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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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Supply Chain Flexibility in an uncertain Environment: exploratory Findings from Five Case Studies

Daniel Dumke — Mon, 07 Nov 2011 12:47:00 +0000

This is another look at flexibility strategies to reduce uncertainty in supply chains. This time from the point of view of five Chinese companies in the apparel industry.

Method

The authors use a case study to “illustrate and examine the different flexibility strategies adopted by supply chain participants as a result of different environmental uncertainties.”
The five companies cover different parts of the apparel supply chain. A garment and a fabric manufacturer (companies A and E, respectively), two trading companies (C and D) and a brand company (B). This diverse sample should enable the authors to make more general deductions from the generated data.
Figure 1 shows some relevant background information for the companies.

Figure 1: Case Study Companies (Yi et al., 2011; click to enlarge)

Results

The first questions revolved around the perceived uncertainties experienced by the participants. All companies mentioned that emergent orders, uncertainties about material cost and the aggressiveness of the competition are perceived as major uncertainties (figure 2).

Figure 2: Perceived Uncertainties by the Companies (Yi et al., 2011; click to enlarge)

Several different supply chain strategies were employed, a summary is displayed in figure 3.

Figure 3: Flexibility Strategies employed (Yi et al., 2011; click to enlarge)

The authors especially wanted to highlight the influence of different environmental aspects on the chosen strategies. No pattern emerged when analyzing which flexibility strategies are used for which uncertainties.
So next the authors examined the impact of the general level of uncertainty experienced by the companies and compared it with the supply chain flexibility level chosen.
The authors came up with a matrix (figure 4). Where they contrast SC uncertainty and flexibility. Companies D and B find themselves in the conservative corner while E, C and A employ a high level of flexibility to combat the uncertainties. From the interviews the authors also deducted the future positions of the companies A and B, which are indicated as A’ and B’.

Figure 4: Supply Chain Flexibility vs. Uncertainty (Yi et al., 2011)

Next the authors discuss their findings and reach four conclusions:

A low level of uncertainty in the supply chain leads to the adoption of a conservative flexibility strategy.
A high level of uncertainty in the supply chain leads to the adoption of an agile flexibility strategy.
An aggressive flexibility strategy can be proactively adopted through restructuring a firm’s operating system to reduce environmental uncertainties.
An aggressive flexibility strategy can be proactively adopted through creating new opportunities to improve a firm’s supply chain flexibility.

Conclusion

I like case study research, since usually you can gain some really genuine and new insights, in this case: What are other companies doing to contain uncertainty and how are they employing flexibility for that?

In this case I liked the paper a lot as well… up to the matrix. I don’t like matrices where the axes are not independent, because that’s not how you generate a matrix. Take the Growth-Share-Matrix, where you have the axis market growth and market share. The one is dependent on the market and the other on one company’s share in it. Relation to one another: Independent.
Here we have uncertainty on one axis and a strategy to reduce uncertainty on the other. So of course most companies would lie somewhere in the middle. So there is not much to learn from it. Of course there is not a one-to-one relationship, but anyway.

I had several more points to complain (number of interviews also only five, conclusions drawn are directly linked to their flawed matrix-framework and no quantitative measures to assess the flexibility and uncertainty levels).
But I still think the strategies mentioned from the interviews are still worth considering when choosing your own strategies.

Reference:

Yi, C.Y., Ngai, E.W.T., & Moon, K.-L. (2011). Supply chain flexibility in an uncertain environment: exploratory findings from five case studies Supply Chain Management: An International Journal, 16 (4), 271-283

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Pricing in Times of Disruption

Daniel Dumke — Wed, 10 Aug 2011 16:13:00 +0000

Many articles, including my own research show, that companies tend to focus largely on risk mitigation measures concerning the supply side. Only little is done to include demand side risks or demand side measures into the mitigation of supply chain risks. The study “Pricing During Disruptions: A Cause of the Reverse Bullwhip Effect” focusses on optimal pricing measures during a disruption. And so it helps to close the gap a little bit.

You can download a preprint of today’s paper at SSRN.

Reverse Bullwhip Effect

During a disruptions demand can change quickly. Due to a real or felt shortage customers are likely to order more than they actually need. This effect can be described by the Reverse Bullwhip Effect:

Whenever there is a perceived shortage of supply, it amplifies as it propagates down the supply chain. In fact, forward and reverse bullwhip effects often act as a system. If you start with a sudden upturn in demand, it gets amplified as it goes upstream, which creates a perceived shortage that amplifies as it propagates downstream. This creates a panic and downstream consumers overstate their demand, which amplifies again as it goes upstream. In turn, a greater scarcity is felt, and so on. Each of these effects feeds the other.

Method

The authors establish a mathematical model of a two tier supply chain, containing a single manufacturer (M) and a single (aggregated) demand (C). The process is established as follows:

Before the interaction, the manufacturer is hit by a disruption with a decreasing effect on capacity. The recovery takes place slowly over the course of several periods. The following steps are executed in each period:

M realizes its current capacity

M sets a price

C orders a specific number of products according to its predetermined behavior

The manufacturer has three price setting strategies at its disposal:

Naive: The price is set only based on the capacity and the long term demand curve of the customer, any short term behavior of the customer is ignored
One Period Correction: The deviation between the long term demand and the actual order of the customer is taken into account for the pricing decision.
Regression pricing: A regression analysis between set price and customer orders is included into the decision making process of the manufacturer.

The customer’s order behavior also includes historical prices. Two demand curves are specified, a long term demand curve, where the demand is linear in price, and a short run demand curve where the price change is included as well (figure 1).

Figure 1: Short Term Demand Behavior (Rong et al. 2009)

Results

The results show that the one period correction strategy results in a more volatile customer ordering process and lower revenues than both the naive and regression pricing strategies. Also in these terms the regression pricing strategy performs

worse than the naive strategy. The Reverse Bullwhip Effect is shown to occur in the disruption setting and almost always leads to reduced revenues.

Conclusion

From my point of view the study emphasizes four things:

All strategies involve active price changes by the company. Even though the naive strategy sounds very “lazy” it still involves using the available knowledge to optimize the profits of the manufacturer, including adapting prices.

The limited knowledge of the manufacturer is the major obstacle in the reduction of the Reverse Bullwhip Effect and improved revenues.

As for the Bullwhip Effect itself, the effects might be even worse with longer supply chains

An open question for me would also be how a more realistic (i.e. slower) price setting algorithm would affect the strategies.

Reference:

Rong, Y., Shen, Z.-J. M., & Snyder, L V. (2011). Pricing During Disruptions: A Cause of the Reverse Bullwhip Effect SSRN

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