1: $kost (ldkost, mb)$ – int64int32nag_int array: ldkost, the first dimension of the array, must satisfy the constraint $ldkost \geq ma$ .
The coefficients $c_{i j}$ , for $i = 1, 2, \dots, m_{a}$ and $j = 1, 2, \dots, m_{b}$ .
2: $k15 (m)$ – int64int32nag_int array: $k15 (i)$ must be set to the availabilities $A_{i}$ , for $i = 1, 2, \dots, m_{a}$ ; and $k15 (m_{a} + j)$ must be set to the requirements $B_{j}$ , for $j = 1, 2, \dots, m_{b}$ .
3: $maxit$ – int64int32nag_int scalar: The maximum number of iterations allowed.

Constraint: $maxit \geq 1$ .

Optional Input Parameters

1: $ma$ – int64int32nag_int scalar: Default: the first dimension of the array kost.
The number of sources, $m_{a}$ .

Constraint: $ma \geq 1$ .
2: $mb$ – int64int32nag_int scalar: Default: the second dimension of the array kost.
The number of destinations, $m_{b}$ .

Constraint: $mb \geq 1$ .
3: $m$ – int64int32nag_int scalar: Default: the dimension of the array k15.
The value of $m_{a} + m_{b}$ .

Output Parameters

1: $k15 (m)$ – int64int32nag_int array: The contents of k15 are undefined.
2: $numit$ – int64int32nag_int scalar: The number of iterations performed.
3: $k6 (m)$ – int64int32nag_int array: $k6 (k)$ , for $k = 1, 2, \dots, m_{a} + m_{b} - 1$ , contains the source indices of the optimal solution (see k11).
4: $k8 (m)$ – int64int32nag_int array: $k8 (k)$ , for $k = 1, 2, \dots, m_{a} + m_{b} - 1$ , contains the destination indices of the optimal solution (see k11).
5: $k11 (m)$ – int64int32nag_int array: $k11 (k)$ , for $k = 1, 2, \dots, m_{a} + m_{b} - 1$ , contains the optimal quantities $x_{i j}$ which, sent from source $i = k6 (k)$ to destination $j = k8 (k)$ , minimize $z$ .
6: $k12 (m)$ – int64int32nag_int array: $k12 (k)$ , for $k = 1, 2, \dots, m_{a} + m_{b} - 1$ , contains the unit cost $c_{i j}$ associated with the route from source $i = k6 (k)$ to destination $j = k8 (k)$ .
7: $z$ – double scalar: The value of the minimized total cost.
8: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: On entry, the sum of the availabilities does not equal the sum of the requirements.

$ifail = 2$: During computation maxit has been exceeded.

$ifail = 3$

On entry,

maxit < 1

$ifail = 4$

On entry,	$ma < 1$ ,
or	$mb < 1$ ,
or	$m \neq ma + mb$ ,
or	$ma > ldkost$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

All operations are performed in integer arithmetic so that there are no rounding errors.

Further Comments

An accurate estimate of the run time for a particular problem is difficult to achieve.

Example

A company has three warehouses and three stores. The warehouses have a surplus of

12

units of a given commodity divided among them as follows:

Warehouse	Surplus
1	1
2	5
3	6

The stores altogether need

12

units of commodity, with the following requirements:

Store	Requirement
1	4
2	4
3	4

Costs of shipping one unit of the commodity from warehouse

i

to store

j

are displayed in the following matrix:

		Store
		1	2	$3$
	1	8	8	11
Warehouse	2	5	8	14
	3	4	3	10

It is required to find the units of commodity to be moved from the warehouses to the stores, such that the transportation costs are minimized. The maximum number of iterations allowed is

200

Open in the MATLAB editor: h03ab_example

function h03ab_example


fprintf('h03ab example results\n\n');

m = 3 + 3;
kost = [int64(8), 8, 11;
                5,  8, 14;
                4,  3, 10];
k15  = [int64(1); 5; 6;
                4;  4; 4];
maxit = int64(200);

[k15, numit, k6, k8, k11, k12, z, ifail] = ...
h03ab( ...
       kost, k15, maxit);

fprintf('Total cost = %5.1f\n\n', z);
fprintf('Goods   from   to\n');
for j = 1:m-1
  fprintf('%4d%7d%6d\n',k11(j),k6(j),k8(j));
end

h03ab example results

Total cost =  77.0

Goods   from   to
   4      3     2
   2      3     3
   1      2     3
   1      1     3
   4      2     1

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox