The determination of a cost efficient raceway network for a proposed irrigation scheme in Canterbury

Abstract

If sufficient water is available the New Zealand Government has indicated that about $100,000,000 could be spent on irrigation schemes in the next twenty years. The greater proportion of these costs will be spent on the construction of races which will bring water to the farms. The design and layout of these races is presently determined subjectively by planners on the basis of their experience and judgement.

The aim of this study is to use an optimizing procedure to determine the least cost layout of these irrigation races. The Rakaia area was chosen because of the likelihood of a scheme for the area and the author’s association with an economic report evaluating irrigation in the area. A review of existing procedure s showed that a. Modified form of the linear programming transhipment model would provide a convenient framework for solving the problem.

Some problems were encountered because the linear transhipment model was required to incorporate a non-linear objective function. The non-linear objective function, the minimizing of water transportation costs, follows from the decreasing per unit water transportation costs which arises from economies of size in race construction. A number of people have modified the transhipment model to incorporate a decreasing cost curve and it was decided to use a modification of the Logan and King (1964) plant location model in this study. This modification, like others which incorporate a decreasing cost curve, will not guarantee an unique optimal solution but it is likely to give a solution which is very close to it.

Water transportation cost data for this study were obtained from recently completed schemes and supplied by the Ministry of Works. Regression analysis was used on this cost data to estimate equations which would give the relationship between the quantity of water and the different .components of race construction costs.

Farms’ demands for water were based on past and present design criteria but a case is put to design future schemes on the basis of a farm's most likely usage for water.

The results showed that the model developed in this study can be used to design the layout of an irrigation scheme. Furthermore the resultant scheme costs are very likely to be considerably cheaper than if the scheme had been designed using the present subjective methods. The model could also examine quickly the effect of changes in costs, design criteria and in the variation in farm water demands. Some further developments of the model were outlined but the accuracy of the results, like those in this study, are dependent on obtaining reliable data and employing a variety of search procedures to obtain a good optimal solution.