POLICY-ITERATION ALGORITHM

Denso QR Bar Code Decoder In .NET FrameworkUsing Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in Visual Studio .NET applications.

v1 = 0 g + 09v1 + 01v2 v2 = 0 g + 08v2 + 01v3 + 005v4 + 005v5 v3 = 0 g + 07v3 + 01v4 + 02v5 v4 = 5 g + v1 v5 = 10 g + v6 v6 = 0 g + v1 v6 = 0 The solution of these linear equations is given by g(R (3) ) = 04338, v1 (R (3) ) = 04338, v2 (R (3) ) = 47717, v3 (R (3) ) = 65982, v4 (R (3) ) = 50000, v5 (R (3) ) = 95662, v6 (R (3) ) = 0 Step 2 (policy improvement) The test quantity Ti (a, R (3) ) has the values T2 (0, R (3) ) = 47717, T2 (1, R (3) ) = 7, T3 (0, R (3) ) = 65987, T3 (1, R (3) ) = 70000, T4 (0, R (3) ) = 68493, T4(1) (1, R (3) ) = 50000 This yields the new policy R (4) = (0, 0, 0, 1, 2, 2) Step 3 (convergence test) The new policy R (4) is identical to the previous policy R (3) and is thus average cost optimal The minimal average cost is 04338 per day Remark 642 Deterministic state transitions For the case of deterministic state transitions the computational burden of policy iteration can be reduced considerably Instead of solving a system of linear equations at each step, the average cost and relative values can be obtained from recursive calculations The reason for this is that under each stationary policy the process moves cyclically among the recurrent states The simpli ed policy-iteration calculations for deterministic state transitions are as follows: (a) Determine for the current policy R the cycle of recurrent states among which the process cyclically moves (b) The cost rate g(R) equals the sum of one-step costs in the cycle divided by the number of states in the cycle (c) The relative values for the recurrent states are calculated recursively, in reverse direction to the natural ow around the cycle, after assigning a value 0 to one recurrent state

QR Code ISO/IEC18004 Printer In .NET FrameworkUsing Barcode maker for .NET Control to generate, create QR Code image in VS .NET applications.

DISCRETE-TIME MARKOV DECISION PROCESSES

QR Code ISO/IEC18004 Decoder In Visual Studio .NETUsing Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.

(d) The relative values for transient states are computed rst for states which reach the cycle in one step, then for states which reach the cycle in two steps, and so forth It is worthwhile pointing out that the simpli ed policy-iteration algorithm may be an ef cient technique to compute a minimum cost-to-time circuit in a deterministic network

Drawing Bar Code In .NET FrameworkUsing Barcode maker for .NET framework Control to generate, create barcode image in .NET framework applications.

LINEAR PROGRAMMING APPROACH

Decode Barcode In VS .NETUsing Barcode scanner for .NET Control to read, scan read, scan image in .NET framework applications.

The policy-iteration algorithm solves the average cost optimality equation (643) in a nite number of steps by generating a sequence of improved policies Another way of solving the optimality equation is the use of a linear program for the average cost case The linear programming formulation to be given below allows the unichain assumption in Section 64 to be weakened as follows Weak unichain assumption For each average cost optimal stationary policy the associated Markov chain {Xn } has no two disjoint closed sets This assumption allows non-optimal policies to have multiple disjoint closed sets The unichain assumption in Section 64 may be too strong for some applications; for example, in inventory problems with strictly bounded demands it may be possible to construct stationary policies with disjoint ordering regions such that the levels between which the stock uctuates remain dependent on the initial level However, the weak unichain assumption will practically always be satis ed in realworld applications For the weak unichain case, the minimal average cost per time unit is independent of the initial state and, moreover, the average cost optimality equation (643) applies and uniquely determines g as the minimal average cost per time unit; see Denardo and Fox (1968) for a proof This reference also gives the following linear programming algorithm for the computation of an average cost optimal policy Linear programming algorithm

Generate QR Code In Visual C#Using Barcode generation for .NET framework Control to generate, create Quick Response Code image in .NET framework applications.

Step 1 Apply the simplex method to compute an optimal basic solution (xia ) to the following linear program:

Draw QR Code In VS .NETUsing Barcode drawer for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.

QR Code Maker In VB.NETUsing Barcode drawer for .NET Control to generate, create Quick Response Code image in .NET framework applications.

Barcode Maker In .NETUsing Barcode encoder for .NET Control to generate, create barcode image in .NET framework applications.

Encode Rationalized Codabar In VS .NETUsing Barcode maker for .NET Control to generate, create Ames code image in VS .NET applications.

USS Code 128 Creator In C#Using Barcode encoder for VS .NET Control to generate, create Code 128C image in VS .NET applications.

Bar Code Printer In JavaUsing Barcode printer for Java Control to generate, create bar code image in Java applications.

UCC - 12 Generator In JavaUsing Barcode generation for Java Control to generate, create UPC Symbol image in Java applications.

USS Code 128 Reader In .NETUsing Barcode reader for .NET framework Control to read, scan read, scan image in .NET framework applications.