Implementing the recursive APL code for dynamic programming

ABSTRACT

Despite the importance and wide applicability of dynamic programming technique in optimization, the complexity and uniqueness of various dynamic programming models often make the comprehension of their solution procedures difficult, particularly for a novice. Although it can be argued that, unlike the Simplex method in linear programming, no general dynamic programming algorithm exists, with the recursive capability of APL, it is feasible to develop a “systematic” solution approach for deterministic dynamic programming. In this paper, we introduce a set of such APL code developed be solve various types of dynamic programming problems with minor modifications on some of its key functions to accommodate the nature of each type of dynamic programming problems.

REFERENCES

• 1: Bellman, R., Dynumic Progrumming, R-in- University Press, 1957.
• 2: Dmardo, E.. Dynamic Progrcamming Models Md Applicdonr, h&e-Hal, 1982.
• 3: Howard, R. A., "Dynamic Prop amming", Monogemeti Science, 12.5, pp. 317448.1966.
• 4: Nemhauser, G., Introdudon to Dynamic Programming, John Wiley & Sons, 1966.
• 5: Wagner, H. M. and Whitin, T. M.. "Dynamic Version of the Economic Lot Size Model", Munugement Science, pp. 89-96. 1958.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Routing and layout

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms, Languages