Multiple depot inventory systems with stock transfer are used by many companies especially when demand is high relative to storage capacity. The key issues in such systems are how many of each item to hold at each depot and what to do if there is a demand for an item at a depot that has none of that item in stock. This study was motivated by the inventory problem faced by a UK car part retailer that groups its depots into pairs. The company's policy for dealing with a demand at a depot that cannot be satisfied from local stock is to either transfer the item from the other depot in the group or to place an emergency order. The object of this paper is to characterise an optimal policy for this problem and to propose a method of calculating the parameters of such a policy.inventory systems, Markov decision models, dynamic programming

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.Markov Decision Processes, Inventory, Start-up Firms

Abstract. 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 twodimensional 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. IntroductionStochastic dynamic programming models are attractive for multireservoir control problems because they allow the non- This paper proposes a method of determining an operating policy for a broad class of reservoir networks that is practical for systems with many reservoirs. The operating policy for a particular reservoir is determined by solving a stochastic dynamic programming model with a three-dimensional representation of the volumes of water stored in the reservoirs. This representation consists of a detailed model of the particular reservoir, an approximate model of reservoirs whose releases can reach that reservoir, and an approximate model of the remainder of the system. The justification for this decomposition is the belief that the factors which most influence the decision as to how much water to release from a reservoir are the volume of water stored in that reservoir, the volume of water to take from reservoirs above that reservoir, the volume of water to pass on to reservoirs below that reservoir, and the effect of these factors on immediate and future rewards. There are several advantages to this approach to the problem: the solution time increases quadratically with the number of reservoirs in the system, so large problems can be tackled; the operating policy for a reservoir can be determined independently, so decision making can be decentralized and parallel processing can be used; the operating policy for a reservoir is a function of few variables, making it easy to implement; and the method can be applied to any acyclic network of reservoirs in which the release from a reservoir enters at most one other reservoir.Section 2 describes a general model of a multireservoir system. Section 3 indicates how this model can be solved by discrete dynamic programming. This solution method will be referred to as the "full method." In section 4 we present an alternative solution method for the general model which uses decomposition and aggregation techniques. This method will be referred to as the "aggregate method." Section 5 presents a comparison of the solution methods we consider. 333

PurposeTo demonstrate the successful use of lifestage segmentation and survival analysis to identify cross‐selling opportunities.Design/methodology/approachThe study applies lifestyle analysis and Cox's regression analysis model to behavioural and demographic data describing 10,979 UK customers of a large international insurance company.FindingsThere 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/implicationsThe 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 enhanced by incorporating a wider range of customer characteristics into the analysis.Practical implicationsThe findings show clear differences in behaviour across the segments identified, providing a basis on which marketing planners might differentiate marketing and communication strategies for particular products market segments.Originality/valueThe paper illustrates the adaptation of survival analysis methodology, familiar in other disciplines but comparatively rare in marketing, to the cross‐selling of financial services. It shows how planners cannot only identify customers most likely to repurchase but also predict the timeframe in which that will take place.

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