Thomas Welsh Archibald

An aggregate stochastic dynamic programming model of multireservoir systems

We present a new method of determining an operating policy for a multireservoir system in which the operating policy for a reservoir is determined by solving a stochastic dynamic programming model consisting of that reservoir and a two-dimensional representation of the rest of the system. The method is practical for systems with many reservoirs because the time required to determine an operating policy only increases quadratically with the number of reservoirs in the system and because the operating policy for a reservoir is a function of few variables. We apply the method to examples of multireservoir systems with between 3 and 17 reservoirs and show that the operating policies determined are very close to optimal.

Should Start-up Companies Be Cautious? Inventory Policies Which Maximise Survival Probabilities

New start-up companies, which are considered to be a vital ingredient in a successful economy, have a different objective than established companies: They want to maximise their chance of long-term survival. We examine the implications for their operating decisions of this different criterion by considering an abstraction of the inventory problem faced by a start-up manufacturing company. The problem is modelled under two criteria as a Markov decision process; the characteristics of the optimal policies under the two criteria are compared. It is shown that although the start-up company should be more conservative in its component purchasing strategy than if it were a well-established company, it should not be too conservative. Nor is its strategy monotone in the amount of capital it has available. The models are extended to allow for interest on investment and inflation.

Identifying cross‐selling opportunities, using lifestyle segmentation and survival analysis

Purpose – To demonstrate the successful use of lifestage segmentation and survival analysis to identify cross‐selling opportunities.Design/methodology/approach – The study applies lifestyle analysis and Coxs regression analysis model to behavioural and demographic data describing 10,979 UK customers of a large international insurance company.Findings – There are clear differences between the lifestage segments identified with respect to customer characteristics affecting the likelihood of a second purchase from the company and the timeframes within which that is likely to take place. The “mature” segments appear to offer greater opportunities for retention and cross‐selling than the “younger” segments.Research limitations/implications – The study was limited by the type of data available for analysis, which related mainly to life insurance and pension products characterised by low transaction frequency. Different results might be expected for banking or credit‐and‐loan products. The findings could be enh...

An index heuristic for transshipment decisions in multi-location inventory systems based on a pairwise decomposition

In multi-location inventory systems, transshipments are often used to improve customer service and reduce cost. Determining optimal transshipment policies for such systems involves a complex optimisation problem that is only tractable for systems with few locations. Consequently simple heuristic transshipment policies are often applied in practice. This paper develops an approximate solution method which applies decomposition to reduce a Markov decision process model of a multi-location inventory system into a number of models involving only two locations. The value functions from the subproblems are used to estimate the fair charge for the inventory provided in a transshipment. This estimate of the fair charge is used as the decision criterion in a heuristic transshipment policy for the multi-location system. A numerical study shows that the proposed heuristic can deliver considerable cost savings compared to the simple heuristics often used in practice.

Modelling replenishment and transshipment decisions in periodic review multilocation inventory systems

Effective models of key operational decisions in multilocation inventory systems are important for a successful retail sector. This paper argues that much of the existing research in this area is not applicable to a highly competitive retail environment, particularly if periodic review replenishment policies are used. The paper develops a model of a periodic review multilocation inventory system that is suitable for this environment and investigates the characteristics of optimal replenishment and transshipment decisions. This motivates the development of three simple heuristic transshipment policies that are practical for systems with many locations. The results of a numerical study involving systems with five locations suggest that the performance of these heuristic policies is often close to optimal and can be considerably better than the performance of commonly used policies.

Controlling multi-reservoir systems

The paper extends the results of the form of the optimal policy for a hydroelectric reservoir problem from the one-reservoir case to multi-reservoir cases. The importance of these new results in practice is that they allow more efficient solution algorithms to be developed. Since multi-reservoir problems are extremely difficult to solve, such algorithms are of great value.

Analysing maintenance data to gain insight into systems performance

The high cost of maintenance in the processing industry implies the need for optimal planning of maintenance strategy. In order to achieve this there is a need to understand the underlying failure processes, which are often very complex. In this paper, a new semi-parametric approach, combining Cox regression with density kernal smoothing, is introduced to estimate the underlying performance. The approach has been applied to several processes and it allowed insight into each process, which would not have been achieved if traditional approaches had been used. Particularly, the refurbishment of processes had a significant impact on the rate failure. This paper concludes by assessing this impact of refurbishment on the maintenance programme.

The use of simple calibrations of individual locations in making transshipment decisions in a multi-location inventory network

Demands occur at each location in a network of stock-holding retail outlets. Should a location run out of stock between successive replenishments, then subsequent demands may be met either by transshipping from another location in the network or by an emergency supply from a central depot. We deploy an approximate stochastic dynamic programming approach to develop a class of interpretable and implementable heuristics for making transshipment decisions (whether and from where to transship) which make use of simple calibrations of the candidate locations. The calibration for a location depends upon its current stock, the time to its next replenishment and the identity of the location needing stock. A numerical investigation shows strong performance of the proposed policies in comparison with standard industry practice (complete pooling, no pooling) and a recently proposed heuristic. It points to the possibility of substantial cost savings over current practice.

Indexability and Index Heuristics for a Simple Class of Inventory Routing Problems

We utilise and develop Whittles restless bandit formulation to analyse a simple class of inventory routing problems with direct deliveries. These routing problems arise from the practice of vendor-managed inventory replenishment and concern the optimal replenishment of a collection of inventory holding locations controlled centrally by a decision maker who is able to monitor inventory levels throughout the network. We develop a notion of location indexability from a Lagrangian relaxation of the problem and show that (subject to mild conditions) the locations are indeed indexable. We thus have a collection of location indices in closed form, namely, real-valued functions of the inventory level (one for each location), which measure in a natural way (namely, as a fair charge for replenishment) each locations priority for inclusion in each days deliveries. We discuss how to use such location indices to construct heuristics for replenishment and assess a greedy index heuristic in a numerical study where it performs strongly. A simpler approximate index analysis is available for the case in which the demand at each location is Poisson. This analysis permits a more explicit characterisation of the range of holding cost rates for which (approximate) location indexability is guaranteed.

Serial and parallel value iteration algorithms for discounted Markov decision processes

Abstract This paper examines several serial value iteration solution algorithms for Markov decision processes and develops efficient analogous parallel algorithms. The results include a comparison of the computational performance of both the serial and the parallel algorithms and explain how the performance depends upon the properties of the problems being solved.