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Mathematical Modeling and Distribution Design for Agricultural Products in Bangladesh

Mohammad Khairul Islam
Department of Mathematics, Directorate of Secondary and Higher Education, Dhaka-1000, Bangladesh

Md. Mahmud Alam
Department of Mathematics, Dhaka University of Engineering and Technology, Gazipur-1707, Bangladesh

Mohammed Forhad Uddin
Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh

Gazi Mohammad Omar Faruque
Department of Computer Science and Engineering, University of South Asia, Dhaka-1213, Bangladesh.

Abstract/ Executive Summary:

In this paper, we have formulated a mixed-integer linear programming (MILP) model for the distribution design of Agricultural products in Bangladesh. The scheme of distribution is very important for the supply chain network (SCN), which is choosing the suitable distribution center (DC) for the distribution of the products. This study is a real-life distribution problem. To developed this model, we have collected data from various market players who are directly or indirectly involved in the Agriculture sector. We have to solve this model, by using a mathematical programming language (AMPL). We have verified a multi-stage SCN, which includes producer, DC and customer. Also this model is to optimize profit, allocations of the products and most useable DC which satisfied most of the customer demands. Finally, we can analyze the profit for the uncertainty parameters.

Keywords: Supply chain, Agricultural products, Distribution center, Optimization, Mixed integer lnear program

Location: In Bangladesh

Start Date:

End Date:

Program Area: Farm Mechanization

Commodity: Farming System

Objectives:

To determine the optimized profit, allocations of the products and how many DC to use.

Methodology:

We tend to develop our MILP model by in gathering information for Agricultural product optimization in at random elite samples of 235 market players who are directly or indirectly concerned in agricultural business from three districts (Mymensingh, Kishorgonj and Jamalpur) in Bangladesh, additionally in gathering information from some super shop market like Agora, Shwapno and some big size Agricultural products distributor in Dhaka town. We've collected total prices of SCN style like fixed prices, labor prices, holding prices, transportation prices, packing prices and personnel prices. Subsequently calculated profit dividing total come back by total investment. We’ve additionally collected secondary information from East Pakistan Bureau of Statistics (BBS), Directorate of Agricultural Marketing (DAM), Statistics Department of Bangladesh Bank (SDBB), Bangladesh Journal of Agricultural Economics (BJAE), NGOs reports and Newspapers. Before the mathematical formulation of MILP model, we have discussed basic notations, parameters and decision variables that are relevant with our work in this study. In mathematical optimization, linear programming maximizes (or minimizes) a linear objective function subject to at least one or a lot of constraints. Mixed number programming adds one further condition that a minimum of one in every of the variables will solely whole number values. The technique finds broad use in research. The objective function is to optimize the maximum profit as well as optimal distribution center which satisfy most of the customer demands. Constraint (2) assurance that the total amount of specific product shipped from l^th production location for a particular customer via k^th distribution center is equal to the total demand of the specific product from that customer. Constraint (3) ensure that the total amount of specific product shipped from l^th production location via all distribution center for all customer is not greater than total capacity of all distribution center. Constraint (4) presents that a distribution center is used when and only if there is a demand for any product. Constraint (5) guarantees that each customer is allocated to exactly one distribution center. To find the solution of the formulated MILP model, we have solved the required model by using AMPL (AMPL Student Version 20121021) with the appropriate solver MINOS. We have developed an AMPL code, which consists of an (a) AMPL model file, containing the actual program, (b) AMPL data file, containing data for the various parameters and (c) AMPL run file. This program has accomplished on a Core-I3 machine with a 3.60 GHz processor and 4.0 GB RAM. In this section, we have presented profits comparison for different uncertainty parameters. Due to the volume details, optimal solutions are not presented in this paper. If readers are interested then they can contact with the corresponding authors. Finally, we are able to create a forecast that the corporate should be wariness for the large natural cataclysm and have to be compelled to take some plans like advance assortment of merchandise that don't seem to be raw or increase range of inventories within the standard locations etc so they need to not fall in risk in such things and haven't to delay in deliveries ordered by customers. Within the next section, we've got drawn a conclusion regarding our work.

Source of Information: Asian Journal of Probability and Statistics, 6(1): 34-42, 2020; Article no.AJPAS.53328; ISSN: 2582-0230

Article Link (Online Journal): DOI: 10.9734/AJPAS/2020/v6i130152

Funding Source:

Total Budget (Tk.) :

Achievement/Findings:

In this paper, the MILP model is developed for the integrated SCN design which is solved by the well-known branch and bound Algorithm applying A Mathematical Programming Language (AMPL). MINOS optimization solver was applied to optimize the problem and find the optimal solution. We developed a MILP model and analyzed the business policy of agricultural products in Bangladesh. We collected one-year data to develop this model. The formulated MILP model is to maximize the total profit, allocations of the products and also to optimize the most useable DC which satisfied most of the customer demands. Finally, we can analyze the profit for the uncertainty parameters. Some of the significant findings can be summarized as follows: Firstly, the illustrated numerical example apparently shows that the MILP model shows the distribution centers 4 and 5 are most profitable than other distribution centers because these two distribution centers are satisfied most of the customer demands. Secondly, for the increase of uncertainty probability then the profit has decreased gradually. We are confident that this is the first work with agricultural products business policy in Bangladesh. We hope that this work will be helpful to the researchers, businessmen of agricultural products and common readers to know about the system of profitable agricultural products marketing. The future research of our interest is to optimize the whole system of the SCN design of agricultural products in Bangladesh, like a producer- local wholesaler-urban wholesaler-retailer and consumer. Also, formulate the coordination model among the participants of SCN. Further, comparison this MILP model with MILFP model for various parameters.

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