Renovation of a distribution network of poultry products: Application city of Tlemcen (ALGERIA) Fethi BOUDAHRIa, Zaki SARIa
Mohammed BENNEKROUFb
University of Tlemcen Department of electrical Engineering Manufacturing Enginneering Loboratery of Tlemcen Tlemcen, Algeria E-mail:
[email protected]
University of Mascara (Algeria) Manufacturing Enginneering Loboratery of Tlemcen Tlemcen, Algeria E-mail:
[email protected]
Abstract— the supply chain of agricultural products has received a great deal of attention lately due to issues related to public health. Something that has become apparent is that in the near future the design and operation of agricultural supply chains will be subject to more stringent regulations and closer monitoring, in particular those for products destined for human consumption (agri-foods). The supply chain of agri-foods, as any other supply chain, is a network of organizations working together in different processes and activities in order to bring products and services to the market, with the purpose of satisfying customers’ demands. This work is a study for renovating the distribution network of multi poultry product from slaughterhouses to the retailer in the city of Tlemcen (Algeria). For this concrete case we chose two products namely chicken and turkey-cock meat. The objective of our problem is to determine the centroid of customer clusters (set of retailers), and the location/allocation of slaughterhouses in such a way that total logistics costs (location and transportation costs) are minimized, in such a way that capacity of vehicles and slaughterhouses are respected. As mentioned in our paper, the entire problem is decomposed into two sub problems, and each sub problem is solved in sequential manner, to get the final solution. LINGO optimization solver (Version12) has been used to get the solution to the problem. Keywords- Agri_foods Supply chain; distribution network; chicken meat; slaughterhouses; optimization. I.
complex and harder to manage than other supply chains. Agri-food supply chains (ASC) identified for two types; the first one is the supply chain of fresh agri-foods, and the second one is the supply chain for non-perishable agri-foods. Fresh products include highly perishable crops such as fresh milk, meat, fruits and vegetables whose useful life can be measured in days; non-perishable products are those that can be stored for longer periods of time such as grains, potatoes, and nuts [4]. II.
B. location Problems The location problem is to determine the location of one or more sites, so as to optimize a mathematical function that depends on distances between these sites and a set of potential users. The study of location theory began formally in 1909 when Albert Weber considers a problem of locating a warehouse to minimize the total distance between the warehouses and customers. After Weber, Hakimi in 1960 had considered a more general problem that considers the location of one or more sites in a network in order to minimize the total distance between customers and these sites, or to minimize the maximum distance.
INTRODUCTION
The term agri-food supply chains (ASC) has been coined to describe the activities from production to distribution that bring agricultural or horticultural products from the farm to the table [1]. ASC are formed by the organizations responsible for production (farmers), distribution, processing, and marketing of agricultural products to the final consumers. The supply chain of agri-foods, as any other supply chain, is a network of organizations working together in different processes and activities in order to bring products and services to the market, with the purpose of satisfying customers’ demands [2]. What differentiates ASC from other supply chains is the importance played by factors such as food quality and safety [3]. Other relevant characteristics of agri-foods include their limited shelf life, their demand and price variability, which makes the underlying supply chain more
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STATE OF THE ART
A. Design supply chains: A given general production-distribution network with all existing and potential facilities comprise three stages: production stage, distribution stage and customer stage. The network design problem consists in selecting the facilities to open in order to form a production-distribution with minimal overall costs and the highest customer service levels [5]. The design problems of supply chains are often complex by nature due to their direct relationship with economic, organizational and social sector. For this reason, the design of a successful logistics network (in its various forms: location, production, distribution, routing, location/allocation, choice of suppliers, etc. ...) has attracted, in recent years, the attention of industrial and scientific community.
The paper [6] gave the basic version of this problem as follows:
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Minimize the sum of fixed costs of the locations and variable costs related to transportation. Constrained: Meet the entire demand from open sites.
constant and no delivery time between distributions centers (DCs). The problem is to select suppliers, the location of distribution centers and the allocation suppliers to distribution centers (DCs) and allocation the retailers to distribution centers (CDs), with the aim to minimize the total fixed distribution centers location costs, running inventory and safety stock costs at the distribution centers and transportation costs through the network. The authors have found that the problem is NP-hard, have proposed the Lagrangian relaxation approach to solve this problem. The authors present in their paper [10] a metaheuristic called "Heuristic Concentration (HC)" and have shown how this method improves the performance of a heuristic exchange of a single element in solving the problem. The authors of the paper [11] presented a literature review of models of plant location and planning strategy for supply chain. The authors have noted the interest shown by several researchers treating stochastic cases. The authors’ note that the tactical and operational decisions (routing and mode of transport) strongly depend on the decision of the location of sites and that integration decisions in Supply Chain Management is less studied. The authors gave in this paper [4] the main contributions in the field of production and distribution planning for agrifoods. The authors have focused particularly on those models that have been successfully implemented. Then, they have classified this model according to relevant features, such as the optimization approaches used, the type of crops modeled and the scope of the plan. The authors conclude that: • The use of integrated planning models in the agri-food supply chain is still very limited. • The second planning models dealing with perishable products very often fail to incorporate realistic stochastic. The authors of the article [12] presented a solution for the CCCP (capacitated centered clustering problem) using the CS (clustering search) algorithm that uses the concept of hybrid metaheuristics, combining metaheuristics with a local search in a clustering process. the authors of the paper have proposed in their paper [13] a novel algorithm to solve the transportation problem of the cross-docking network. The objective of this work is to minimize the total shipping cost of transporting pallets from a set of I suppliers to a set of J customers through K crossdocking distribution centers. Ant Colony Optimization (ACO) algorithm was used to solve the problem on hand. Authors have solved a numerical example for verification and demonstrative purposes. They found that our proposed solution reduces significantly the shipping cost in the network of cross-docks. The authors discuss in their paper [14] the location routing problem (LRP) and consider a discrete (LRP) with two levels: a set of potential capacitated distribution centers (DC) and a set of ordered customers. The different grouping procedures used by the authors were tested on a large number of instances (adapted from data in the literature) and the results were
C. Problems allocation The allocation problem is to assign processing or manufacturing to the sites and determine the flow between the various network sites. This problem is expressed as follows [6]: Minimize the sum of costs of production and transportation. Constrained: Meeting demand. Provision of raw materials. Respect the available capacity at the supply Respect the available capacity at the production Respect the available capacity at the distribution Balance the flow. D. location-allocation Problems In a location-allocation problem, we distinguish the term localization that refers to the determination of the locations of sites (sites of production or distribution centers), and the term allocation that refers to assigning activities to production sites, distribution centers or customers. This location-allocation problem is expressed as follows [6]: Minimize the sum of fixed costs related to facilities and variable costs related to production and transportation. Constrained: Meeting demand Provision of raw materials Respect the available capacity at the supply Respect the available capacity at the production Respect the available capacity at the distribution Balance the flow Ensure that when a site is closed, no product is manufactured in this site and the material flows entering and leaving this site are void. The authors have proposed in their paper [7] a new genetic algorithm for the problem of site locations (facilities). This algorithm is simple and gives good solutions. The purpose of the model is to select the best location of the P sites to serve N points (areas) of application to minimize the distance between these sites and demand points. The algorithm used to give two solutions: the best and the bad; and then it will select the best that does not change after several iterations. the authors of the paper [8] defined the classic problem of localization of P-median as the location of P facilities to cover the requested command with the minimization of the total transport cost. They assume in their work that these costs are directly proportional to the distance covered and the quantity of products transported. The authors of the article [9] have addressed the design problem where plants location and supplier selection decisions are integrated. In this study, they assumed that the retailer will make a random demand for one type of product and delivery time between each supplier and each distribution center is
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Vlij: volume of product l at customer cluster j delivers by slaughterhouse i; FCi: Fixed cost for establishing a slaughterhouse i; Dij: Distance from slaughterhouse i to the centroid of customer cluster j; Cost of transporting one unit per kilometers; Qli : Slaughterhouse Capacity i for product l;
compared so as to obtain some guidelines concerning the choice of a suitable clustering technique. The authors the paper [1] provides a literature review on existing performance indicators and models, and discuss their usefulness in agri-food supply chains. The authors have studied in their work [15] the impact of poultry slaughter house modernization and updating of food safety management systems on the microbiological quality and safety of products. III.
C. Decision Variables Yjk = 1, if the customer k is assigned to customer cluster j, = 0, otherwise; Z ij = 1, if the customer cluster j is allocated to slaughterhouse i, = 0, otherwise; X i = 1, if the slaughterhouse i is open, = 0 otherwise;
PROBLEM DESCRIPTION
Our problem is to determine the centroid of the cluster customers (set of retailers), and location / allocation between the slaughterhouses and the cluster customers (set of retailers). A cluster of customers includes customers in the closest distance with a condition that the amount of demands from different customers of this customer clusters (sets of retailers) is less than the capacity of the truck transport used. We used two types of transport trucks; one capacity of 400 units, other 800 units. it was assumed that the volume or weight of the turkey-cock is 5 times larger than chicken. Once the customer clusters are defined with their positions and capabilities, it remains for us to locate the different slaughterhouses and allocate the customer clusters to slaughterhouse, in such a way that capacity of vehicles (truck transport) and slaughterhouses are respected.
D. Model formulation The mathematical model formulated for the minimization of Total Cost (TC) transportation in the city of Tlemcen (Algeria) (see Fig.1) in order to cover the entire order requested. Since the problem is highly complex, it cannot be solved in a single stage. For this purpose, the entire problem (objective criterion) is decomposed into two sub problems; each sub problem is solved in a sequential manner, while accounting for dependence between them. The objective criterion is decomposed into the following sub problems:
A. Assumptions The assumptions made in this model are given as follows: (1) The demand delivered to customers each day as an average of the order. (2) The capacity of each customer cluster (sets of retailers) must not exceed vehicles capacity. (3) The Processing capacity in slaughterhouses is always less than the sum of orders for each customer clusters assigned to this slaughterhouse i. (4) The location/allocation plan covers a planning horizon within which no substantial changes are incurred in customer demands and in the transportation infrastructure.
(1) Capacitated [Sub problem 1].
Centered Clustering Problem (CCCP)
(2) Location- Allocation Problem [Sub problem 2].
B. Model parameters i : Index for slaughterhouse; i∈ I, j : Index for customer clusters; j ∈ J k : Index for customers; k ∈ K l : Index for products; l ∈L I = {1,……..r} for Set of slaughterhouse; J = {1,……..t} for Set of customer clusters; K = {1,……..s} for Set of customers; L = {1,……..p} for Set of products; xi , yi : Geometric position of the slaughterhouse i; x’j , y’j : Geometric position of the customer cluster j; x k , yk :Geometric position of the customer k; nj :Number of customers assigned to customer cluster j; Qj: Capacity of a vehicle that travels to the customer cluster j; Dclk: Demand of customer k for product l; Dcclj: The demand for a product l by the customer cluster j;
figure 1.
Map of Tlemcen city
a) Capacitated Centered Clustering Problem (CCCP) The calculated centroid of each customer cluster has been used for allocating customer cluster with each slaughterhouse. Capacitated Centered Clustering Problem (CCCP) [13] is a generalization of the Capacitated P-Median Problem (CPMP), which can be viewed as the problem of defining a set of p
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clusters with limited capacity and minimum dissimilarity between the formed clusters, where each cluster has a centroid located at the geometric centre of its points and covers all the demands of a set of m points. The mathematical model of CCCP is given as follows:
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