Recent & Upcoming Talks

We study the relationship between lead times and the bullwhip effect produced by the order-up-to policy. The usual conclusion in the literature is that longer lead-time increase the bullwhip effect, we show that this is not always the case. Indeed, it seems to be rather rare. We achieve this by first showing that a positive demand impulse response leads to a bullwhip effect that is always increasing in the lead time when the order-up-to policy is used to make supply chain inventory replenishment decisions. By using the zeros and poles of the z-transform of the demand process, we reveal when this demand impulse is positive. To make concrete our approach in a nontrivial example we study the ARMA(2,2) demand process.

We study the dynamic consequences of lost sales when there is insufficient inventory to satisfy demand. Demand is assumed to be independently and identically distributed and drawn from a normal distribution. We consider the industrially popular order-up-to policy with unit lead time is used to make replenishment orders. In this scenario, we obtain expressions for the order and inventory distributions, allowing us to quantify the Bullwhip and Net Stock Amplification ratios. We show that both these metrics are equivalent. We also determine the mean inventory levels held, and the achieved fill rate. We do this when the lost sales are fully observable, and when the lost sales are unobservable.

I will be involved in three talks at the POMS Annual Conference in Washington this year. The three talks are: 1) Gaalman, G., Disney, S.M. and Wang, X., ‘When the Bullwhip Effect is an Increasing Function of the Lead Time’, Friday, May 03, 16.30 - 18:00, Columbia 7, 2) Disney, S.M., Purvis, L. and Meng, X., ‘Production optimization for short shelf-life products’, Monday, May 06, 08.00 - 09.30, Lincoln West, and 3) Hosoda, T., Disney, S.M. and Zhou, L., ‘Yield Paradox in Closed Loop Supply Chains with Auto- and Cross-correlated Demand and Return Processes’, Friday, May 03, 04:30 - 06:00, Piscataway. Hope to see you there!

Using block diagrams, z-transforms and Tsypkin’s relation I show how to obtain the variances of the orders and inventory levels maintained by the proportional order-up-to policy. Assuming demand is uncorrelated and normally distributed, a proportional feedback controller equal to the golden ratio minimizes a weighted sum of the variances. One may also minimize the inventory and capacity costs maintained by this replenishment policy.

We investigate the emerging trend of near-shoring a small part of the global production back to local SpeedFactories. The short lead time of the responsive SpeedFactory reduces the risk of making large volumes in advance, yet it does not involve a complete re-shoring of demand. Using a breakeven analysis we investigate the lead time, demand, and cost characteristics that make dual sourcing with a SpeedFactory desirable compared to off-shoring to a single supplier. We extend the celebrated order-up-to replenishment policy to settings where capacity costs exist and demonstrate their excellent performance. We highlight the significant impact of autocorrelated and non-stationary demand series

Recent Posts

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Projects

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Setting the Cadence of Your Pacemaker: A Lean Workbook for Reducing Mura

This visual workbook shows the practical lean manager how to solve the bullwhip problem.

Forecasting and production planning at Yeo Valley

I am currently in the middle of a 2-year project aimed at improving the forcasting and production planning processes within Yeo Valley, one of the largest organic dairy producers in the UK.

Teaching and Exec-Ed

I am currently teaching the following Masters courses at Cardiff University:

  • Operations Management
  • Project Management

In the past I have taught the following courses at Cardiff University:

  • Operations Analtyics (Masters)
  • Logistics and Transport Modeling (Undergraduate and Masters)
  • Supply Chain Modeling (Masters, service teaching for the Mathematics Department)
  • Operations Analysis (MBA, Exec MBA, and Part-time MBA)
  • Lean Operations (Exec MBA, and Part-time MBA)

I have also taught the following courses at Boston University, USA:

  • Project Management (Undergraduate)
  • Global Services and Supply Chain Management (Masters)
  • Quantitative and Qualitative Decision Making (Online Masters)

I also deliver exec-ed training, including:

  • Lexmark (Supply Chain Dynamics)
  • Yeo Valley (Dynamic Value Stream Mapping)
  • UK Intellectual Property Office (Operations Management)
  • ACME Automotive Industry of India (Dynamic Value Stream Mapping)

I have recently developed a 1-2 day course for Exec-Ed delivery entitled “Setting the cadence of your pacemaker”. The course shows you how to use dynamic value stream mapping to solve the bullwhip problem. Topics covered include: replenishment strategy selection, forecasting, designing replenishment decisions, detailed scheduling, and supplier MRP. If you are interested in this type of training please contact me.

Apps & Add-ins

Shiny Apps

Shiny

Click here to be re-directed to a web-based Shiny App designed to support a paper on SpeedFactories that I am currently writing.

Click here to be re-directed to a web-based Shiny App that explores the Economic Order Quantity decision. This simple Shiny App was developed as part of a Shiny Hack Day I ran on May 15, 2019 in Cardiff Business School.

Click here to be re-directed to a web-based Shiny App that explores the Standard Normal Distribution. This simple Shiny App is useful for determining safety stocks, fill rates and the like in many operations management settings.

Excel Add-ins

Many of the mathematical functions required in operations management (OM) scenarios are not available in Microsoft Excel. To address this issue, I have created an Add-in that adds some OM functionality to Excel. The Add-in can be downloaded here.

To install this Add-in:

  1. Save the file onto your computer.
  2. Open Excel.
  3. Select Files/Options/Add-in/Manage Add-ins.
  4. Click ‘Go’.
  5. Browse to the folder where you saved the Add-in.
  6. Select the .xla file.
  7. Confirm the Operations Analysis Add-in is ticked in list of available Add-ins.

When you have done this, the following functions should now be available in Excel:

=InvLossFun(x)

Gives the inverse of the standard normal distribution function evaluated at x. This is a useful function when determining safety stock levels when net stock levels are normally distributed. This function has also been incorporated into my Shiny App for the standard normal distribution that is available here.

=LambertW(mode,z)

Gives the real solutions to the Lambert W function on the principle branch (when mode = 1) and the alternative branch (when mode = -1), evaluated at z. This function is useful for identifying stability boundaries (see Warburton et al. (2004)) and bullwhip expressions (see Warburton and Disney (2007)) in continuous time systems and also for identifying the Net Present Value of the cash flows in the EOQ problem (see Disney and Warburton (2013).

=CBk(phi_range,theta_range,k)

Calculates a critical bullwhip condition for ARMA(p,q) demand in the Order-Up-To policy with a lead-time of k periods. If CBk is positive bullwhip is generated. If CBk is negative bullwhip is avoided. This criteria even works with non-stationary demand. The maximum allowable k is set to 100 as otherwise it slows up the computer. More information can be found in Gaalman et al., (2018).

  • phi_range is an ordered list of the auto-regressive components of demand process.
  • theta_range is an ordered list of the moving components of the demand process.
  • k is the lead-time (without the sequence of events delay).

=DampedTrend(range, alpha, beta, phi, Tp, WIPQuery)

Calculates the Damped Trend forecast with a smoothing constant for the level of alpha, a smoothing constant for the trend of beta, a damping parameter of phi. More information can be found in Li and Disney, (2015).

  • range is the demand data that is to be forecasted.
  • alpha is the smothing constant used to predict the level.
  • beta is the smoothing constant used to predict the trend.
  • phi is the is the damping co-efficient that shapes the future demand projections.
  • WIPQuery. If WIPQuery is False then the Tp+1 period ahead forecast is calculated. If WIPQuery is True then the forecast calculated the sum of the forecasts over the next Tp periods.
  • Tp the forecast horizon over which you forecast. In the order-up-to policy Tp is the lead-time (without the sequence of events delay)

Note: When phi = 1, Holts forecasts are generated. When beta = 0, exponential smoothing forecasts are generated.

=Fillrate(mu1,sigma1,mu2,sigma2,rho)

Calculates the fill rate when demand and inventory is normally distributed. Both demand and inventory can be correlated, cross-correlated, and possibly negative in some periods which makes this calculation much more robust than many other other fillrate formulas. More information can be found in Disney et al., (2015).

  • mu1 is the mean of the opening inventory (opening inventory = previous closing inventory + demand),
  • sigma1 is the standard deviation of the opening inventory,
  • mu2 is the mean demand,
  • sigma2 is the standard deviation of demand and
  • rho is the Pearson Correlation Coefficient between the opening inventory and demand.

=FillrateInv(mu1,sigma1,mu2,sigma2,rho,FR,openTNS)

Calculates the safety stock required to achive a target fill rate when demand and inventory is normally distributed. Both demand and inventory can be correlated, cross-correlated, and possibly negative in some periods which makes this calculation much more robust than many other other fill rate formulas. More information can be found in Disney et al., (2015).

  • mu1 is the mean of the opening inventory (opening inventory = previous closing inventory + demand).
  • sigma1 is the standard deviation of the opening inventory.
  • mu2 is the mean demand.
  • sigma2 is the standard deviation of demand.
  • rho is the Pearson Correlation Coefficient between the opening inventory and demand.
  • FR is the targt fill rate that you wish to receive.
  • openTNS is the current safety stock (target net stock) used in the opening inventory data.

I am keen to add more functionality to my Operations Analysis Add-in. If you have an idea of something useful to add, please contact me.

CV

Please click here for a summary one page CV. My complete CV and full publication list is available here.

Contact

  • +44(0)2920 876310
  • S07, Aberconway Building, Column Drive, Cardiff Business School, Cardiff University, Cardiff, CF10 3EU, United Kingdom.
  • My regular office hours are 9:30 to 11:30 on Wednesdays. Alternatively, you may email for an appointment.