 4.

Figure 4: Profit vs. Contract Flexibility (Tang and Tomlin, 2008)

Process risks

Flexibility via flexible manufacturing processes
Flexible manufacturing requires a plant to be adaptable to produce a multitude of different products.
In this model process flexibility is modeled by the number of products (h) which can be produced by one plant. Different forms are shown in figure 5.

Figure 5: Different Flexibility Systems (Tang and Tomlin, 2008)

The calculations shows that increased process flexibility can also increase profits in an uncertain scenario (figure 6).

Figure 6: Profit vs. Degree of Process Flexibility (Tang and Tomlin, 2008)

Demand risks

Flexibility via postponement
Further flexibility is gained by postponing product differentiation decisions until the latest possible point during the production process.
In this model two products are sold at a market, demand for them is uncertain. Postponing product differentiation (shown in figure 7). Calculating profits for two different random processes (Independent and Identically Distributed (IID) and Random Walk (RW) Model), shows that also increase in postponement leads to increasing profits (figure 8).

Figure 7: Scheme for Product Postponement (Tang and Tomlin, 2008)

Figure 8: Profit vs. Postponement Flexibility (Tang and Tomlin, 2008)

Flexibility via responsive pricing
Case studies show the value of price adaptability to steer customer demand.
In this model the company is able to postpone the pricing decision for the selling season until the time t. Up to this point in time the company is therefore able to observe demand. Timing flexibility increases as t increases. From this it can also be shown that increasing flexibility leads to better profits with uncertain demand. Figure 9 has the results.

Figure 9: Profits vs. Pricing Flexibility (Tang and Tomlin, 2008)

Conclusion

The authors took some effort to generate five different models to analyze the flexibility cases. Nonetheless, I would judge the models to be quite specific for the cases, which is good for the research, but also poses the question: Will these results hold true in any case? For any company and supply chain?
There are other results (e.g. by Tomlin und Wang, 2005, which indicate that flexibility might not be the right choice for risk averse companies, which might be better of by choosing a dedicated strategy instead)

But if you keep this caveat in mind this work is a strong proponent of flexibility as a tool to increase resilience in an uncertain environment.

Reference:

Tang, C., & Tomlin, B. (2008). The power of flexibility for mitigating supply chain risks International Journal of Production Economics, 116 (1), 12-27 DOI: 10.1016/j.ijpe.2008.07.008

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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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Supply Chain Design - Robust Planning with differentiated Supplier Selection

Daniel Dumke — Wed, 13 Oct 2010 13:28:00 +0000

This is the third contribution to my series on doctoral dissertations on Supply Chain Risk Management. An immense effort and dedication is spent on these works only to find the results hidden in the libraries. So the goal is raise interest in the research of my peers.

Author / Topic

This dissertation was written by Stephanie Freiwald in 2005 as her doctoral thesis at the University of Bochum. It was published by Peter Lang, Frankfurt a.M. and can be ordered here from amazon.deor your local library. The title can be translated as:

Supply Chain Design – Robust Planning with differentiated Supplier Selection

Summary

In her work Freiwald builds a mathematical model of a four echelon supply chain (supplier, producer, distributor / inventory, customer) starting with a literature review of existing models. Building up from there she first adds variables to include sophisticated criteria for the supplier selection extending the traditional price-only selection.

Robustness can be oriented towards the models optimality, reliability, result-robustness and goal robustness. So as the next step the author set the goal to include robustness to uncertainty and unsettled preferences of the decision maker to the model.

As a final step the author applies her model to an industrial case, with the goal to find optimal, robust solutions for an Supply Chain Design problem.

Conclusion

Stephanie Freiwald’s work stands apart in including multiple aspects of the supply chain design problem into one concise model for optimization without neglecting the implementation of such a “theoretical” model.

Reference:

Stephanie Freiwald (2005). Supply Chain Design – Robuste Planung mit differenzierter Auswahl der Zulieferer Peter Lang, Frankfurt a.M., Dissertation

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