Selected Publications

We investigate the dynamics of a closed-loop supply chain with first-order auto-regressive (AR(1)) demand and return processes. We assume these two processes are cross-correlated. The remanufacturing process is subject to a random triage yield. Remanufactured products are considered as-good-as-new and used to partially satisfy market demand; newly manufactured products make up the remainder. We derive the optimal linear policy in our closed-loop supply chain setting to minimise the manufacturer’s inventory costs. We show that the lead-time paradox can emerge in many cases. In particular, the auto- and cross-correlation parameters and variances of the error terms in the demand and the returns, as well as the remanufacturing lead time, all influence the existence of the lead-time paradox. Finally, we propose managerial recommendations for manufacturers.
European Journal of Operational Research, 269 (1), 313–326, 2018

To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier’s production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre-established price, we examine whether the supplier should offer advance-order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance-order discount contract is Pareto-improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre-specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance-order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first-best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto-improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one-supplier-one-manufacturer case continue to hold when we have two manufacturers.
Production and Operations Management, 26 (12), 2175–2186, 2017

Production plans often span a whole week or month, even when independent production lots are completed every day and service performance is tallied daily. Such policies are said to use staggered deliveries, meaning that the production rate for multiple days are determined at a single point in time. Assuming autocorrelated demand, and linear inventory holding and backlog costs, we identify the optimal replenishment policy for order cycles of length P. With the addition of a once-per-cycle audit cost, we optimize the order cycle length P* via an inverse-function approach. In addition, we characterize periodic inventory costs, availability, and fill rate. As a consequence of staggering deliveries, the inventory level becomes cyclically heteroskedastic. This manifests itself as ripples in the expected cost and service levels. Nevertheless, the cost-optimal replenishment policy achieves a constant availability by using time-varying safety stocks; this is not the case with suboptimal constant safety stock policies, where the availability fluctuates over the cycle.
European Journal of Operational Research, 249 (3), 1082–1091, 2016

We study the impact of stochastic lead times with order crossover on inventory costs and safety stocks in the order-up-to (OUT) policy. To motivate our research we present global logistics data which violates the traditional assumption that lead time demand is normally distributed. We also observe that order crossover is a common and important phenomenon in real supply chains. We present a new method for determining the distribution of the number of open orders. Using this method we identify the distribution of inventory levels when orders and the work-in-process are correlated. This correlation is present when demand is auto-correlated, demand forecasts are generated with non-optimal methods, or when certain ordering policies are present. Our method allows us to obtain exact safety stock requirements for the so-called proportional order-up-to (POUT) policy, a popular, implementable, linear generalization of the OUT policy. We highlight that the OUT replenishment policy is not cost optimal in global supply chains, as we are able to demonstrate the POUT policy always outperforms it under order cross-over. We show that unlike the constant lead-time case, minimum safety stocks and minimal inventory variance do not always lead to minimum costs under stochastic lead-times with order crossover. We also highlight an interesting side effect of minimizing inventory costs under stochastic lead times with order crossover with the POUT policy—an often significant reduction in the order variance.
European Journal of Operational Research, 248, 473–486, 2016

Recent Publications

More Publications

. Avoiding the capacity cost trap: Three means of smoothing under cyclical production planning. International Journal of Production Economics, 201, 149-162, 2018.

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. Mitigating variance amplification under stochastic lead-time: The proportional control approach. European Journal of Operational Research, 256 (1), 151-162, 2017.

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. Revisiting rescheduling: MRP nervousness and the bullwhip effect. International Journal of Production Research, 55 (7), 1992–2012, 2017.

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. Exploring nonlinear supply chains: the dynamics of capacity constraints. International Journal of Production Research, 55 (14), 4053–4067, 2017.

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. The impact of product returns and remanufacturing uncertainties on the dynamic performance of a multi-echelon closed-loop supply chain. International Journal of Production Economics, 183, 487–502, 2017.

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. Revisiting activity sampling: a fresh look at binomial proportion confidence intervals. European Journal of Industrial Engineering, 10 (6), 724-759, 2016.

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. The bullwhip effect: progress, trends and directions. European Journal of Operational Research, 250 (3), 691–701, 2016.

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. Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand. Internaitonal Journal of Production Economics, 170, 501–512, 2015.

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. The impact of information sharing, random yield, correlation, and lead times in closed loop supply chains. European Journal of Operaional Research, 246, 827–836, 2015.

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. Coordinating lead times and safety stocks under autocorrelated demand. European Journal of Operational Research, 232 (1), 52–63, 2014.

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Recent & Upcoming Talks

If you would like me to give a talk, please get in touch.

Dual Sourcing and Smoothing Under Non-stationary Demand Time Series: Re-shoring with Speed Factories
Nov 6, 2018 12:05 PM

Recent Posts

My current work-in-progress with Robert Boute (KULeuven) and Jan Van Mieghem (NorthWestern) on Speed Factories has been summarised into a nice article appearing in Kellogg Insight.



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.

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.

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 2-5 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.


Please click here for my one page CV. Please email me for my complete CV.

Shiny Apps

Coming soon. I will shortly be developing some shiny apps to host here!


  • +44 2920 876310
  • S07, Aberconway Building, Colum 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.