Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time

A Branch-and-Cut based Pricer for the Capacitated Vehicle Routing Problem

openIl Capacitated Vehicle Routing Problem, abbreviato come CVRP, è un problema di ottimizzazione combinatoria d'instradamento nel quale, un insieme geograficamente sparso di clienti con richieste note deve essere servito da una flotta di veicoli stazionati in una struttura centrale. Negli ultimi due decenni, tecniche di Column generation incorporate all'interno di frameworks branch-price-and-cut sono state infatti l'approccio stato dell'arte dominante per la costruzione di algoritmi esatti per il CVRP. Il pricer, un componente critico nella column generation, deve risolvere il Pricing Problem (PP) che richiede la risoluzione di un Elementary Shortest Path Problem with Resource Constraints (ESPPRC) in una rete di costo ridotto. Pochi sforzi scientifici sono stati dedicati allo studio di approcci branch-and-cut per affrontare il PP. L'ESPPRC è stato tradizionalmente rilassato e risolto attraverso algoritmi di programmazione dinamica. Questo approccio, tuttavia, ha due principali svantaggi. Per cominciare, peggiora i dual bounds ottenuti. Inoltre, il tempo di esecuzione diminuisce all'aumentare della lunghezza dei percorsi generati. Per valutare la performance dei loro contributi, la comunità di ricerca operativa ha tradizionalmente utilizzato una serie d'istanze di test storiche e artificiali. Tuttavia, queste istanze di benchmark non catturano le caratteristiche chiave dei moderni problemi di distribuzione del mondo reale, che sono tipicamente caratterizzati da lunghi percorsi. In questa tesi sviluppiamo uno schema basato su un approccio branch-and-cut per risolvere il pricing problem. Studiamo il comportamento e l'efficacia della nostra implementazione nel produrre percorsi più lunghi comparandola con soluzioni all'avanguardia basate su programmazione dinamica. I nostri risultati suggeriscono che gli approcci branch-and-cut possono supplementare il tradizionale algoritmo di etichettatura, indicando che ulteriore ricerca in quest'area possa portare benefici ai risolutori CVRP.The Capacitated Vehicle Routing Problem, CVRP for short, is a combinatorial optimization routing problem in which, a geographically dispersed set of customers with known demands must be served by a fleet of vehicles stationed at a central facility. Column generation techniques embedded within branch-price-and-cut frameworks have been the de facto state-of-the-art dominant approach for building exact algorithms for the CVRP over the last two decades. The pricer, a critical component in column generation, must solve the Pricing Problem (PP), which asks for an Elementary Shortest Path Problem with Resource Constraints (ESPPRC) in a reduced-cost network. Little scientific efforts have been dedicated to studying branch-and-cut based approaches for tackling the PP. The ESPPRC has been traditionally relaxed and solved through dynamic programming algorithms. This approach, however, has two major drawbacks. For starters, it worsens the obtained dual bounds. Furthermore, the running time degrades as the length of the generated routes increases. To evaluate the performance of their contributions, the operations research community has traditionally used a set of historical and artificial test instances. However, these benchmark instances do not capture the key characteristics of modern real-world distribution problems, which are usually characterized by longer routes. In this thesis, we develop a scheme based on a branch-and-cut approach for solving the pricing problem. We study the behavior and effectiveness of our implementation in producing longer routes by comparing it with state-of-the-art solutions based on dynamic programming. Our results suggest that branch-and-cut approaches may supplement the traditional labeling algorithm, indicating that further research in this area may bring benefits to CVRP solvers

A dynamic programming approach to multi-objective time-dependent capacitated single vehicle routing problems with time windows

A single vehicle performs several tours to serve a set of geographically dis- persed customers. The vehicle has a finite capacity and is only available for a limited amount of time. Moreover, tours' duration is restricted (e.g. due to quality or security issues). Because of road congestion, travel times are time-dependent: depending on the departure time at a customer, a different travel time is incurred. Furthermore, all customers need to get delivered in their specicified time windows. Contrary to most of the literature, we con- sider a multi-objective cost function: simultaneously minimizing the total time traveled including waiting times at customers due to time windows, and maximizing the total demand fulfilled. Efficient dynamic programming algorithms are developed to compute the Pareto set of routes, assuming a specific structure for time windows and travel time profiles

Physiology-Aware Rural Ambulance Routing

In emergency patient transport from rural medical facility to center tertiary hospital, real-time monitoring of the patient in the ambulance by a physician expert at the tertiary center is crucial. While telemetry healthcare services using mobile networks may enable remote real-time monitoring of transported patients, physiologic measures and tracking are at least as important and requires the existence of high-fidelity communication coverage. However, the wireless networks along the roads especially in rural areas can range from 4G to low-speed 2G, some parts with communication breakage. From a patient care perspective, transport during critical illness can make route selection patient state dependent. Prompt decisions with the relative advantage of a longer more secure bandwidth route versus a shorter, more rapid transport route but with less secure bandwidth must be made. The trade-off between route selection and the quality of wireless communication is an important optimization problem which unfortunately has remained unaddressed by prior work. In this paper, we propose a novel physiology-aware route scheduling approach for emergency ambulance transport of rural patients with acute, high risk diseases in need of continuous remote monitoring. We mathematically model the problem into an NP-hard graph theory problem, and approximate a solution based on a trade-off between communication coverage and shortest path. We profile communication along two major routes in a large rural hospital settings in Illinois, and use the traces to manifest the concept. Further, we design our algorithms and run preliminary experiments for scalability analysis. We believe that our scheduling techniques can become a compelling aid that enables an always-connected remote monitoring system in emergency patient transfer scenarios aimed to prevent morbidity and mortality with early diagnosis treatment.Comment: 6 pages, The Fifth IEEE International Conference on Healthcare Informatics (ICHI 2017), Park City, Utah, 201

Approximating multi-objective time-dependent optimization problems

In many practical situations, decisions are multi-objective in nature. Furthermore, costs and profits are time-dependent, i.e. depending upon the time a decision is taken, different costs and profits are incurred. In this paper, we propose a generic approach to deal with multi-objective time-dependent optimization problems (MOTDP). The aim is to determine the set of Pareto solutions that capture the interactions between the different objectives. Due, to the complexity of MOTDP, an efficient approximation based on dynamic programming is developed. The approximation has a provable worst case performance guarantee. Even though the approximate Pareto set consists of less solutions, it represents a good coverage of the true set of Pareto solutions. Numerical results are presented showing the value of the approximation

Paints supply chain optimisation

Imperial Users onl

Quantum annealing for vehicle routing and scheduling problems

Metaheuristic approaches to solving combinatorial optimization problems have many attractions. They sidestep the issue of combinatorial explosion; they return good results; they are often conceptually simple and straight forward to implement. There are also shortcomings. Optimal solutions are not guaranteed; choosing the metaheuristic which best fits a problem is a matter of experimentation; and conceptual differences between metaheuristics make absolute comparisons of performance difficult. There is also the difficulty of configuration of the algorithm - the process of identifying precise values for the parameters which control the optimization process. Quantum annealing is a metaheuristic which is the quantum counterpart of the well known classical Simulated Annealing algorithm for combinatorial optimization problems. This research investigates the application of quantum annealing to the Vehicle Routing Problem, a difficult problem of practical significance within industries such as logistics and workforce scheduling. The work devises spin encoding schemes for routing and scheduling problem domains, enabling an effective quantum annealing algorithm which locates new solutions to widely used benchmarks. The performance of the metaheuristic is further improved by the development of an enhanced tuning approach using fitness clouds as behaviour models. The algorithm is shown to be further enhanced by taking advantage of multiprocessor environments, using threading techniques to parallelize the optimization workload. The work also shows quantum annealing applied successfully in an industrial setting to generate solutions to complex scheduling problems, results which created extra savings over an incumbent optimization technique. Components of the intellectual property rendered in this latter effort went on to secure a patent-protected status

Bulk wheat transportation and storage problem of public distribution system

This research investigates the multi-period multi-modal bulk wheat transportation and storage problem in a two-stage supply chain network of Public Distribution System (PDS). The bulk transportation and storage can significantly curtail the transit and storage losses of food grains, which leads to substantial cost savings. A mixed integer non-linear programming model (MINLP) is developed after studying the Indian wheat supply chain scenario, where the objective is to minimize the transportation, storage and operational cost of the food grain incurred for efficient transfer of wheat from producing states to consuming states. The cost minimization of Indian food grain supply chain is a very complex and challenging problem because of the involvement of the many entities and their constraints such as seasonal procurement, limited scientific storages, varying demand, mode of transportation and vehicle capacity constraints. To address this complex and challenging problem of food grain supply chain, we have proposed the novel variant of Chemical Reaction Optimization (CRO) algorithm which combines the features of CRO and Tabu search (TS) and named it as a hybrid CROTS algorithm (Chemical reaction optimization combined with Tabu Search). The numerous problems with different sizes are solved using the proposed algorithm and obtained results have been compared with CRO. The comparative study reveals that the proposed CROTS algorithm offers a better solution in less computational time than CRO algorithm and the dominance of CROTS algorithm over the CRO algorithm is demonstrated through statistical analysis