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   1: /*

   2:  * Copyright (C) 2013 changedi

   3:  *

   4:  * Licensed under the Apache License, Version 2.0 (the "License");

   5:  * you may not use this file except in compliance with the License.

   6:  * You may obtain a copy of the License at

   7:  *

   8:  * http://www.apache.org/licenses/LICENSE-2.0

   9:  *

  10:  * Unless required by applicable law or agreed to in writing, software

  11:  * distributed under the License is distributed on an "AS IS" BASIS,

  12:  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

  13:  * See the License for the specific language governing permissions and

  14:  * limitations under the License.

  15:  */

  16: package com.jybat.dp;

  17:  

  18: //Discounted Profits Problem

  19: //A discounted DP problem from Winston/Venkataramanan

  20: //pp.779--780

  21: //Used a reproductionFactor of 2 instead of 1.2 so number of

  22: //fish takes on integral values, without the need to use a

  23: //round or a floor function.

  24: public class DPP {

  25:     private static int T = 2; // planning horizon T=2 years

  26:     private static double interestRate = 0.05; // assume 5% interest rate

  27:     private static int initialFishAmount = 10; // initially 10,000 fish in lake

  28:     private static int reproductionFactor = 2; // in 1 year 100% more fish

  29:  

  30:     private static double revenue(int xt) {

  31:         // simply assume that the sale price is $3 per fish, no matter what

  32:         return 3.0 * xt;

  33:     }

  34:  

  35:     private static double cost(int xt, int b) {

  36:         // simply assume that it costs $2 to catch (and process) a fish, no

  37:         // matter what

  38:         return 2.0 * xt;

  39:     }

  40:  

  41:     // t is stage number, each stage represents one year

  42:     // b is current number of fish in lake (scaled to thousands)

  43:     public static double f(int t, int b) {

  44:         if (t == T + 1)// T+1 is outside planning horizon

  45:             return 0.0;

  46:         // xt is the number of fish to catch and sell

  47:         // during year t

  48:         int xt;

  49:         double max = Double.MIN_VALUE;

  50:         for (xt = 0; xt <= b; xt++) {

  51:             double earn = revenue(xt) - cost(xt, b) + 1 / (1 + interestRate)

  52:                     * f(t + 1, reproductionFactor * (b - xt));

  53:             if (earn > max)

  54:                 max = earn;

  55:         }

  56:         return max;

  57:     }

  58:  

  59:     /**

  60:      * @param args

  61:      */

  62:     public static void main(String[] args) {

  63:         System.out.println(f(1, initialFishAmount));

  64:     }

  65:  

  66: }