Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.

Effetto della temperatura di conservazione del latte, dalla raccolta all'affioramento, sulla microflora del latte, del sieroinnesto e del formaggio Trentingrana

This PhD research is part of a project addressed to improve the quality of Grana Trentino production. The objectives were to evaluated if milk storage and collection procedures may affect cheese-making technology and quality. Actually the milk is collected and delivered to the cheese factory just after milking in 50 L cans without refrigeration or in tanks cooled at 18 °C. This procedure is expensive (two deliveries each day) and the milk quality is difficult to preserve as temperatures are not controlled. The milk refrigeration at the farm could allow a single delivery to the dairy. Therefore it could be a good strategy to preserve raw milk quality and reduce cheese spoilage. This operation may, however, have the drawbacks of favouring the growth of psychrotrophic bacteria and changing the aptitude of milk to coagulation. With the aim of studying the effect on milk and cheese of traditional and new refrigerated technologies of milk storage, two different collection and creaming technologies were compared. The trials were replicated in three cheese factories manufacturing Grana Trentino. Every cheese-making day, about 1000 milk liters were collected from always the same two farms in the different collection procedures (single or double). Milk was processed to produce 2 wheels of Grana trentino every day. During the refrigerated trials, milk was collected and stored at the farm in a mixed tank at 12 or 8 °C and then was carried to the dairy in truck once a day. 112 cheese making day were followed: 56 for traditional technology and 56 for the refrigerated one. Each one of these two thechnologies lead to different ways of creaming: long time in the traditional one and shorter in the new one. For every cheese making day we recorded time, temperatures and pH during the milk processing to cheese. Whole milk before ceraming, cream and skim milk after creaming, vat milk and whey were sampled during every cheese-making day for analysis. After 18 months ripening we opened 46 cheese wheels for further chemical and microbiological analyses. The trials were performed with the aim of: 1 estimate the effect of storage temperatures on microbial communities, physico-chemical or/and rheological differences of milk and skim milk after creaming. 2 detect by culture dependent (plate counts) and indipendent (DGGE) methodolgies the microbial species present in whole, skimmed milk, cream and cheese sampled under the rind and in the core; 3 estimate the physico-chemical characteristics, the proteolytic activity, the content of free aminoacids and volatile compounds in 18 months ripened Grana Trentino cheeses from different storing and creaming of milk technologies. The results presented are remarkable since this is the first in-deep study presenting microbiological and chemical analysis of Grana Trentino that even if belonging to Grana Padano Consortium, it is clearly different in the milk and in the manufacturing technology.