The multi-handler knapsack problem under uncertainty

The Multi-Handler Knapsack Problem under Uncertainty is a new stochastic knapsack problem where, given a set of items, characterized by volume and random profit, and a set of potential handlers, we want to find a subset of items which maximizes the expected total profit. The item profit is given by the sum of a deterministic profit plus a stochastic profit due to the random handling costs of the handlers. On the contrary of other stochastic problems in the literature, the probability distribution of the stochastic profit is unknown. By using the asymptotic theory of extreme values, a deterministic approximation for the stochastic problem is derived. The accuracy of such a deterministic approximation is tested against the two-stage with fixed recourse formulation of the problem. Very promising results are obtained on a large set of instances in negligible computing time

Stochastic programming for City Logistics: new models and methods

The need for mobility that emerged in the last decades led to an impressive increase in the number of vehicles as well as to a saturation of transportation infrastructures. Consequently, traffic congestion, accidents, transportation delays, and polluting emissions are some of the most recurrent concerns transportation and city managers have to deal with. However, just building new infrastructures might be not sustainable because of their cost, the land usage, which usually lacks in metropolitan regions, and their negative impact on the environment. Therefore, a different way of improving the performance of transportation systems while enhancing travel safety has to be found in order to make people and good transportation operations more efficient and support their key role in the economic development of either a city or a whole country. The concept of City Logistics (CL) is being developed to answer to this need. Indeed, CL focus on reducing the number of vehicles operating in the city, controlling their dimension and characteristics. CL solutions do not only improve the transportation system but the whole logistics system within an urban area, trying to integrate interests of the several. This global view challenges researchers to develop planning models, methods and decision support tools for the optimization of the structures and the activities of the transportation system. In particular, this leads researchers to the definition of strategic and tactical problems belonging to well-known problem classes, including network design problem, vehicle routing problem (VRP), traveling salesman problem (TSP), bin packing problem (BPP), which typically act as sub-problems of the overall CL system optimization. When long planning horizons are involved, these problems become stochastic and, thus, must explicitly take into account the different sources of uncertainty that can affect the transportation system. Due to these reasons and the large-scale of CL systems, the optimization problems arising in the urban context are very challenging. Their solution requires investigations in mathematical and combinatorial optimization methods as well as the implementation of efficient exact and heuristic algorithms. However, contributions answering these challenges are still limited number. This work contributes in filling this gap in the literature in terms of both modeling framework for new planning problems in CL context and developing new and effective heuristic solving methods for the two-stage formulation of these problems. Three stochastic problems are proposed in the context of CL: the stochastic variable cost and size bin packing problem (SVCSBPP), the multi-handler knapsack problem under uncertainty (MHKPu) and the multi-path traveling salesman problem with stochastic travel times (mpTSPs). The SVCSBPP arises in supply-chain management, in which companies outsource the logistics activities to a third-party logistic firm (3PL). The procurement of sufficient capacity, expressed in terms of vehicles, containers or space in a warehouse for varying periods of time to satisfy the demand plays a crucial role. The SVCSBPP focuses on the relation between a company and its logistics capacity provider and the tactical-planning problem of determining the quantity of capacity units to secure for the next period of activity. The SVCSBPP is the first attempt to introduce a stochastic variant of the variable cost and size bin packing problem (VCSBPP) considering not only the uncertainty on the demand to deliver, but also on the renting cost of the different bins and their availability. A large number of real-life situations can be satisfactorily modeled as a MHKPu, in particular in the last mile delivery. Last mile delivery may involve different sequences of consolidation operations, each handled by different workers with different skill levels and reliability. The improper management of consolidation operations can cause delay in the operations reducing the overall profit of the deliveries. Thus, given a set of potential logistics handlers and a set of items to deliver, characterized by volume and random profit, the MHKPu consists in finding a subset of items which maximizes the expected total profit. The profit is given by the sum of a deterministic profit and a stochastic profit oscillation, with unknown probability distribution, due to the random handling costs of the handlers.The mpTSPs arises mainly in City Logistics applications. Cities offer several services, such as garbage collection, periodic delivery of goods in urban grocery distribution and bike sharing services. These services require the planning of fixed and periodic tours that will be used from one to several weeks. However, the enlarged time horizon as well as strong dynamic changes in travel times due to traffic congestion and other nuisances typical of the urban transportation induce the presence of multiple paths with stochastic travel times. Given a graph characterized by a set of nodes connected by arcs, mpTSPs considers that, for every pair of nodes, multiple paths between the two nodes are present. Each path is characterized by a random travel time. Similarly to the standard TSP, the aim of the problem is to define the Hamiltonian cycle minimizing the expected total cost. These planning problems have been formulated as two-stage integer stochastic programs with recourse. Discretization methods are usually applied to approximate the probability distribution of the random parameters. The resulting approximated program becomes a deterministic linear program with integer decision variables of generally very large dimensions, beyond the reach of exact methods. Therefore, heuristics are required. For the MHKPu, we apply the extreme value theory and derive a deterministic approximation, while for the SVCSBPP and the mpTSPs we introduce effective and accurate heuristics based on the progressive hedging (PH) ideas. The PH mitigates the computational difficulty associated with large problem instances by decomposing the stochastic program by scenario. When effective heuristic techniques exist for solving individual scenario, that is the case of the SVCSBPP and the mpTSPs, the PH further reduces the computational effort of solving scenario subproblems by means of a commercial solver. In particular, we propose a series of specific strategies to accelerate the search and efficiently address the symmetry of solutions, including an aggregated consensual solution, heuristic penalty adjustments, and a bundle fixing technique. Yet, although solution methods become more powerful, combinatorial problems in the CL context are very large and difficult to solve. Thus, in order to significantly enhance the computational efficiency, these heuristics implement parallel schemes. With the aim to make a complete analysis of the problems proposed, we perform extensive numerical experiments on a large set of instances of various dimensions, including realistic setting derived by real applications in the urban area, and combinations of different levels of variability and correlations in the stochastic parameters. The campaign includes the assessment of the efficiency of the meta-heuristic, the evaluation of the interest to explicitly consider uncertainty, an analysis of the impact of problem characteristics, the structure of solutions, as well as an evaluation of the robustness of the solutions when used as decision tool. The numerical analysis indicates that the stochastic programs have significant effects in terms of both the economic impact (e.g. cost reduction) and the operations management (e.g. prediction of the capacity needed by the firm). The proposed methodologies outperform the use of commercial solvers, also when small-size instances are considered. In fact, they find good solutions in manageable computing time. This makes these heuristics a strategic tool that can be incorporated in larger decision support systems for CL

A Generalized Bin Packing Problem for parcel delivery in last-mile logistics

Abstract In this paper, we present a new problem arising at a tactical level of setting a last-mile parcel delivery service in a city by considering different Transportation Companies (TC), which differ in cost and service quality. The courier must decide which TCs to select for the service in order to minimize the total cost and maximize the total service quality. We show that the problem can be modeled as a new packing problem, the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), where the items are the parcels to deliver and the bins are the TCs. The aim of the GBPPI is to select the appropriate fleet from TCs and determine the optimal assignment of parcels to vehicles such that the overall net cost is minimized. This cost takes into account both transportation costs and service quality. We provide a Mixed Integer Programming formulation of the problem, which is the starting point for the development of efficient heuristics that can address the GBPPI for instances involving up to 1000 items. Extensive computational tests show the accuracy of the proposed methods. Finally, we present a last-mile logistics case study of an international courier which addresses this problem

The Generalized Bin Packing Problem with bin-dependent item profits

In this paper, we introduce the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), a variant of the Generalized Bin Packing Problem. In GBPPI, various bin types are available with their own capacities and costs. A set of compulsory and non-compulsory items are also given, with volume and bin-dependent profits. The aim of GBPPI is to determine an assignment of items to bins such that the overall net cost is minimized. The importance of GBPPI is confirmed by a number of applications. The introduction of bin-dependent item profits enables the application of GBPPI to cross-country and multi-modal transportation problems at strategic and tactical levels as well as in last-mile logistic environments. Having provided a Mixed Integer Programming formulation of the problem, we introduce efficient heuristics that can effectively address GBPPI for instances involving up to 1000 items and problems with a mixed objective function. Extensive computational tests demonstrate the accuracy of the proposed heuristics. Finally, we present a case study of a well-known international courier operating in northern Italy. The problem approached by the international courier is GBPPI. In this case study, our methodology outperforms the policies of the company

The multi-stage dynamic stochastic decision process with unknown distribution of the random utilities

We consider a decision maker who performs a stochastic decision process over a multiple number of stages, where the choice alternatives are characterized by random utilities with unknown probability distribution. The decisions are nested each other, i.e. the decision taken at each stage is affected by the subsequent stage decisions. The problem consists in maximizing the total expected utility of the overall multi-stage stochastic dynamic decision process. By means of some results of the extreme values theory, the probability distribution of the total maximum utility is derived and its expected value is found. This value is proportional to the logarithm of the accessibility of the decision maker to the overall set of alternatives in the different stages at the start of the decision process. It is also shown that the choice probability to select alternatives becomes a Nested Multinomial Logit model

The multi-stage dynamic stochastic decision process with unknown distribution of the random utilities

We consider a decision maker who performs a stochastic decision process over a multiple number of stages, where the choice alternatives are characterized by random utilities with unknown probability distribution. The decisions are nested each other, i.e. the decision taken at each stage is affected by the subsequent stage decisions. The problem consists in maximizing the total expected utility of the overall multi-stage stochastic dynamic decision process. By means of some results of the extreme values theory, the probability distribution of the total maximum utility is derived and its expected value is found. This value is proportional to the logarithm of the accessibility of the decision maker to the overall set of alternatives in the different stages at the start of the decision process. It is also shown that the choice probability to select alternatives becomes a Nested Multinomial Logit model

A Machine Learning-based DSS for mid and long-term company crisis prediction

In the field of detection and prediction of company defaults and bankruptcy, significant effort has been devoted to evaluating financial ratios as predictors using statistical models and machine learning techniques. This problem becomes crucially important when financial decision-makers are provided with predictions on which to act, based on the output of prediction models. However, research has shown that such predictors are sufficiently accurate in the short-term, with the focus mainly directed towards large and medium-large companies. In contrast, in this paper, we focus on mid- and long-term bankruptcy prediction (up to 60 months) targeting small and/or medium enterprises. The key contribution of this study is a substantial improvement of the prediction accuracy in the short-term (12 months) using machine learning techniques, compared to the state-of-the-art, while also making accurate mid- and long-term predictions (measure of the area under the ROC curve of 0.88 with a 60 month prediction horizon). Extensive computational tests on the entire set of companies in Italy highlight the efficiency and accuracy of the developed method, as well as demonstrating the possibility of using it as a tool for the development of strategies and policies for entire economic systems. Considering the recent COVID-19 pandemic, we show how our method can be used as a viable tool for large-scale policy-making

The stochastic multi-path traveling salesman problem with dependent random travel costs.

The objective of the stochastic multi-path Traveling Salesman Problem is to determine the expected minimum-cost Hamiltonian tour in a network characterized by the presence of different paths between each pair of nodes, given that a random travel cost with an unknown probability distribution is associated with each of these paths. Previous works have proved that this problem can be deterministically approximated when the path travel costs are independent and identically distributed. Such an approximation has been demonstrated to be of acceptable quality in terms of the estimation of an optimal solution compared to consolidated approaches such as stochastic programming with recourse, completely overcoming the computational burden of solving enormous programs exacerbated by the number of scenarios considered. Nevertheless, the hypothesis regarding the independence among the path travel costs does not hold when considering real settings. It is well known, in fact, that traffic congestion influences travel costs and creates dependence among them. In this paper, we demonstrate that the independence assumption can be relaxed and a deterministic approximation of the stochastic multi-path Traveling Salesman Problem can be derived by assuming just asymptotically independent travel costs. We also demonstrate that this deterministic approximation has strong operational implications because it allows the consideration of realistic traffic models. Computational tests on extensive sets of random and realistic instances indicate the excellent efficiency and accuracy of the deterministic approximation

Stochastic single machine scheduling problem as a multi-stage dynamic random decision process

In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time

Mixing quantitative and qualitative methods for sustainable transportation in Smart Cities

L'abstract è presente nell'allegato / the abstract is in the attachmen