Optimizing Supply Shortage Decisions in Base Stock Distribution Operations

This paper addresses policies and agreements between suppliers and customers for handling supply shortages in base-stock systems under uncertain demand. We investigate the impacts that backlogging and expediting decisions have on inventory and transportation costs in these systems and develop a model for deciding whether a supplier should completely backlog, completely expedite, or employ some combination of backlogging and expediting shortages. Our results indicate that practical cases exist where some combination of both expediting and backlogging supply shortages outperforms either completely expediting or backlogging all shortages. Including transportation costs in our model provides incentive to employ `hybrid' policies that partially expedite and partially backlog excess demands within a given period. Our model demonstrates how inventory policy decisions directly impact transportation costs and provides a heuristic approach for jointly minimizing expected inventory and transportation costs.     

Awareness, Belief, and Communication Reaching Consensus

This article studies graph-theoretical conditions under which communication will lead to consensus among players about their decisions in circumstances where there are more than two players and they interact in pair without public announcement. It is shown that consensus on their decisions can be guaranteed if the communication graph contains no cycle. Where none of the requirements for player's knowledge is imposed as in the standard model of knowledge with partitional information structure.     

The money-burning refinement: With an application to a political signalling game

We define an equilibrium refinement in signalling games by allowing agents to refine the game by burning money whenever they can act. We apply the refinement in a model where the public is unsure about the ability of an agent, say a government, to foresee the effects of long-term decisions. A government with ample information about the consequences of decisions should invest either immediately or not at all. Poorly informed agents should wait for better information. We identify pooling equilibria in which excessive rush or waiting occurs. The money-burning refinement may eliminate both rash and waiting pooling equilibria, but it involves wasting money and, for high discount factors, a decrease in welfare.First version August 1997/This version March 2004For valuable suggestions and comments I would like to thank Hans-Jörg Beilharz, Eric van Damme, Ulrich Erlenmaier, Ami Glazer, Paul Grout, Volker Hahn, Hans Haller, Majia Halonen, Martin Hellwig, Verena Liessem, Till Requate, Gisèle Umbhauer, seminar participants in Bristol, Heidelberg and Mannheim and at the Conference of the European Public Choice Society 1998 in Goeteborg, two anonymous referees, and the associate editor.     

ADAPT: An Adaptive Approach to Media Decisions

A firm's market changes under the impact of the firm's advertising. Feedback information on the market response allows the firm to learn about such changes and to adapt its subsequent media decisions accordingly. This paper presents an adaptive media model (ADAPT) that utilizes feedback information to revise certain parameters in a media decision model. Simulation experiments conducted with the ADAPT model demonstrate how different types of feedback information affect the media decisions and thereby the expected net profit contributions from sales. It is shown how the economic value of feedback information depends on the characteristics of the firm's market and also on the revision rules applied for updating the parameters. The value of the information may actually be negative if it is not used "intelligently".     

Asymptotic results on a class of adaptive multi-treatment designs

The play-the-winner (PW) rule is an important method in clinical trials where patients can be assigned to one of the two treatments. In the PW rule, the probability of the next patient to be assigned to a particular treatment only depends on the response of the current patient. In this paper, we consider a general kind of PW rule for multi-treatment adaptive designs, in which the probability that a treatment is assigned to the next patient depends upon both the response of the previous patient and an estimated parameter, e.g., the observed success rate. Using this kind of adaptive designs, more information of previous stages are used to update the model at each stage, and more patients may be assigned to better treatments. The strong consistency and the asymptotic normality are established for the allocation proportions.     

Collaboration and sharing mechanisms in improving corporate social responsibility

This paper investigates the effects of the collaboration between an upstream and a downstream firm regarding their decisions of prices and levels of corporate social responsibility (CSR) efforts. The firms collaborate with each other by sharing their costs or benefits to improve their profitabilities and CSR performances. Three collaborative models are developed for considering that collaboration may be undertaken by either or both firms, and each model has both profit- and cost-sharing mechanisms. We derive and characterize the consumer valuation and the firms’ decisions at equilibrium with respect to the changes in the sharing scheme, and further identify the impacts of each sharing mechanism. Moreover, a Nash bargaining game is developed for examining the choices of sharing scheme under the negotiation between the firms. Finally, we provide economic and managerial insights for socially concerned companies.     

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.     

National and store brand advertising strategies

As the propensity of premium store brands (SBs) increases, retailers must consider different ways to drive sales besides promotional strategies. With this in mind, we consider a national brand (NB) and a (premium) SB co-existing in a market. Each brand has to decide the amount to invest in advertising its product and the prices to charge its customers, which can be determined separately or in unison. When either advertising expenditures or pricing decisions are set, each brand must keep in mind that the advertising efforts and revenue may spillover between the two brands, customers who intend to purchase the NB may end up purchasing the SB and vice versa. We derive an analytical model of the situations described and characterize equilibrium advertising decisions. We find that the characteristics of a premium SB may depend on which marketing/promoting instrument (advertising or pricing) is the primary method for driving demand; and in some situations an NB may be better off to not advertise at all and instead let the premium SB carry out all of the advertising.     

Possibility and cost in decision analysis

The thesis of this paper is that a practically relevant decision theory must be based on the concept of possibility. As the concept is interpreted here it covers all the obstacles the decision-maker is facing. In many situations the contemplation of possibility is quite as relevant as the usual concentration on utility and probability. There is a traditional economic concept which conforms to an emphasis on obstacles or possibility in decision-making: opportunity cost. The opportunity cost of a decision is the value of the highest valued possible decision which is inhibited as a result of the decision actually taken. However as opportunity cost is usually interpreted decisions are dichotomized as either possible or impossible to perform. It is argued in the paper that this dichotomization is not very realistic. In reality there must be allowed for a continuum of states between the plain impossibility and the complete possibility. This gradual view of possibility could be dealt with if the fuzzy set theory is used. In the paper it is shown how some relevant concepts regarding possibility could be based on fuzziness and how these concepts could be used to analyze practical situations. A method to deal simultaneously with possibility and probability is stated.     

Generalized lot sentencing rule for estimating the value of production lot for sale

In the traditional lot sentencing rule, a buyer arrives to one of two decisions regarding lot disposition; either accept or reject a lot. However, it is more appropriate to consider choices between those two extreme decisions. A clear case where the traditional lot sentencing rule is not flexible is when a buyer purchases a lot from an English auction. In this paper, we propose a model that helps a buyer in estimating the value of a production lot. This model can be used by a bidder before the bidding process starts to estimate the value of an auctioned lot. The model provides an action plan that includes the estimated acquisition cost as a function of the number of defective items found in a random sample. Unlike the traditional lot sentencing rule, the proposed rule is more flexible and provides buyers with wider range of possible actions.     

Determining appropriate levels of data aggregation in a linear programming model

LP models as aids to annual budgeting are often too large to be economically viable unless they employ some form of aggregation. The degree of aggregation is usually determined informally and/or intuitively when the formulation is developed. This note describes some experiments and results with a model where the level of aggregation in the generated LP may be controlled by user-supplied parameter values. The effect of various aggregation levels may then be investigated in a straightforward, explicit manner while the model is still being developed. The information thus gained may serve as a guide to the most appropriate aggregation level for any particular subsequent planning use of the model. The approach adopted here for annual budgeting may prove practical and useful in other application areas where the main disadvantage expected of an otherwise satisfactory LP formulation is the size of the LP model and consequent excessive computing time required.     

Insurance and saving: some further results

The purpose of this paper is to provide a joint treatment of the saving and insurance decisions which have very often been dealt with separately in the economic literature. In the present model any decrease in the current consumption level can be used to finance either insurance purchase or an increase in the stock of safe assets held in financial institutions (called ‘deposits’ or ‘contingency reserves fund’ for brevity).The most important result is that, under decreasing temporal risk aversion, deposits and insurance are pure substitutes in the Hicksian sense. Besides, it is shown among other comparative statics results that insurance is not necessarily an inferior good, contrarily to the prevailing view in the literature. Finally, we indicate under which conditions a separation theorem between consumption, insurance and deposits holds. These conditions are either a fair insurance premium or a constant temporal risk aversion. Finally our results are compared to related ones in the literature.     

How much information do we need?

Modern technology is succeeding in delivering more information to people at ever faster rates. Under traditional views of rational decision making where individuals should evaluate and combine all available evidence, more information will yield better decisions. But our minds are designed to work in environments where information is often costly and difficult to obtain, leading us to use simple fast and frugal heuristics when making many decisions. These heuristics typically ignore most of the available information and rely on only a few important cues. Yet they make choices that are accurate in their appropriate application domains, achieving ecological rationality through their fit to particular information structures. This paper presents four classes of simple heuristics that use limited information—recognition-based heuristics, one-reason decision mechanisms, multiple-cue elimination strategies, and quick sequential search mechanisms—applied to environments from stock market investment to judging intentions of other organisms to choosing a mate. The findings that ecological rationality can be achieved with limited information are also used to indicate how our mind’s design, relying on decision mechanisms tuned to specific environments, should be taken into account in our technology’s design, creating environments that can enable better decisions.     

Scheduling for Known but Irregular Batch-Wise Demand

The paper deals with the batch size problem, given that demand is batch-wise and the times and quantities of the first n demands are known. This is found to be a problem in dynamic programming.A treatment is devised which may often enable that part of the demand to be scheduled optimally which must be procured before further information becomes available; which solves the problem in such cases. In other cases the final decision between the surviving possibilities may have to be based on possibly non-optimal criteria. Where it is known that the nth demand is the last, the problem can be solved completely.Details of computational methods are given, including worked examples. The methods appear suitable for computer programming, but are in any case (relatively) fast by hand; a solution may normally be obtained in, say, 5n minutes or less, except where the individual demands are much smaller than the optimum batch size (in which case other—approximate—methods may be preferred and would be unlikely to incur much penalty).     

Discovering implied constraints in precedence graphs with alternatives

During automated problem solving it may happen that some knowledge that is known at the user level is lost in the formal model. As this knowledge might be important for efficient problem solving, it seems useful to re-discover it in order to improve the efficiency of the solving procedure. This paper compares three methods for discovering certain implied constraints in the constraint models describing manufacturing (and other) processes with serial, parallel, and alternative operations. In particular, we focus on identifying equivalent nodes in the precedence graph with parallel and alternative branches. Equivalent nodes correspond to operations that either must be all simultaneously present or none of them can be present in the schedule. Such information is frequently known at the user level, but it is lost in the formal model. The paper shows that identifying equivalent nodes is an NP-hard problem in general, but it is tractable if the graph has a nested structure. As the nested structure is typical for real-life processes and workflows, we use the nested graphs to experimentally compare the proposed methods.     

Integrated capacity and inventory management with capacity acquisition lead times

We model a make-to-stock production system that utilizes permanent and contingent capacity to meet non-stationary stochastic demand, where a constant lead time is associated with the acquisition of contingent capacity. We determine the structure of the optimal solution concerning both the operational decisions of integrated inventory and flexible capacity management, and the tactical decision of determining the optimal permanent capacity level. Furthermore, we show that the inventory (either before or after production), the pipeline contingent capacity, the contingent capacity to be ordered, and the permanent capacity are economic substitutes. We also show that the stochastic demand variable and the optimal contingent capacity acquisition decisions are economic complements. Finally, we perform numerical experiments to evaluate the value of utilizing contingent capacity and to study the effects of capacity acquisition lead time, providing useful managerial insights.     

Multi-Level Strategic Evaluation of Hospital Plans and Decisions

Strategic decision making in hospitals involves the assessment of linkages between decisions that are typically made in a hierarchical fashion. In hospitals, as in most large organizations, overall system performance is a function of how well the critical decisions are integrated. This paper focuses on the multi-level nature of the decisions and policies that typically need to be evaluated in hospital planning, highlighting that both optimization and simulation approaches may be required. An application involving a large general purpose urban hospital is used to illustrate the interdependency between the levels in the planning hierarchy. An optimization model is formulated to deal with facility layout and capacity allocation while a simulation model is proposed to capture the complexities of hospital operations. The linkages and information feedback between the models are shown to be critical in the design of a system that performs well and facilitates strategic hospital planning.     

An Extension of Generalized Linear Models to Finite Mixture Outcome Distributions

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the analysis of categorical and count outcomes when standard generalized linear models (GLMs) cannot adequately express variability observed in the data. We propose an extension of GLMs where the response follows a finite mixture distribution and the regression of interest is linked to the mixture’s mean. This approach may be preferred over a finite mixture of regressions when the population mean is of interest; here, only one regression must be specified and interpreted in the analysis. A technical challenge is that the mixture’s mean is a composite parameter that does not appear explicitly in the density. The proposed model maintains its link to the regression through a certain random effects structure and is completely likelihood-based. We consider typical GLM cases where means are either real-valued, constrained to be positive, or constrained to be on the unit interval. The resulting model is applied to two example datasets through Bayesian analysis. Supporting the extra variation is seen to improve residual plots and produce widened prediction intervals reflecting the uncertainty. Supplementary materials for this article are available online.     

A Monte Carlo simulation approach to the characterization of uncertainties in cancer staging and radiation treatment decisions

Radiation treatment (RT) for cancer is a critical medical procedure that occurs in a complex environment that is subject to uncertainties and errors. We employed a simulation (a variant of Monte Carlo) model that followed a cohort of hypothetical breast cancer patients to estimate the probability of incorrect staging and treatment decisions. As inputs, we used a combination of literature information and expert judgement. Input variables were defined as probability distributions within the model. Uncertainties were propagated via simulation. Sensitivity and value-of-information analyses were then conducted to quantify the effect of variable uncertainty on the model outputs. We found a small but non-trivial probability that patients would be incorrectly staged and thus be subjected to inappropriate treatment. Some routinely used tests for staging and metastasis detection have very limited informational value. This work has implications for the methods used in cancer staging and subsequent risk assessment of treatment errors.