Yaşam döngüsünü tamamlamış ürünler için seçimli ve periyodik envanter rotalama problemi

Our study is motivated from a biodiesel production facility in Istanbul that collects waste vegetable oils from source points such as restaurants and hospitals that generate waste in large amounts and are dispersed throughout the city. The production facility uses the collected waste oil as raw material for biodiesel production. The manager of this facility needs to decide which of the present source points to include in the collection program, which of them to visit on each day, which periodic routing schedule to repeat over an infinite horizon and how many vehicles to operate such that the total collection, inventory and purchasing costs are minimized while the production requirements and operational constraints are met. For this selective and periodic inventory routing problem: First, we propose a ow-based mixed integer linear programming (MILP) formulation and test it on a real-world problem with 36 scenarios. We generate lower bounds using a partial linear relaxation model, and observe that the solutions obtained through our model are within 3:28% of optimality on the average. Several insights regarding the customer selection, routing and production decisions are acquired with further sensitivity analysis. Secondly, we compare alternative formulations and test them on six scenarios. Here, we compare three alternatives to optimize the visiting schedule and observe that our first proposed MILP model yields the best solutions. Thirdly, we propose a Lagrangian Relaxation approach for the solution of single vehicle problems. The relaxed model decomposes into two mixed integer programming models that optimize the visit schedule and the collection route in each period separately. We test the performance of this solution approach and compare the lower bounds obtained by the Lagrangian relaxation method to the ones obtained by solving the proposed MILP model within a pre-specified time limit.