Mathematical modelling of the expansion planning of the national grain storage system

Abstract

Cereal Food, the basic need for human and other animals is produced periodically. Such a periodic supply of cereal food is stored for ensuring future uninterrupted supply to both private and public sectors for continuous consumption. The periodic produced food supply can only be approached zero, while a certain supply is imminent. Governments in almost of allover the world are committed to establish food security by ensuring all time availability of food to vulnerable section of the society, adopting appropriate measures against production fluctuation, maintaining price stabilization, ensuring uninterrupted supply to meet the demand etc. For food security it requires application of various management techniques. One important objective would be the determination of the optimum capacity and location of warehousing spaces. The various issues and problems such as selecting the appropriate storage mix, demolition of inefficient storages, determining the expansion volumes associated with the above decisions unless correctly addressed can seriously affect the overall operation of the total system of food security in future periods. In the present work, four models have been developed. These are related to (i) expansion storage capacity determination at national level, (ii) storage size and location determination at regional level for both public and private sectors, (iii) hierarchical planning of storages at the sub-regional level and (iv) production estimation for different crops. The objective is to determine the size, type and location of additional amount of storage space required over existing storage space available. This additional storage space is ascertained as the total aggregate at the national level and then at the regional and subregional levels. This space is required when confronted with a highly fluctuating production and/or price situation. Further, the optimum policy of storage mix and VI operational mix to be undertaken in a planning period, is determined in accordance with stock load duration. The models also identify the security inventory level, import and export volumes, inter and intra regional transfer volumes arising out of the production and consumption need. The capacity determination model (Model-I) determines the expanded storage capacity needed along with storage mix and operational planning at the national level. The involvement of tbe public Grain Board/Corporation/Cooperatives historically in food grain management has been considered and criteria was set so that the total cost of capital, operational and maintenance was minimized. Under such a system the planning is made to addrcss tbe desired growth, technology change and optimum operation of the system. The Model-II determines, on the basis of thc output of Model-I, the optimum size and locations of the storage space required at the national or regional leveL The objective is to minimize the overall total cost of transportation, construction of additional storages and imports and exports. The set of constraints in this model includes cereal stock balance at the various regions and ports. As mentioned, using the model-I output, the model-II determines the national public sector involvement in expansion storage capacities. Considering a free market economy, involvement of both private and public sectors has been incorporated in Model-II. Accordingly Model-II has been modified where additional capacity constraint in Model-II from the output of Model-I is withdrawn. The hierarchical planning model (Model-III), determines the optimum expansion capacities at the sub-region/district levels. This model minimizes the difference between the total storage space of the sub-regions and the respective region to arrive at the optimum result. VII To build up the constraint equations, the stock balance for the sub-regions and terminal silo of the region, imports and exports to and from the region, intra-regional movement of the stock, production fluctuation of the sub-regions have been considered. Model-IV is an econometric model for estimating the cereal production of a country. The - relevant factors responsible for production have been included in the model as the independent variables. All the above models are generalised models and thus applicable to any country irrespective of surplus or deficit situations. However, modifications in the models may be necessary to suit any specific requirements of a country. In order to demonstrate the applicability of the models, in this thesis, Bangladesh has been considered as a case study. The results obtained are found consistent with the real-life situation. It is hoped that these models would go a long way to serve as useful planning tools for the food management personnel involved in the expansion programme of the national grain storage system of any country.