Multistage Decision Process Research Articles

Strategies for value: Quality, productivity, and innovation in R&D/technology organizations

AbstractThe nature of value and how R&D/technology organizations provide value are considered. Value is defined in terms of three dimensions: quality, productivity, and innovation. This framework provides the basis for formulation of value strategies in terms of where value is to be provided, how it will be provided, enterprise designs that support these intentions, benchmarking to identify gaps, and specification of action plans. Implementation of value strategies is discussed relative to strategies for change, multistage decision processes, organizational implications, balanced scorecards, and adaptation of strategies to different types of enterprises. Illustrations of multistage decision criteria and balanced scorecards for R&D/technology organizations are provided. © 2001 John Wiley & Sons, Inc. Syst Eng 4: 87–106, 2001

IT—Information Technology: Tillage System Selection: a Mathematical Programming Model incorporating Weather Variability

A farm-level mathematical programming model to analyse the economics of alternative tillage and cropping systems for cereal grain and oilseed production is presented. The modelling technique used is discrete stochastic sequential programming (DSSP), which allows for a multi-stage decision process and stochastic field time constraints. Decision variables are cropping activities, integer tractor and equipment investments and scheduling of tillage and drilling operations. The model is applied to a representative farm with medium to heavy clay soil. Tillage systems assessed are mouldboard plough tillage, chisel plough tillage and direct drilling. The results show that a tillage system characterized by lower capital and labour requirements may be as profitable as a conventional system, despite lower crop yields. Further, the results reveal that there is an interaction between the machinery system and optimal crop mix. A test of the importance of considering field time variability indicates that a deterministic model has a tendency to underestimate optimal machinery sizes.

Fuzzy stochastic dynamic programming for marketing decision support

One of the most important goals in marketing is to realize the highest profit by applying appropriate means to optimize the process of acquiring customers. To assist the marketer in making marketing decisions, this paper introduces a stochastic dynamic programming model for the process of acquiring customers. It is actually a stochastic multistage decision process, whose state space consists of granularized information on customers and whose transitions are controlled by marketing actions. Then it shows how to control this process using fuzzy constraints and how to characterize the goal of maximizing profit by a fuzzy set. After an overview of approaches in dynamic programming under fuzziness given by Bellman and Zadeh, this paper further presents a new model of fuzzy stochastic dynamic programming to solve the decision problem for a stochastic system with implicitly defined termination time. It is argued that this study can facilitate research and development of both financial engineering and e-commerce. © 2000 John Wiley & Sons, Inc.

Conditional Decision Processes with Recursive Function

We consider stochastic optimization of not necessarily additive but recursive functions over multistage decision processes. Without assuming any monotonicity, we optimize a regular process by a direct dynamic programming approach. On the regular decision process, we propose two related conditional decision processes: an a posteriori conditional decision process and an a priori. When the Markov transition law degenerates into a deterministic dynamics, the two conditional processes reduce to the same deterministic decision process. The conditional processes with monotonicity are optimized by the usual backward dynamic programming. We show that under additional convexity the regular process dominates the a priori in maximum value function and the a priori does the a posteriori. We show that the a posteriori process illustrates Kreps and Porteus's dynamic choice problem. The numerical example also verifies the dominance relation in three optimal value functions.

A time-average fuzzy reward criterion in fuzzy decision processes

The optimization problem of long-run time-average fuzzy rewards in multi-stage decision processes with fuzzy transitions is discussed. The rewards are estimated by a fuzzy expectation, which is defined by possibility measures generated by fuzzy goals and t-norms. An optimal policy and an optimal payoff are given for the optimization problem.

Optimization of pump-treat-inject (PTI) design for the remediation of a contaminated aquifer: multi-stage design with chance constraints

A large scale groundwater remediation project using pump-and-treat (PAT) or pump-treat-inject (PTI) cannot be designed as a single time-step operation, because of uncertainties associated with the system. The changes in concentrations in reality may differ significantly from predicted ones. Instead, a multi-stage decision process is formulated and solved as a two-level hierarchical optimization model. Cost serves as the objective function, while contaminant concentration and total cleanup time are constraints. The entire cleanup time is divided into several stages. The number of wells for both pumping and injection is treated as a decision variable in each design stage. At the basic level, well locations and pumping/injection rates are sought so as to maximize mass removal of contaminants. At the upper level, the number of wells for pumping and injection is optimized, so as to minimize the cost, taking maximum contaminant level (MCL) as a constraint. Indices for the equivalent centroid and areal extent of a contaminant plume are proposed and used to initiate well locations at each design stage.

OPTIMIZATION MODEL FOR CONSTRUCTION PROJECT DURATIONS USING A MULTISTAGE DECISION PROCESS

The optimization of project duration is often performed during the planning stage of a construction project. Though there are four types of activity time-cost functions used in the optimization of project duration, most of the methods used in the optimization of project duration are only appropriate for a particular type of activity time-cost function. In order to overcome this limitation, this paper constructs an analytical model for optimizing project duration which is applicable to various types of activity time-cost functions. Based on the concept of a multistage decision process, the objective function and the expressions of both serial recurrence and parallel recurrence are established. In addition, the computation algorithms for both recurrence expressions which can reduce the computer memory space used and unnecessary computation are also developed. Finally, every optimal combination of project duration and its corresponding minimum project cost can be computed efficiently. The optima] allocation of activity time and its corresponding cost from each recurrence stage for the specific project duration can also be obtained.

Controlling activity interval times in LOB scheduling

A new scheduling method is presented in this paper which overcomes the inability of the line of balance (LOB) method to control the interval times between adjacent activities in a repetitive construction unit. The interval times are analysed and then expressed as functions of the number of repetitive construction units, the difference between construction times of adjacent activities and the sequence of repetitive construction units. In order to overcome the LOB problem, this paper presents a new scheduling method, the multistage linear scheduling (MLS) method, based on the concept of a multistage decision process. With the MLS method, the project's completion time is smaller or equal to that estimated with the LOB method. The sum of construction times of each activity in all units is the same as that estimated with the LOB method. However, no interval times are generated. The adjacent activities in a repetitive construction unit can progress continuously (not allowed under the LOB method). Therefore, the MLS method can be used to schedule a repetitive project which has necessary practical constraints on the interval times. This results in the retention of construction quality, safety and efficiency.

Responding to customer enquiries in Make-to-Order companies: problems and solutions

Make-to-order companies are in the business of supplying products in response to a customer order in competition with other companies, on the basis of price, technical expertise, delivery time and reliability in meeting due dates. Dealing properly with enquiries is the major problem that MTO companies face. A lack of co-ordination between sales and production at the customer enquiry stage often leads to confirmed orders being delivered later than promised and/or being produced at a loss. The treatment of an enquiry is a multi-stage decision process. The initial decision is whether or not to prepare a bid, and if so, how much effort to put into the specification and estimation process. The MTO company has the choice of putting in a lot of effort to prepare a competitive bid or making a quick estimate with a high safety margin to allow for errors and unforeseen problems expecting further later negotiation with the customer. Consideration has to be given to the likely accuracy of the cost estimates produced. The feasibility of being able to produce the order with the current work load at different delivery times needs to be evaluated together with any extra costs incurred. An input/output planning approach based on the control of a hierarchy of backlogs of work is proposed to produce a dynamic capacity planning model to determine the capacity to provide at each work centre in future time periods, allocating overtime, transferring operators, process as split batches etc. In setting the price and lead time to quote to the customer, the probability of winning the order plays an important role. A model based on a chi-squared analysis of data on past enquiries is proposed to divide the market into sectors of similar orders. It is extended to produce a strike rate matrix for each sector giving the probability if winning orders in that sector as a function of the price and lead time quoted. A general model for the whole enquiry process is presented, together with a decision support/expert system. This indicates where the qualitative judgmental rules, typically used by companies, could be used to advantage.

Responding to customer enquiries in make-to-order companies Problems and solutions

Make-to-order companies are in the business of supplying products in response to a customer order in competition with other companies, on the basis of price, technical expertise, delivery time and reliability in meeting due dates. Dealing properly with enquiries is the major problem that MTO companies face. A lack of co-ordination between sales and production at the customer enquiry stage often leads to confirmed orders being delivered later than promised and/or being produced at a loss. The treatment of an enquiry is a multi-stage decision process. The initial decision is whether or not to prepare a bid, and if so, how much effort to put into the specification and estimation process. The MTO company has the choice of putting in a lot of effort to prepare a competitive bid or making a quick estimate with a high safety margin to allow for errors and unforeseen problems expecting further later negotiation with the customer. Consideration has to be given to the likely accuracy of the cost estimates produced. The feasibility of being able to produce the order with the current work load at different delivery times needs to be evaluated together with any extra costs incurred. An input/output planning approach based on the control of a hierarchy of backlogs of work is proposed to produce a dynamic capacity planning model to determine the capacity to provide at each work centre in future time periods, allocating overtime, transferring operators, process as split batches etc. In setting the price and lead time to quote to the customer, the probability of winning the order plays an important role. A model based on a chi-squared analysis of data on past enquiries is proposed to divide the market into sectors of similar orders. It is extended to produce a strike rate matrix for each sector giving the probability if winning orders in that sector as a function of the price and lead time quoted. A general model for the whole enquiry process is presented, together with a decision support/expert system. This indicates where the qualitative judgmental rules, typically used by companies, could be used to advantage.

Markov-type fuzzy decision processes with a discounted reward on a closed interval

We formulate a new multi-stage decision process with Markov-type fuzzy transition, which is termed Markov-type fuzzy decision process. In the general framework of the decision process, both of state and action are assumed to be fuzzy itself. The transition of states is defined using the fuzzy relation with Markov property and the discounted total reward is described as a fuzzy number on a closed bounded interval. To discuss the optimization problem, a partial order of convex fuzzy numbers is introduced. In this paper the discounted total reward associated with an admissible stationary policy is characterized by a unique fixed point of the contractive mapping. Moreover, the optimality equation for the fuzzy decision model is derived under some continuity conditions. Also, an illustrated example is given to explain the theoretical results and the computation in the paper.

Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming

Many problems faced by decision makers are characterized by a multistage decision process with uncertainty about the future and some decisions constrained to take on values of either zero or one (for example, either open a facility at a location or do not open it). Although some mathematical theory exists concerning such problems, no general-purpose algorithms have been available to address them. In this article, we introduce the first implementation of general purpose methods for finding good solutions to multistage, stochastic mixed-integer (0, 1) programming problems. The solution method makes use of Rockafellar and Wets' progressive hedging algorithm that averages solutions rather than data. Solutions to the induced quadratic (0,1) mixed-integer subproblems are obtained using a tabu search algorithm. We introduce the notion of integer convergence for progressive hedging. Computational experiments verify that the method is effective. The software that we have developed reads standard (SMPS) data files.

STOCHASTIC DECISION-MAKING IN A FUZZY ENVIRONMENT

In this paper we consider multistage decision processes in Bellman and Zadeh's paper "Decision-making in a fuzzy environment" from a mathematical view-point. We propose another recursive equation which solves both stochastic and deterministic multistage decision processes in a fuzzy environment in their sense. Our result for deterministic processes coincides with their result. However, our result for stochastic processes is more or less different from theirs. Our "stochastic" recursive equation is derived through invariant imbedding. On the other hand, their "stochastic" recursive equation is a direct analogy for their deterministic one. As an example, we illustrate their numerical data, which verify the equality between simultaneous and sequential optimizations.

Dynamic programming approach to multiple objective control problem having deterministic or fuzzy goals

Multiple Objective Control problems (MOCP) are dynamic optimization problems of control systems that can be framed as multistage decision processes. Generalized Dynamic Programming or Multiple Objective Dynamic Programming is a useful technique to solve MOCP. Levary has first given the dynamic programming approach to solve a multiple objective optimization problem involving goal objectives. His formulation is valid if there is only a single decision variable in each stage. Generally, in control problems, such as Multiple Goal Control Problem (MGCP), a decision vector is involved in each stage. Therefore, in this paper Levary's formulation is extended to MGCP and is illustrated with an example. When the MOCP has fuzzy goals, it is formulated as Fuzzy Goal Control Problem (FGCP). A new formulation of dynamic programming approach to FGCP is proposed here as Dynamic Fuzzy Goal Control Problem (DFGCP) and the method of finding its solution is illustrated with an example.

Determination of the best main serial chain in nonserial dynamic programming networks

Nonserial network structures abound in production lines, chemical processing systems, communication networks and many other multi-stage decision processes. Algorithms based on dynamic programming have been developed to solve these systems. In solving these nonserial systems it turns out that the storage demand largely depends on the choice of the main serial chain in the network, i.e., the chain of stages to which the loops are connected. The purpose of this paper is to determine the best main serial chain that minimizes the storage demand in the looped networks. Based on complexity analysis, the characteristics of the best main serial chain in various nonserial loop structures are examined. A graph theoretic approach is employed for the problem of finding the best main chain in those systems.

Brand Retrieval, Consideration Set Composition, Consumer Choice, and the Pioneering Advantage

Recent research on the pioneering advantage has shown that consumers often prefer pioneering brands to follower brands. Recent research on consumer choice suggests that information about brands is filtered through a series of sequential cognitive processes. This study attempts to integrate these two separate lines of research by investigating the effects of pioneering on each stage of the multistage decision process. A within-subjects longitudinal experiment was conducted to simulate brand order of entry into a new market. We also developed a sequential logit model to isolate the direct impact of pioneering on each stage of the decision process while controlling for indirect effects of pioneering on previous stages. The results revealed that the pioneering brand (vs. followers) is more likely to be retrieved, considered, and selected. Moreover, the results revealed that consumers are more likely to bypass consideration set formation when the choice decision is simple (vs. complex). Theoretical and practical implications of the results are discussed.

On the existence and uniqueness theorems of solutions for the systems of mixed monotone operator equations with applications

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].

Decentralized voltage control in multiarea power system

AbstractThis paper discusses the feasibility of a decentralized voltage control scheme for large‐scale power systems. The algorithm is intended to apply to a reactive normal operating state from an emergency state caused by illcondition and also to keep the operating state away from approaching unstable boundaries in preventive control. The procedure for releasing voltage deviation (over/under voltage) is formulated as a multistage decision process over a certain time interval. The optimization problem is transformed into a two‐point boundary value problem using the discrete maximum principle and is solved easily by using the discrete Riccati equation.For a large‐scale power system, control values must be computed from a large number of state variables, and this inevitably prolongs the slow dynamics with controllers. The centralized control system in a large‐scale system cannot be justified from the economical and technical viewpoints. To resolve the foregoing problems, a decentralized voltage control system incorporating slow voltage dynamics is presented.

Robust contingency plans for transportation investment planning

A multistage decision process for transportation investment planning is described. Most transportation investment problems inherently involve multiple criteria and uncertainty. To deal with the variations arising from changes in external environments, robust contingency plans should be integrated in the planning process-not after plans are developed-to account for uncertainty. With the proposed decision process, a multiple criteria decision-making (MCDM) method is first used to select a set of good potential designs (or potential solutions). Corresponding optimal contingency plans for each design under uncertainty are then prepared. Robustness considerations are used in making the final selection among contingency plans. To demonstrate the proposed decision-making process, a scenario approach is applied to develop a multistage decision-making process for transportation investment planning problems. Finally, an example of regional transportation investment is presented to illustrate the method. >

Practical method for generation expansion planning based on dynamic programming

AbstractThis paper presents an efficient method which provides the optimal generation mix and the optimal generation construction process. The approximation method in which the dynamic programming technique and gradient method are combined is applied to determine the optimal generation mix with hydropower generation technologies. The successive approximations dynamic programming (SADP) technique, which is very suitable for high‐dimensional multistage decision process problems, is used for obtaining the optimal generation construction process. The effectiveness and feasibility of the developed technique are demonstrated on a practical power system model which has five types of generation technologies including a hydropower generation technology.