Prof. Alan C. McKinnon, PhD

Publications

Professor of Logistics

Publications

Journal Articles (Peer-Reviewed)

Copy reference link   DOI: 10.1007/s10479-018-2773-7

Abstract: Capacity acquisition is often capital- and time-consuming for a business, and capacity investment is often partially or fully irreversible and difficult to change in the short term. Moreover, capacity determines the action space for service/production scheduling and lead-time quotation decisions. The quoted lead-time affects the customer’s perceived service quality. Thus, capacity acquisition level and lead-time quotation affect a firm’s revenue/profit directly or indirectly. In this paper, we investigate a joint optimization problem of capacity acquisition, delivery lead-time quotation and service-production scheduling with cyclical and lead-time-dependent demands. We first explore the structural properties of the optimal schedule given any capacity and lead-time. Then, the piecewise concave relationship between the delay penalty cost and the capacity acquisition level is found. Thereby, an efficient and effective polynomial time algorithm is provided to determine the optimal capacity acquisition level, delivery lead-time quotation and service/production schedule simultaneously. Furthermore, a capacity competition game among multiple firms is addressed. The numerical studies show that capacity equilibrium often exists and converges to a unique solution.

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Copy reference link   DOI: 10.1016/j.ejor.2017.09.039

Abstract: Spare parts are necessary for ensuring the functioning of the critical equipment of many companies, and as such, they play a central role in these companies’ operations. Inventory control of spare parts is particularly challenging due to the nature of their demand, which is usually slow-moving, erratic and lumpy. As inventory policies rely on the forecasted lead-time demand distribution and this choice impacts the performance of the system, an ill-suited hypothesized distribution may result in high preventable costs. In this study, we contribute to the empirical literature by analyzing what distributions best fit spare parts demand. We use the Kolmogorov Smirnov (K–S) goodness-of-fit test to find the best-fitting distributions to our data and compare our results to those in the literature. Furthermore, we implement a slightly modified K–S test that places greater emphasis on differences in the right tail of the distribution, mirroring real-world inventory applications, and less emphasis on the left tail. Finally, we link the goodness-of-fit of the distributions to their inventory performance. Our first dataset comes from the German renewable energy industry and is composed of the weekly demand for more than 4000 items over the period 2011–2013. The second dataset comes from the Royal Air Force. It is composed of monthly demand for 5000 items over the period 1996–2002.

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Copy reference link   DOI: 10.1016/j.ejor.2017.06.049

Abstract: Companies commonly allocate their inventories across multiple locations based on their historical sales rates. However, random fluctuations in customer purchases, such as those caused by weather conditions and other external factors, might cause significant deviations from expected demand, leading to excess stock in some locations and stockouts in others. To fix this mismatch, companies often turn to lateral transshipments, e.g., the movement of stock between locations of the same echelon.In this paper, we examine multi-location inventory systems under periodic review with multiple opportunities for proactive transshipments within one order cycle. If stockouts occur, demand is lost with no opportunity to backorder. The objective of our model is to find an optimal policy that indicates the sources and the destinations of transshipments as well as the number of units, to maximise the profit of the network. We create a dynamic program that can, in principal, be solved to optimality using Bellman’s equation. However, the size of the state and decision spaces makes it impossible to find the optimal policy for real-world sized problem instances. Thereby, we use forward approximate dynamic programming to find a near-optimal transshipment policy.Finally, we conduct an extensive numerical study to gauge the performance of our transshipment policy. For small size instances, we compare our policy to the optimal one. For larger scale instances, we consider other practically oriented heuristics. Our numerical experiments show that our proposed algorithm performs very well compared to state-of-the-art methods in the literature.

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Copy reference link   DOI: 10.1057/jors.2015.63

Abstract: Consider a risk-averse decision maker in the setting of a single-leg dynamic revenue management problem with revenue controlled by limiting capacity for a fixed set of prices. Instead of focussing on maximising the expected revenue, the decision maker has the main objective of minimising the risk of failing to achieve a given target revenue. Interpreting the revenue management problem in the framework of finite Markov decision processes, we augment the state space of the risk-neutral problem definition and change the objective function to the probability of failing a certain specified target revenue. This enables us to obtain a dynamic programming solution that generates the policy minimising the risk of not attaining this target revenue. We compare this solution with recently proposed risk-sensitive policies in a numerical study and discuss advantages and limitations.

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Copy reference link   DOI: 10.1016/j.dss.2016.01.003

Abstract: Revenue management (RM) is making a significant impact on pricing research and practice, from aviation and hospitality industries to retailing. However, empirical data conditions in retail are distinct to other industries, in particular in the large number of products within and across categories. To set profitable static prices with established RM models, the data is often simplified by data pruning (the exclusion of subsets of data that are deemed irrelevant or unsuitable) and data aggregation (the combination of disparate data points). However, the impact of such data preprocessing, despite being ubiquitous in retailing, is insufficiently considered in current RM research. This could induce potential sources of bias for the demand model estimates, as well as subsequent effects on the price optimization system, the optimized price set, and the profit maxima, which have not yet been investigated. This paper empirically studies the impact of two commonly used data preprocessing techniques in retail RM, data pruning and data aggregation, using simulated and empirical retail scanner data. We numerically assess potential biases introduced by data preprocessing using a systems perspective in estimating a two-stage demand model, the resulting price elasticities, optimized price sets, and the ensuing profit that it yields. Results show that both data aggregation and data pruning bias demand model estimates, albeit with different effect, but both produce less profitable price sets than unbiased reference solutions. The results demonstrate the practical importance of data preprocessing as a cause for estimation bias and suboptimal pricing in retail price optimization systems.

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Copy reference link   DOI: 10.1016/j.ijpe.2015.03.027

Abstract: Abstract Consider a single-leg dynamic revenue management problem with fare classes controlled by capacity in a risk-averse setting. The revenue management strategy aims at limiting the down-side risk, and in particular, value-at-risk. A value-at-risk optimised policy offers an advantage when considering applications which do not allow for a large number of reiterations. They allow for specifying a confidence level regarding undesired scenarios. We introduce a computational method for determining policies which optimises the value-at-risk for a given confidence level. This is achieved by computing dynamic programming solutions for a set of target revenue values and combining the solutions in order to attain the requested multi-stage risk-averse policy. We reduce the state space used in the dynamic programming in order to provide a solution which is feasible and has less computational requirements. Numerical examples and comparison with other risk-sensitive approaches are discussed.

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Copy reference link   DOI: 10.1016/j.cor.2014.12.004

Abstract: Abstract Consider a dynamic decision making model under risk with a fixed planning horizon, namely the dynamic capacity control model. The model describes a firm, operating in a monopolistic setting and selling a range of products consuming a single resource. Demand for each product is time-dependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer requests for product classes. We investigate risk-sensitive policies in this setting, for which risk concerns are important for many non-repetitive events and short-time considerations. Numerically analysing several risk-averse capacity control policies in terms of standard deviation and conditional-value-at-risk, our results show that only a slight modification of the risk-neutral solution is needed to apply a risk-averse policy. In particular, risk-averse policies which decision rules are functions depending only on the marginal values of the risk-neutral policy perform well. From a practical perspective, the advantage is that a decision maker does not need to compute any risk-averse dynamic program. Risk sensitivity can be easily achieved by implementing risk-averse functional decision rules based on a risk-neutral solution.

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Copy reference link   DOI: 10.1016/j.ejor.2009.11.020

Abstract: We consider the problem of a firm selling multiple products that consume a single resource over a finite time period. The amount of the resource is exogenously fixed. We analyze the difference between a dynamic pricing policy and a list-price capacity control policy. The dynamic pricing policy adjusts prices steadily resolving the underlying problem every time step, whereas the list pricing policy sets static prices once but controls the capacity by allowing or preventing product sales.As steady price changes are often costly or unachievable in practice, we investigate the question of how much riskier it is to apply a list pricing policy rather than a dynamic pricing policy. We conduct several numerical experiments and compare expected revenue, standard deviation, and conditional-value-at-risk between the pricing policies. The differences between the policies show that list pricing can be a useful strategy when dynamic pricing is costly or impractical.

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Copy reference link   DOI: 10.1057/rpm.2010.33

Abstract: In recent years, many traditional practitioners of revenue management (RM) such as airlines or hotels were confronted with aggressive low-cost competition. In order to stay competitive, these firms responded by reducing fare restrictions that were originally meant to fence off customer segments. In markets where traditional practitioners faced low-cost competition, unrestricted fares were introduced. Some markets, including airline long-haul markets, were unaffected. And here restrictions could be maintained. We develop choice-based network RM approaches for such a mixed fare environment that can handle both the traditional opening or closing of restricted fare classes as well as handling pricing of the unrestricted fares simultaneously. Owing to technical constraints of the reservation system, we have a limit on the number of price points for each unrestricted fare. It is natural to ask then how these price points shall be chosen. To that end, we formulate the problem as a dynamic programme and approximate it with a mixed integer linear program (MIP) that selects the best price points out of a potentially large set of price candidates for each unrestricted fare. Numerical experiments illustrate the quality of the obtained price structure and that computational effort is relatively low, given that we need to tackle the large-scale MIP with column generation techniques.

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Copy reference link   DOI: 10.1002/nav.20321

Abstract: We develop a competitive pricing model which combines the complexity of time-varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. Each firm adopts, at the beginning of the planning horizon, a (single) price to be employed throughout the horizon. On the basis of each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan. We establish the existence of a price equilibrium and associated optimal dynamic lotsizing plans, under mild conditions. We also design efficient procedures to compute the equilibrium prices and dynamic lotsizing plans.

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Copy reference link   DOI: 10.1287/opre.1070.0392

Abstract: We consider a family of N items which are produced in or obtained from the same production facility. Demands are deterministic for each item and each period within a given horizon of T periods. If in a given period an order is placed, setup costs are incurred. The aggregate order size is constrained by a capacity limit. The objective is to find a lot-sizing strategy that satisfies the demands for all items over the entire horizon without backlogging, and which minimizes the sum of inventory carrying, fixed and variable order costs. All demands, cost parameters and capacity limits may be time-dependent. In the basic (JS)-model, the setup cost of an order does not depend on the composition of the order. The (JIS)-model allows for item-dependent setup costs in addition to the joint setup costs.We develop and analyze a class of so-called progressive interval heuristics. A progessive interval heuristic solves a (JS) or (JIS) problem over a progressively larger time-interval, always starting with period 1, but fixing the setup variables of a progressively larger number of periods at their optimal values in earlier iterations. Different variants in this class of heuristics allow for different degrees of flexibility in adjusting continuous variables determined in earlier iterations of the algorithm.For the (JS)-model and the two basic implementations of the progressive interval heuristics, we show under some mild parameter conditions, that the heuristics can be designed to be epsilon-optimal for any desired value of epsilon > 0 with a running time that is polynomially bounded in the size of the problem. They can also be designed to be simultaneously asymptotically optimal and polynomially bounded.A numerical study covering both the (JS) and the (JIS) model, shows that a progressive interval heuristic generates close-to-optimal solutions with modest computational effort and that it can be effectively used to solve large-scale problems.

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Copy reference link   DOI: 10.1002/9780470400531.eorms0272

Abstract: This chapter reviews multi-product dynamic pricing models for a revenue maximizing monopolist firm. The baseline model studied in this chapter is of a seller that owns a fixed capacity of a resource that is consumed in the production or delivery of some type of product. The seller selects a dynamic pricing strategy for the offered product so as to maximize its total expected revenues over a finite time horizon. We then review how this model can be extended to settings where the firm is selling multiple products that consume this firm's capacity, and finally highlight a connection between these dynamic pricing models and the closely related model where prices are fixed, and the seller dynamically controls how to allocate capacity to requests for the different products. Methodologically, this chapter reviews the dynamic programming formulations of the above problems, as well as their associated deterministic (fluid) analogues. It highlights some of the key insights and pricing heuristics that are known for these problems, and briefly mentions possible extensions and areas of current interest.

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Book Chapters

Working Papers

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Abstract: The railway industry offers similar revenue management opportunities to those found in the airline industry. The railway industry caters for the delivery and management of cargo as well as the transport of passengers. Unlike the airline industry, the railway industry has seen relatively little attention to revenue management problems.We provide an overview of the published literature for both passenger and freight rail revenue management. We include a summary of the some the available models and include some possible extensions. From the existing literature and talks with industry, it is clear that that there is room to exploit revenue management techniques in the railway industry, an industry that has revenues of $60 billion in the US and promises huge growth in Europe in the forthcoming years.

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