IMA Journal of Management Mathematics - Advance Access

Calculating the accuracy of hierarchical estimation

Strijbosch, L. W. G., Moors, J. J. A. — Thu, 12 Nov 2009 01:39:02 PST

Instead of forecasting demand for individual items separately, hierarchical forecasting is often used: total demand is forecasted for a collection of items; this total forecast then is broken down to produce the desired individual demand forecasts. To allow analytical analyses, we considered in a previous paper the simpler problem of hierarchical estimation. So from a random sample of demand periods, we estimated both the total demand for a number of items and the fraction of this total that an individual item takes; multiplying these two quantities gives the hierarchical estimate for each individual demand. From the joint distribution of the individual demands, we here present a fast and general method for finding the bias and variance of the corresponding hierarchical estimator. The method is compared with our previous results and two new applications are added.

Spare parts management: a review of forecasting research and extensions

Boylan, J. E., Syntetos, A. A. — Thu, 12 Nov 2009 01:39:01 PST

Spare parts are very common in many industries and forecasting their requirements is an important operational issue. In recent years, there have been advances in forecasting methods for spare parts, demand information sharing strategies and the design of forecast support systems. Some work has also been done on the value of judgemental adjustment of statistical forecasts. In this paper, these developments are reviewed and avenues for further research are explored.

Call planning in European pharmaceutical sales force management

Agnetis, A., Messina, E., Pranzo, M. — Mon, 09 Nov 2009 04:03:35 PST

In this paper, a mathematical model for the allocation of sales representatives is presented. The model takes into account some special features of pharmaceutical marketing, such as customer profiling (physicians), sales response functions and multi-product (drug) promotion procedures. The main peculiarity of the model is that it is suitable to those markets (such as European markets) where the detailed information about historical physician prescriptions is not available to pharmaceutical companies. A heuristic procedure has been designed and run to plan nationwide representative calls to more than 46000 physicians. A computational study, based on real data from a major pharmaceutical company, shows the feasibility of this algorithmic approach, resulting in significantly enhanced productivity. Moreover, the algorithm can be also employed as a tool to evaluate costly strategic options concerning sales force sizing and training.

A balanced team-generating model for teams with less than nine persons

van de Water, H., Bukman, C. — Wed, 14 Oct 2009 02:16:15 PDT

According to Belbin, each person can be characterized by nine role types. He provided a clear insight into the internal group relationships and the clarification of the roles needed for a team to work efficiently. The resulting teams are called balanced teams.This paper elaborates on a team balancing model. One of the difficulties in designing a balanced team is caused by the question of how to choose the nine necessary team roles when a team consists of less than nine persons. In that situation, one of the possible primary roles in a team must be replaced by a secondary role or even a tertiary role. A mathematical model is introduced that gives one the opportunity to assign the most suitable roles as primary and secondary roles to a team consisting of less than nine persons to generate a balanced team in terms of Belbin. A practical application is given.

Assessing performance in Greek bauxite mining by means of frontier estimation methodologies

Tsolas, I. E. — Tue, 22 Sep 2009 07:08:23 PDT

This paper employs for the first time data envelopment analysis (DEA) and stochastic frontier analysis (SFA) as two performance measurement competing approaches to assess efficiency in the Greek mining industry. These two frontier estimation methodologies overcome the limitations of the partial productivity measures by explicitly considering two inputs and one output in the measurement of efficiency for the period 1970–1996. The paper is also innovative in utilizing a bootstrapping approach in DEA to aggregated industry (time series) data as an alternative to the more common DEA point estimates. In particular, the bootstrapping approach used relies on the homogeneity assumption that the distribution of the efficiency scores is independently distributed over the sample; the results from DEA and SFA are more comparable under this assumption as it corresponds to the independence assumption regarding the distribution of the inefficiency term in SFA. The two different approaches to performance evaluation, as used here, do not provide confirmation of each other's findings since they are based on different principles and treat the data in different ways. Although the joint use made here of DEA and SFA provides results that are consistent with points of view that have regarded these two approaches as mutually exclusive alternatives, this paper demonstrates that from a policy perspective DEA and SFA can be utilized in tandem on a common data set to assess the efficiency and investigate the return to scale patterns at the sectoral level.

On the selection of k routes in multiobjective hazmat route planning

Caramia, M., Giordani, S., Iovanella, A. — Tue, 22 Sep 2009 07:08:23 PDT

Hazardous material (hazmat) transportation has received several attention in the past. On the one hand, this is motivated by the practical interest that hazmat transportation covers for safety reasons; on the other hand, it has attracted the study of those researchers working on vehicle routing since relevant hazmat transportation issues are concerned with finding routes with minimum cost and minimum risk. The former objective is mainly related to the carrier point of view, whereas the latter objective takes into account the government point of view. In this paper, we propose a new approach for planning routes for hazmat shipments that selects k efficient paths with respect to the minimization of length, time (cost) and risk; in particular, the selection is made by choosing k representative paths among the set of efficient paths, with high spatial dissimilarity. This allows one to guarantee an equitable distribution of the risk over the network. The proposed approach first exploits the Martins’ algorithm to find the set of efficient paths, and the k-means algorithm to partition the latter set into k classes of paths, minimizing the total variance of the objective vector values of the paths in the same class. Next, one path from each one of the k classes is chosen by heuristically solving the problem of selecting paths maximizing the total spatial dissimilarity. Computational results are presented on random graphs and on a real-life case study.

Organization size and the optimal investment in cash

Higson, A., Yoshikatsu, S., Tippett, M. — Fri, 14 Aug 2009 07:04:01 PDT

Miller & Orr (1966, Q. J. Econ., 80, 413–435) formulate a cash management model under which an organization's cash flow evolves in terms of a stationary random walk. This, in turn, implies that the organization's demand for cash will not grow over time. However, as organizations grow one would expect the demand for cash to grow as well. Given this, we formulate a cash management model under which movements in an organization's cash balance hinge on its current rate of output or an equivalent size measure. Cash is withdrawn and invested in interest-bearing securities when the cash to output ratio becomes too high, while securities are sold and the proceeds deposited in a non-interest-bearing bank account when the cash to output ratio becomes too low. The control limits are determined so as to minimize the expected annual cost of a unit of output. Our analysis shows that when organization's cash flows follow a non-stationary process, the optimal cash management policies are profoundly different to those obtained under the Miller & Orr(1966) model.

Modelling two-echelon serial inventory systems with perishable items

Olsson, F. — Tue, 04 Aug 2009 06:40:33 PDT

This paper deals with a continuous review, two-echelon serial (two locations) inventory system with perishable items. Transportation times and the lifetime of items are fixed. When the age of an item has reached its lifetime, the item is useless and consequently discarded from the system. The downstream location faces Poisson demand, and demand that cannot be met immediately is backordered. In this paper, we develop an efficient approximate technique for evaluation of (S – 1, S) policies. In a simulation study, we evaluate the quality of our approximation. The results reveal that our approximate technique works well in most cases.

Cournot equilibria in oligopolistic electricity markets

Vespucci, M. T., Allevi, E., Gnudi, A., Innorta, M. — Wed, 08 Jul 2009 07:12:27 PDT

Electricity markets are undergoing a liberalization process aiming at introducing competition and enhancing efficiency. In liberalized markets, quantities and prices are determined by the interactions among the different players: power producers determine their production levels so as to maximize their own profits, while energy prices and demand levels to be satisfied are decided by an independent system operator (ISO). Deregulated electricity markets are very often oligopolistic, therefore the market equilibrium resulting from the interactions among power producers and ISO can be well represented by oligopolistic models. Thus, models based on game theory are used to describe the oligopolistic strategic interactions between the firms involved, representing the market as a non-cooperative game where players decide their strategy in order to maximize their profit. This paper presents a model that describes the strategic interactions of firms based on the assumption that the generation firms are Cournot oligopolists. A linear demand curve is assumed. Moreover, a new iterative algorithm is presented for determining the Cournot equilibrium and a case study is discussed.

Hedging mean-reverting commodities

Broll, U., Clark, E., Lukas, E. — Thu, 25 Jun 2009 05:10:07 PDT

This paper uses the expected utility framework to examine the optimal hedging decision for commodities with mean-reverting price processes. The derived results show that when commodity prices follow a mean-reverting process, the optimal hedge ratio differs significantly from the classical results found under standard geometric Brownian motion. Hence, a failure to accommodate mean reversion when it exists can lead to systematic biases in hedging decisions.

Stochastic scenario decomposition for multistage stochastic programs

Higle, J. L., Rayco, B., Sen, S. — Thu, 25 Jun 2009 05:10:06 PDT

Over the past decade, several stochastic approaches have been proposed for two-stage stochastic programs. Many of these algorithms have attractive computational as well as conceptual properties (e.g. convergence with probability one). This paper expands the realm of such approaches to multistage convex stochastic programming problems. We present a stochastic scenario decomposition (SSD) algorithm which is a statistically motivated cutting plane algorithm for the solution of multistage stochastic programs. The method is based on solving a dual problem in which the variables correspond to multipliers associated with the non-anticipativity constraints of the primal problem. Our analytical results verify conditions under which SSD identifies an optimal solution asymptotically. We also overcome some computational hurdles resulting from increases in the column dimension of the SSD master problem. We propose a variable aggregation scheme that allows us to solve much smaller master programs without sacrificing solution quality. Our computational results demonstrate the effectiveness of this aggregation scheme in solving the SSD master program.

A dynamic day-ahead paratransit planning problem

Cremers, M. L. A. G., Klein Haneveld, W. K., van der Vlerk, M. H. — Fri, 19 Jun 2009 07:29:22 PDT

We consider a dynamic planning problem for the transport of elderly and disabled people. The focus is on a decision to make one day ahead: which requests to serve with own vehicles and which ones to assign to subcontractors under uncertainty of late requests that are gradually revealed during the day of operation. We call this problem the dynamic day-ahead paratransit planning problem. The developed model is a non-standard two-stage recourse model in which ideas from stochastic programming and online optimization are combined: in the first stage, clustered requests are assigned to vehicles, and in the dynamic second-stage problem, an event-driven simulation is used to cluster the late requests once they are revealed and subsequently assign them to vehicles. A genetic algorithm is used to solve the model. Computational results are presented for randomly generated data sets. Furthermore, a comparison is made to a similar problem we studied earlier in which the simplifying but unrealistic assumption has been made that all late requests are revealed at the beginning of the day of operation.

Indexation of Dutch pension rights in multistage recourse ALM models

Klein Haneveld, W. K., Streutker, M. H., van der Vlerk, M. H. — Wed, 17 Jun 2009 12:57:14 PDT

Indexation (correction for inflation) of defined benefit pension rights is an important topic in the current pension debate fostered by the ageing of populations. In the Netherlands, pension funds need to formulate policies concerning indexation. We show how indexation decisions can be modelled adequately in multistage recourse asset liability management (ALM) models, which can be used for supporting the policy making. Moreover, for a stylized pension fund, we analyze the working of these indexation decisions in a numerical experiment.

A multistage formulation for generation companies in a multi-auction electricity market

Musmanno, R., Scordino, N., Triki, C., Violi, A. — Wed, 17 Jun 2009 12:57:14 PDT

In this paper, we deal with the definition of a decision model for a producer operating in a multi-auction electricity market. The decisions to be taken concern the commitment of the generation plants and the quantity of energy required to offer to each auction and to cover the bilateral contracts. We propose a multistage stochastic programming model in which the randomness of the clearing prices is represented by means of a scenario tree. The risk is modelled using a Conditional Value at Risk term in the objective function. Experimental results are reported to show the validity of our model and to discuss the influence of the risk parameters on the optimal value.

A stochastic optimization model for gas retail with temperature scenarios and oil price parameters

Tue, 16 Jun 2009 09:58:45 PDT

The paper deals with a new stochastic optimization model, named Optimization Modelling for Gas Seller–Second Stochastic Version (OMoGaS–2SV), to assist companies dealing with gas retail commercialization. We consider temperature as a source of stochasticity, but we take into account also information on energy-related indices. Temperature influences gas consumption of small consumers and is modelled by a mean reverting process. Oil prices and exchange rates influence the energy-related indices to which sell and purchase prices are related. Forward curves of these are analyzed by a vector autoregressive model while exchange rates are modelled by a generalized autoregressive conditional heteroskedasticity model. The profit function depends on the number of contracts with the final consumers, the typology of such consumers, the cost supported to meet the final demand and penalties for daily maximum consumption exceeding daily maximum capacity. Linear constraints related to a maximum daily gas consumption and binary constraints on indexation formulas are included.

Hidden Markov models for financial optimization problems

Roman, D., Mitra, G., Spagnolo, N. — Thu, 11 Jun 2009 06:13:21 PDT

Many financial decision problems require scenarios for multivariate financial time series that capture their sequentially changing behaviour, including their extreme movements. We consider modelling financial time series by hidden Markov models (HMMs), which are regime-switching-type models. Estimating the parameters of an HMM is a difficult task and the multivariate case can pose serious implementation issues. After the parameter estimation, the calibrated model can be used as a scenario generator to describe the future realizations of asset prices. The scenario generator is tested in a single-period mean–conditional value-at-risk optimization problem for portfolio selection.

Network reliability design via joint probabilistic constraints

Beraldi, P., Bruni, M. E., Guerriero, F. — Thu, 11 Jun 2009 06:13:20 PDT

Network reliability is an important issue in network planning and operation. While there is a flourishing literature on reliability measurement both theoretical and computational, very little effort has been made to address practical applicability of reliability concepts in real network design problems. This work attempts to bridge the gap between theory and practice by relating reliability concepts to design criteria, useful in several practical contexts. In particular, the problem of finding a minimum cost network design, satisfying some reliability constraints is addressed. An integer programming model is developed to represent mathematically the proposed network design problem. For its solution, two heuristics approaches are devised and implemented. Their performance is evaluated on a set of well-known test problems. The computational results collected are very encouraging, showing that the developed methods determine good quality solutions, in a limited amount of time.

Word-of-mouth and dynamical inhomogeneous markets: an efficiency measure and optimal sampling policies for the pre-launch stage

Agliari, E., Burioni, R., Cassi, D., Neri, F. M. — Thu, 28 May 2009 16:17:21 PDT

An important assumption lying behind innovation diffusion models and word-of-mouth (WOM) processes is that of homogeneous mixing: at any time, the individuals making up the market are uniformly distributed in space. When the geographical parameters of the market, such as its area extension, become important, the movement of individuals must be explicitly taken into account. The authors introduce a model for a ‘microlevel’ process for the diffusion of an innovative product based on a WOM mechanism, and they explicitly consider the inhomogeneity of markets and the spatial extent of the geographical region where the process takes place. This results in an unexpected behaviour of macro (aggregate) level measurable quantities. The authors study the particular case of the prelaunch stage where a product is first presented to the market through free sample distribution. The first triers of the samples then inform the other potential customers via WOM; additional advertising is absent. The authors find an unexpected general failure of the WOM mechanism for high market densities and they obtain quantitative results for the optimal sampling policy. By introducing a threshold to discriminate between individuals who will purchase and those who will not purchase according to their individual goodwill, they calculate the length of the prelaunch campaign and the final goodwill as a function of the firm's expenditure. These results are applied to a set of major US urban areas.

Hybrid intensity models for repairable systems

Percy, D. F., Kearney, J. R., Kobbacy, K. A. H. — Mon, 17 Nov 2008 06:03:20 PST

In recent years, several authors have proposed mathematical models for complex repairable systems, extending the common assumptions of minimal repairs and renewals. These models all have weaknesses but we believe that modifications of existing models offer flexible analyses with realistic physical interpretations, enabling us to model the effects of replacements, repairs, preventive maintenance and inspections. These modifications correspond with specific types of superposed renewal processes and bear some resemblance to proportional intensities models, both described by Cox in 1962 and 1972, respectively. We discuss the properties and interpretations of these variants, explaining why we consider them particularly suited to modelling the effects of typical maintenance interventions. Finally, we illustrate an application of these models to repairable systems of five oil pumps, for which maintenance data were recently published, and demonstrate comparable performance with improved robustness.

A preventive maintenance decision model based on multicriteria method PROMETHEE II integrated with Bayesian approach

Cavalcante, C. A. V., Ferreira, R. J. P., de Almeida, A. T. — Wed, 06 Aug 2008 16:09:12 PDT

Different kinds of systems need different maintenance levels and models. Specifically, for systems producing services, we can observe the essential role of maintenance techniques. For these systems, failures have several negative implications, and the cost minimization model, frequently used in a manufacturing system, is not seen as efficient for many maintenance problems. Therefore, a multicriteria decision aid model is proposed in order to deal with conflict among evaluation criteria as well as take into account the preference of the decision maker in the problem. Additionally, the time taken for repair or replacement is also introduced into the model. Thus, decision makers may establish replacement intervals by taking into account two criteria. Also, ‘prior’ probabilities regarding parameters are considered. Therefore, this paper deals with the problem of replacement in service production systems, integrating the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) and the Bayesian approach. A numerical application illustrates the decision model proposed and shows the model's effectiveness regarding the decision-maker preferences.

A maintenance model with minimal and general repair

Kim, M. J., Makis, V. — Tue, 15 Jul 2008 21:23:51 PDT

The purpose of this article is to determine optimal maintenance policies for deteriorating systems subject to failure. Complex systems that deteriorate with usage and age are often subject to random failures of several kinds. Since it is costly to repair or replace failed systems, preventive maintenance is usually carried out while the systems are still operational. This article will be useful in providing maintenance engineers with a methodology to model failing systems and efficiently determine optimal maintenance policies. The problem is formulated and solved in a semi-Markov decision framework with the optimality criterion being the minimization of the long-run expected average cost per unit time. The model developed in this article, which is an extension of recent maintenance models, can be applied to systems that have any finite number of major and/or minor failure states and to systems that permit general repair in operational and major failure states. A new computational approach using an embedded technique is developed that is computationally preferable to the standard policy iteration algorithm when determining the optimal maintenance policy for systems with many states.

Multi-criteria decision model for selecting repair contracts by applying utility theory and variable interdependent parameters

de Melo Brito, A. J., de Almeida Filho, A. T., de Almeida, A. T. — Fri, 11 Jul 2008 19:22:29 PDT

The selection of contracts is a very important stage for the process of outsourcing maintenance in the current trend towards reducing costs and increasing competitiveness by focussing on core competences. The prominence of this theme can be seen in many studies carried out on outsourcing repair and maintenance contracts, most of which deal with qualitative aspects. However, quantitative approaches, such as multi-criteria decision aid, play an important role in helping decision makers (DMs) to deal with multiple and conflicting criteria and uncertainties in the selection process for outsourcing contracts. In this context, several decision models have been developed using different multi-criteria methods. This paper presents a multi-criteria methodology to support the selection of repair contracts in a context where information is imprecise, when DMs are not able to assign precise values to importance parameters of the criteria used for contract selection. Utility functions are integrated with the variable interdependent parameters method to evaluate alternatives through an additive value function regarding mean time to repair, contract cost, the geographical spread of the candidate's (bidder's) service network, the candidate's reputation and the compatibility of company cultures. To illustrate the use of the model, a numerical application is presented.

On modelling of grouped reliability data for wind turbines

Coolen, F. P. A., Spinato, F., Venkat, D. — Fri, 11 Jul 2008 19:22:27 PDT

Energy generation by wind turbines (WTs) has increased enormously during the last decade, and plans for future expansion, in particular large-scale offshore developments, emphasize the need to study reliability of WTs. Substantial data sets on occurrences of failures in WTs are available, but unfortunately they only provide grouped data with little information on individual turbines or maintenance activities. In this paper, we consider the use of basic non-homogeneous Poisson process models, in particular the power law process, to try to deduce from these data the change, through the years, in reliability of WTs and some critical subsystems. Unfortunately, it turns out that there are major problems that avoid clear conclusions to be drawn, as such the main contribution of this paper is a discussion on choice of the use of either calendar time or total time on test as the key time variable in reliability models, and some advice on future data collection, which will be equally important for a range of industrial activities.

Service facilities with Markovian demand and deterministic supply with an application in repair modelling

Csenki, A. — Thu, 10 Jul 2008 22:02:58 PDT

Recent research by the author was concerned with systems modelled by two processes, the ‘supply’ process and the ‘demand’ process. The systems modelled thereby were such that the goods produced were not storable and were lost if not consumed immediately. In the present paper, we continue this earlier research, now assuming that supply is deterministic and demand is modelled by an irreducible Markov process with a finite, partitioned state space. Combining an earlier result with ‘propositional calculus’, a closed-form expression is obtained for the probability that demand will be met by supply during the first k supply periods. As an application, two repair disciplines for a small computer network will be examined. The computational tool used is SCILAB, a free numerical package run on LINUX.

Risk aversion in maintenance: a utility-based approach

Baker, R. — Fri, 27 Jun 2008 23:26:08 PDT

In the author's concept of risk-averse maintenance, introduced in a previous paper, we seek to minimize the disutility of cost per unit time rather than to minimize cost per unit time itself. This gives a maintenance policy that is optimal under risk aversion. This paper extends the earlier work by providing a solution to the problem of combining risk aversion with the cost discounting that arises from the time value of money. The effect of parameter uncertainty, which was touched on in the earlier work, is here shown to lead to a minimax solution when operation for a long period with model uncertainty is planned. The possible use of non-exponential utility functions is discussed. In an attempt to make risk-averse maintenance more meaningful for practitioners, a fresh example of its use, the maintenance of a standby system, is given. A graphical aid to decision support is given, and some useful financial measures of risk, value at risk and expected shortfall, are introduced. These can be used to characterize planned maintenance policies.