engleski

Bi-level supply chain optimization in olive oil industry

The agri-food supply chain, 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. What differentiates an ordinary supply chain from an agri-food supply chain is the deterioration of the fresh products harvested and delivered for the food production. A very important factor making agri-food supply chain harder to manage is the perishability of the agricultural commodities. Namely, the amount and the quality of harvestable fresh products depend a lot on the growing process of the related plants on farmland and the time of their harvesting. Moreover, the deteriorating process of the fresh products starts immediately after they are harvested. Therefore, the time for processing harvested fresh products is very limited unless they are stored in a strictly controlled environment which, on the other hand induces large holding costs. In this work we consider farms growing and harvesting olives which participate in the supply chain as suppliers. On the other side we observe olive oil producers that collect the olives and process them on special machines. The harvesting of olives is made over a time horizon of about two months. The problem is to synchronise the harvest and the delivery of olives with their processing on the machines for producing olive oil. The suppliers decide on the dates of harvesting and delivery of olives, while the olive oil producers decide on the schedule for processing the olives. The goal is to minimize the costs regarding the whole supply chain : the costs of harvesting olives in the inappropriate time, the costs of delivery, inventory holding costs (storing the olives in a special cold storage) and the production costs.An argument for using the bi- level formulation is that it is more applicable in practise due to the fact that it is closer to how the olive oil production is mostly planned in Croatia now. Namely, the present situation is that the farmers most often bring the olives to the production site when they choose to. The consequence is the decay of large amounts of olives which cannot be processed, or even properly stored, in a short time. Also, storing the olives in cold storages with a controlled environment induces enormous costs. Thus, increasing storage capacity would not lead to a satisfying solution. Moreover, in reality it cannot be expected that the farmers will want to completely obey the optimized schedule given by the olive oil producers. On the other hand, planting olives is stimulated in Croatia, and since we cannot compete on the global market in quantities, the potential is recognized in quality. Thus, the optimization of supply chain in olive oil industry is modelled as a bi-level mixed- integer programming problem. At the upper level of decision making there are the suppliers with their two objectives of minimizing the costs of harvesting olives in the inappropriate time and the costs of delivery. At the lower level of decision making there are the producers with their objectives of minimizing the inventory holding and production costs. The decision variables controlled by the leaders are the quantities and the dates of harvest and delivery of different olive types. On the other hand, the decision variables controlled by the followers are the number and the size of batches of different kinds of olive oil produced on each machine for each day, as well as the inventory levels for different types of olives in cold storage on a daily basis. It is proven that even bi-level linear programming problems are NP-hard. Therefore, we propose metaheuristics for solving the described problem of optimizing the supply chain in olive oil industry.

agri-food supply chain; olive oil industry; bi-level optimization; mixed-integer programming; metaheuristics

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