Determining the optimal number of depots in a physical distribution system according to market characteristics

This paper is an extension of an earlier paper to investigate the interactive effects of location, price and demand using mathematical models of distribution systems.The paper considers the additive nature of solutions to depot location problems and shows how this property can be used to advantage in determining the optimal number of depots in a distribution system. The importance of using marginal profit and marginal return on investment in this context is demonstrated.The sensitivity of the results to changes in cost parameters is also discussed.     

Incorporating order-flow into optimal execution

We provide an explicit closed-form strategy for an investor who executes a large order when market order-flow from all agents, including the investor’s own trades, has a permanent price impact. The strategy is found in closed-form when the permanent and temporary price impacts are linear in the market’s and investor’s rates of trading. We do this under very general assumptions about the stochastic process followed by the order-flow of the market. The optimal strategy consists of an Almgren–Chriss execution strategy adjusted by a weighted-average of the future expected net order-flow (given by the difference of the market’s rate of buy and sell market orders) over the execution trading horizon and proportional to the ratio of permanent to temporary linear impacts. We use historical data to calibrate the model to Nasdaq traded stocks and use simulations to show how the strategy performs.     

Incorporating Angular Information into Parametric Models

The problem is considered of fitting a parametrically defined model in two or three dimensions to observed data, when angular information about the measured data points is available. Gauss-Newton methods based on correct separation of variables are developed. Some numerical results are included.     

Incorporating ergonomic risks into assembly line balancing

In manufacturing, control of ergonomic risks at manual workplaces is a necessity commanded by legislation, care for health of workers and economic considerations. Methods for estimating ergonomic risks of workplaces are integrated into production routines at most firms that use the assembly-type of production. Assembly line re-balancing, i.e., re-assignment of tasks to workers, is an effective and, in case that no additional workstations are required, inexpensive method to reduce ergonomic risks. In our article, we show that even though most ergonomic risk estimation methods involve nonlinear functions, they can be integrated into assembly line balancing techniques at low additional computational cost. Our computational experiments indicate that re-balancing often leads to a substantial mitigation of ergonomic risks.     

Incorporating geo-metallurgical information into mine production scheduling

Economic characterization of mining parcels depends upon geo-metallurgical properties, which vary throughout orebody. Mine production scheduling should aim to obtain maximum utility from orebody in such a way as to ensure mine–mill reconciliation. As heterogeneity of geo-metallurgical variables increases, the scheduling will be a very complicated task. Geo-metallurgical and financial data used in the mine production scheduling are based on simulation and/or estimation generated from sparse drilling and unknown future events. Therefore, the scheduling process involves a significant degree of uncertainty. In order to deal with the uncertainty stemmed from geo-metallurgical and financial variables, two approaches are recommended in this paper. Firstly, mine production scheduling is formulated as a problem of stochastic programming with recourse. The extraction periods of mining blocks are treated as the first-stage variables and the block destinations represents a recourse vector. It is observed that the solution is implicitly robust. Secondly, the scheduling is expressed as a maximin problem to extract more uniform metal quantity in periods to coincide with mill requirements instead of maximization of net present value because the blending constraint in the traditional approach forces more uniform production. In the case where there is correlation between grade and geo-metallurgical variables, this model generates reasonably good results.     

Incorporating expertise into decision analysis based DSS

Artificial Intelligence/Expert Systems (AI/ES) techniques are proposed as means of combining the expertise of the experienced decision analyst with the computational methods of Decision Analysis (DA) to provide a user-friendly problem structuring, solution and querying environment which can be accessed directly by those responsible for managerial decisions.Such a system can be implemented as an Expert System shell. The key features of the shell are the inclusion of knowledge from previous problems through problem templates and the use of a combination of natural language and influence diagrams to communicate with users.This shell has the potential to further expand the use of DA by helping to overcome the DA skill shortage and to address some of the difficulties associated with purely AI/ES approaches to complex business problem solving. The greatest benefit of an Expert Decision Analyst is through integration with organisational DSS to support valuable information processing activities such as strategic decision-making.     

The affine inflation market models

Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data.     

Structural stability of market models

A market structure in the Arrow-Debreu framework can be represented by a finite number of traded securities. We examine an interesting structure that exists among markets. The partitioning of the set of all markets. M into its rank classes is a stratification of M. Some properties of an equivalence relation among markets are also studied. Some results on the ‘genericity’ of the properties of market structures are obtained.     

Incorporating inventory and routing costs in strategic location models

We consider a supply chain design problem where the decision maker needs to decide the number and locations of the distribution centers (DCs). Customers face random demand, and each DC maintains a certain amount of safety stock in order to achieve a certain service level for the customers it serves. The objective is to minimize the total cost that includes location costs and inventory costs at the DCs, and distribution costs in the supply chain. We show that this problem can be formulated as a nonlinear integer programming model, for which we propose a Lagrangian relaxation based solution algorithm. By exploring the structure of the problem, we find a low-order polynomial algorithm for the nonlinear integer programming problem that must be solved in solving the Lagrangian relaxation sub-problems. We present computational results for several instances of the problem with sizes ranging from 40 to 320 customers. Our results show the benefits of having an integrated supply chain design framework that includes location, inventory, and routing decisions in the same optimization model.     

Incorporating the potential for human error in maintenance models

The mathematics of delay-time modelling of inspection maintenance is extended to incorporate the existence of human error in the form of fault injection during the inspection process. After briefly discussing the basic delay-time model, modifications are introduced to model maintenance scenarios incorporating human error injected defects within the inspection maintenance process. The effects of human error are investigated with the emphasis on its representation and on the assessment of consequences, the objective being to provide a means of determining the cost of human error and to thereby aid corrective decision-making.     

Incorporating model uncertainty into optimal insurance contract design

In stochastic optimization models, the optimal solution heavily depends on the selected probability model for the scenarios. However, the scenario models are typically chosen on the basis of statistical estimates and are therefore subject to model error. We demonstrate here how the model uncertainty can be incorporated into the decision making process. We use a nonparametric approach for quantifying the model uncertainty and a minimax setup to find model-robust solutions. The method is illustrated by a risk management problem involving the optimal design of an insurance contract.     

Homoclinic bifurcations in heterogeneous market models

We analyze a class of models representing heterogeneous agents with adaptively rational rules. The models reduce to noninvertible maps of R². We investigate particular kinds of homoclinic bifurcations, related to the noninvertibility of the map. A first one, which leads to a strange repellor and basins of attraction with chaotic structure, is associated with simple attractors. A second one, the homoclinic bifurcation of the saddle fixed point, also associated with the foliation of the plane, causes the sudden transition to a chaotic attractor (with self-similar structure).     

Estimating conjectural variations for electricity market models

Agents’ behavior in oligopolistic markets has traditionally been represented by equilibrium models. Recently, several approaches based on conjectural variations equilibrium models have been proposed for representing agents’ behavior in electrical power markets. These models provide insight of market equilibrium sensitivity to agents’ strategies and external variables, and therefore, they are widely applied. Unfortunately, not enough analysis has been done in how these user-supplied parameters, the conjectural variations, should be estimated. This paper proposes a parameter inference procedure based on two stages. The first stage infers historical values of the parameter by fitting the models’ results to historical market data. The second stage is based on a statistical time-series model whose objective is to forecast parameter values in future scenarios. Additionally, results of this procedure’s application to a real-size case are presented.     

Set-valued risk measures for conical market models

Set-valued risk measures on L^p_d{L^p_d} with 0 ≤ p ≤ ∞ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are shown to form the values of a set-valued sublinear (coherent) risk measure. Scalar risk measures with multiple eligible assets also turn out to be a special case within the set-valued framework.     

Incorporating demand uncertainty and forecast error in supply chain planning models

This paper develops a framework for examining the effect of demand uncertainty and forecast error on unit costs and customer service levels in the supply chain, including Material Requirements Planning (MRP) type manufacturing systems. The aim is to overcome the methodological limitations and confusion that has arisen in much earlier research. To illustrate the issues, the problem of estimating the value of improving forecasting accuracy for a manufacturer was simulated. The topic is of practical importance because manufacturers spend large sums of money in purchasing and staffing forecasting support systems to achieve more accurate forecasts. In order to estimate the value a two-level MRP system with lot sizing where the product is manufactured for stock was simulated. Final product demand was generated by two commonly occurring stochastic processes and with different variances. Different levels of forecasting error were then introduced to arrive at corresponding values for improving forecasting accuracy. The quantitative estimates of improved accuracy were found to depend on both the demand generating process and the forecasting method. Within this more complete framework, the substantive results confirm earlier research that the best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. However, size matters, both in the demand uncertainty and forecasting errors. The quantitative differences depend on service level and also the form of demand uncertainty. Unit costs for a given service level increase exponentially as the uncertainty in the demand data increases. The paper also estimates the effects of mis-specification of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high demand uncertainty and high forecast error, improved forecast accuracy should lead to substantial percentage improvements in unit costs. Methodologically, the results demonstrate the need to simulate demand uncertainty and the forecasting process separately.     

Sufficient Poisson jump diffusion market models revisited

Motivated by financial market modeling with spike-like jumps spot prices, we present a simple characterisation of the complete two-dimensional Poisson jump-diffusion market models with possibly discontinuous and degenerate coefficients, extending the standard no-arbitrage and completeness working hypothesis for such markets.

     

Incorporating human behaviour in simulation models of screening for breast cancer

Simulation modelling is widely used in many industries in order to assess and evaluate alternative options and to test strategies or operating rules which are too complex to be modelled analytically. Simulation software has developed its capability in parallel with the growth in computing power since the 1980s. However in practice, the results from the most sophisticated and complex simulation model may not truly reflect what happens in the real world, because such models do not account for human behaviour. For example, in the domain of healthcare simulation is often used to evaluate the outcomes from medical interventions such as new drug treatments. However in reality patients may not complete the course of a prescribed medication, perhaps because they find the side-effects unpleasant. A simulation study designed to evaluate this medication which ignores such behavioural factors may give unreliable results. In this paper we describe a model for screening for breast cancer which includes behavioural factors to model women’s decisions to attend for mammography. The model results indicate that increasing attendance through education or publicity campaigns can be equally as effective as decreasing the intervals between screens. This would have considerable cost implications for healthcare providers.