Traditional Dynamic Programming Research Articles

Dual dynamic programming for linear production/inventory systems

We consider the problem of scheduling production of an inventoried item, using a production technology described by a linear program (LP). Traditional approaches involve using LP to find a schedule for a specific starting inventory, or using dynamic programming (DP) to find a production strategy for any stock level at any stage. Our method solves an LP for each period parametrically, and then uses a backwards recursion, based on the marginal conditions of DP, to generate the optimal operating strategy for the entire horizon in a convenient form. This method is dual to conventional DP in the sense that it finds optimal primal variables (points in the state space) corresponding to a set of critical shadow prices, rather than vice versa. It is more accurate and more efficient than traditional DP, while tests indicate that the computational effort required to produce a complete operating strategy is competitive with that taken to produce a single solution via LP. The method also yields useful insights into the nature of the problem. This paper concentrates on a linear deterministic problem with one inventory, but the method can be generalized. It has been successfully applied to two-dimensional reservoir release and coal stockpiling problems under uncertainty.

Application of heuristic search and information theory to sequential fault diagnosis

The problem of constructing optimal and near-optimal test sequences to diagnose permanent faults in electronic and electromechanical systems is considered. The test sequencing problem is formulated as an optimal binary AND/OR decision tree construction problem, whose solution is known to be NP-complete. The approach used is based on integrated concepts from information theory and heuristic AND/OR graph search methods to subdue the computational explosion of the optimal test-sequencing problem. Lower bounds on the optimal cost-to-go from the information-theoretic concepts of Huffman coding and entropy are derived. These lower bounds ensure that an optimal solution is found using the heuristic AND/OR graph search algorithms; they have made it possible to obtain optimal test sequences to problems that are intractable with traditional dynamic programming techniques. In addition, a class of test-sequencing algorithms that provide a tradeoff between solution quality and complexity have been derived using the epsilon -optimal and limited search strategies.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Implementation Strategies for Salinity Projects

The U.S. Bureau of Reclamation has the responsibility for developing implementation strategies for salinity control projects in the Colorado River Basin. Determining when and which projects should be built depends primarily upon the planning and construction funds available at various times during the program period and other considerations. The paper describes the development of a methodology that is used by Reclamation for analyzing implementation strategies for salinity control projects in the Colorado River Basin. The methodology uses a variant of the more traditional dynamic programming formulations of the capacity expansion problem which allows total project costs to be used as the state variable. Objective‐space dynamic programming was used to efficiently develop multiple solutions for a range of possible funding levels for the life of the program. The solutions allow the evaluation of the sensitivity and effects of various funding scenarios on the overall salinity control program. Examples of the information developed by the methodology and the types of sensitivity analysis that can be conducted are presented.

Optimal inspection policies in a serial production system including scrap rework and repair: An MILP approach

The allocation of inspection effort problem for aerial systems is formulated as a 0-1 mixed integer linear programming problem. This formulation permits any combination of scrap, rework, or repair at each station and allows the problem to be solved using standard MILP software packages. Moreover electronic spread-sheets may be used to easily calculate the relevant coefficients. An additional advantage of this approach when compared with the traditional dynamic programming approach is the ease with which the basic model may be modified. For example, it is shown how the model may easily be modified to include both a material and a production constraint and to select between various material suppliers. Sensitivity analysis is also easily performed with this approach. This model is then used to show that the optimal inspection policy is dependent on whether a production or a material requirement is used.

Efficient Specification and Solution of the Even-aged Rotation and Thinning Problem

Abstract Dynamic programming is frequently used for stand level optimization. In recent years, solution methods have been made available for a number of growth models. However, increasingly complex growth models require network specifications with high dimensionality and its associated high computational cost. This paper presents a more efficient solution algorithm that overcomes the computational burdens of the traditional dynamic programming approach. The algorithm is described using LaGrange multipliers and network theory. An illustrative example is presented, and the computational efficiency of the new method is demonstrated by comparing its performance with an existing dynamic programming algorithm. The scope of applicability of the proposed method is discussed as well as aspects requiring further analysis and research. For. Sci. 33(1):14-29.

Discrete Optimization by Relational Constraint Satisfaction

In pattern matching a basic problem is to determine one or more vectors X that maximize an objective function which is a sum of functions of components of X. When this problem is solved by dynamic programming CPU time and storage requirements grow explosively as the amount of intervariable interaction in the objective function increases. This explosion may be reduced by departing from the traditional dynamic programming method of eliminating successive variables and instead determining a constraint relation between each variable and all others with which it interacts. Discrete relaxation is used to accelerate a backtrack search to find all vectors that satisfy all such constraints. Optimization is achieved by evaluating the objective function for all such vectors. This new method of optimization has been experimentally compared with a classical dynamic programming algorithm running with the same pseudorandomly generated objective functions.