uncertainty

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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Uncertainty in Value Stream Mapping Analysis

Daniel Dumke — Wed, 30 Nov 2011 15:09:00 +0000

Supply chain mapping can be a great tool to foster the understanding and from its results improve a supply chain network overall. Supply chain mapping can also be used to analyze the risks of a supply chain and improve its resilience (for an example in the blog follow this link).
A SC mapping can also lead to implications for risk management, but how do you include existing information about the risks themselves in the analysis?

Braglia et al. (2009) analyze this problem and suggest two approaches to include variability in a value stream mapping (VSM) with the goal of better identification of the wastes in a single plant setting, but I think their insights might also be interesting for a supply chain setting.

Method

Value stream mapping can be described as “a graphical representation of both materials and information flow within a facility”. This permits to analyze the process and make calculations, e.g. regarding the total production lead time (TPLT), the total value-added time (TVAT) and the efficiency of the process (η = TVAT/TPLT)

VSM is not the method of choice for all problems, beside some pros there are also the cons:
Pro

It shows the linkage between product flow and information flow;

it includes information related to production time as well as to inventory levels;

it helps to visualise the production process at the plant level, not just at the single process level.

The main cons include

it is a paper- and pencil-based technique, thus the accuracy level is limited and the number of versions that can be handled is low;

it lacks the spatial structure of the facility layout and how that impacts interoperation material handling delays;

it cannot address the complexity of high-variety low-volume type companies, whose value streams are composed of hundreds of industrial parts and products.

Uncertainty and VSM

The authors suggest two similar approaches to include uncertainty within the VSM: the stochastic and the fuzzy approach.

In the stochastic approach uncertainty is described using distribution function (figure 1) with a mean and standard deviation.

Figure 1: Representation of a Stochastic Variable (Braglia et al., 2009)

In the case of a fuzzy logic the uncertainty is described using a triangle function (figure 2), which can be described by the start and end values (a and c) and the maximum b.

Figure 2: Representation of a Fuzzy Number (Braglia et al., 2009)

Application

When applying one of the mapping approaches the authors suggest to follow the following seven step process:

The analysis starts with the identification of the value stream (i.e. product family) that has to be mapped.

Walking backward in the process (i.e. from the finished good inventory to the raw materials warehouse), practitioners collect all the relevant data and draw a sketch of the actual state map.

[To include the random aspects of the value stream,] the waiting/processing time of each activity is approximated [and represented by a corresponding function.

The actual state map is completed substituting, in the corresponding process boxes and on the timeline, deterministic times with the random variables.

[The TPLTs are calculated using stochastic methods]

Using lean principles possible future state maps are designed and their expected TPLT is evaluated […]

Obtained improvements are evaluated comparing the TPLT.

The major milestones in the process are therefore the completion of the map of the actual state and possible future state maps.

Figure 3 shows the actual state map for a case study company presented in the article. Underneath the map you find the process times with deterministic values, stochastic representation and fuzzy representation of the uncertainty (from top to bottom, click on the image to show a larger version).

Figure 3: Actual State Map (Braglia et al., 2009; click to enlarge)

One example for a possible future state of the supply chain is shown in figure 4, again with the respective lead times.

Figure 4: Future State Map (Braglia et al., 2009; click to enlarge)

Conclusion

Value stream mapping can be used in a supply chain setting as well. And it can help to find bottle-necks – and as shown here the randomness of processes can be included as well. The authors make a great job of explaining the mentioned approaches and sketching the implementation as well.
Sadly, they forgot to describe the advantages of the inclusion of randomness in the value stream mapping: After presenting a second future state the authors do a statistical comparison of the two outcome distributions and conclude: “Therefore both methodologies show that the first solution is definitely better than the second one.”
But, if they had just compared the deterministic process times they would have come to the same conclusion! So where is the point in including the randomness at all?

Reference:

Braglia, M., Frosolini, M., & Zammori, F. (2009). Uncertainty in value stream mapping analysis International Journal of Logistics Research and Applications, 12 (6), 435-453 DOI: 10.1080/13675560802601559

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Agile Supply Chains and Uncertainty

Daniel Dumke — Wed, 27 Apr 2011 12:49:00 +0000

There are many definitions of agility. A supply chain can be defined as agile, when it is flexible and responds quickly to customer needs. Agility can also be seen as a measure to mitigate supply chain risks, building on this thought Dani and Ranganathan (2008) developed a model to mitigate risks using the concept of agility .

Concept for Agile Risk Mitigation

The authors develop the model based on two premises: (1) scenario planning is used to identify supply chain risks and (2) the system is designed to react fast and flexible to mitigate the risk.
Figure 1 shows the resulting concept.

Figure 1: Concept for agile Supply Chain Risk Mitigation (Dani and Ranganathan, 2008)

Two general mitigation “arms” are necessary. One for the foreseen risks which can be mitigated proactively and unforeseen risks which have to be reduced reactively.

Model Validation

This model constitutes a theory build by the authors on recent literature and own experience. To raise the credibility a theory has to be validated. In this case the authors decide to use the Ericsson case (if you are interested, have a look at my review of the case here).
After a breakdown of a Philips semiconductor plant in 2000, Nokia and Ericsson were competing over the remaining capacity. Nokia reacted fast and acquired spare capacity by Philips and other suppliers. Ericsson reacted more slowly and failed to obtain the necessary component and lost about 400 million USD.

When applying the above mentioned model, it is clear that both companies had not thought about this scenario, however Nokia already beforehand had established a fast communication structure which permitted it to react in a fast manner.

Conclusion

The article also contains a extended literature section defining the terms used, building from uncertainty and risk, to risks in supply chains, scenario analysis and the agility concept. Building on that the concept presented on less then one page seems to be quite underweighted. The main statement of the article is that: (1) planning of future scenarios is important to anticipate and mitigate possible risks, (2) depending on the planning mitigation of disruptions happening can be done proactively or reactively. (3) Especially for reactive mitigation the agility of the company plays a major role in the success.

Reference:

Dani, S., & Ranganathan, R. (2008). Agility and supply chain uncertainty: a scenario planning perspective International Journal of Agile Systems and Management, 3 ¾, 178-191

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