Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by an interval instead of a fixed value. We show that the introduction of flexible cargo sizes to the column generation framework is not straightforward, and we handle the flexible cargo sizes heuristically when solving the subproblems. This leads to convergence issues in the branch-and-price search tree, and the optimal solution cannot be guaranteed. Hence we have introduced a method that generates an upper bound on the optimal objective. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that the Dantzig-Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimalityTransportation; integer programming; dynamic programming

A branch and price approach for deployment of multi-tier software services in clouds

This paper considers a service deployment problem that combines service placement and replication level decisions in a cloud computing context. The services are composed of multiple components that are to be placed on nodes in the private cloud of the service provider or, if the private cloud has limited capacity, partly in a public cloud. In the service delivery, the provider has to take into account the quality of service guarantees offered to his end-users. To solve the problem, we develop a branch and price algorithm, where the subproblems both are formulated as a linear mixed integer program and a shortest path problem with resource constraints (SPPRC) on a network with a special structure. The SPPRC can be solved by an exact label-setting algorithm, but to speed up the solution process, we develop a heuristic label-setting algorithm based on a reduced network and simplified dominance rule. Our results show that using the heuristic subproblem solver is efficient. Furthermore, the branch and price algorithm performs better than a previously developed pre-generation algorithm for the same problem. In addition, we analyze and discuss the differences in solutions that utilize resources in a public cloud to different degrees. By conducting this analysis we are able to identify some essential characteristics of good solutions

Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by intervals instead of by fixed values. The flexible cargo sizes have consequences for the times used in the ports because both the loading and unloading times depend on the cargo sizes. We found it computationally hard to find exact solutions to the subproblems, so our method does not guarantee to find the optimum over all solutions. To be able to say something about how good our solution is, we generate a bound on the difference between the true optimal objective and the objective in our solution. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that our Dantzig-Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimality.Transportation Integer programming Dynamic programming

Nested Column Generation applied to the Crude Oil Tanker Routing and Scheduling Problem with Split Pickup and Split Delivery

The split pickup split delivery crude oil tanker routing and scheduling problem is a difficult combinatorial optimization problem, both theoretically and practically. However, because of the large expenses in crude oil shipping it is attractive to make use of optimization that exploits as many degrees of freedom as possible to save transportation cost. We propose a nested column generation algorithm for this particular split pickup split delivery problem which bears several complexities such as a heterogeneous fleet, multiple commodities, many-to-many relations for pickup and delivery of each commodity, sequence dependent vehicle capacities, and cargo quantity dependent pickup and delivery times. Our approach builds on a branch-and-price algorithm in which the column generation subproblems are solved by branch-and-price themselves. We describe our implementation in the branch-cut-and-price framework SCIP and give computational results for realistic test instances. The high quality schedules we obtain for these instances improve on those in previous studies. Key words: Maritime transportation; crude oil; split pickup; split delivery; routing and scheduling; branch-and-price; nested column generatio

Compression and expansion at the right pinch temperature

Heat Integration is extended to the topic of Heat and Work Integration when pressure changing equipment such as compressors and expanders are included in heat exchanger network design. The latter topic is much more complex since heat and work have different energy qualities (exergy). Systematic graphical design methodologies have recently been developed for heat and work integration. The methodologies are based on a set of theorems that have been proven based on thermodynamic and mathematical analyses. The theorems show that minimum exergy consumption can be achieved in many cases when compression/expansion starts at the pinch temperature (Pinch Compression/Expansion). The Grand Composite Curve has been used to determine the maximum portions of streams using Pinch Compression/Expansion. However, the pinch temperatures for hot streams (hot pinch) and cold streams (cold Pinch) are different. They were not well distinguished in previous studies. Based on a recent mathematical optimisation study by the authors on the topic of heat and work integration, it is concluded that the pinch identity (hot or cold) should be the same as the identity of the stream at the inlet of compression/expansion. This paper introduces the new insight with an illustrative example. The insight is then verified by thermodynamic and mathematical analyses of various cases. A simple application of the insight to the self-heat recuperation scheme is investigated. An alternative scheme has been proposed. The total work consumption is reduced by 17.7 % in a thermal process with butane. The new insight is an important addition to the methodologies for heat and work integration that are established in previous studies

Compression and Expansion at the Right Pinch Temperature

Heat Integration is extended to the topic of Heat and Work Integration when pressure changing equipment such as compressors and expanders are included in heat exchanger network design. The latter topic is much more complex since heat and work have different energy qualities (exergy). Systematic graphical design methodologies have recently been developed for heat and work integration. The methodologies are based on a set of theorems that have been proven based on thermodynamic and mathematical analyses. The theorems show that minimum exergy consumption can be achieved in many cases when compression/expansion starts at the pinch temperature (Pinch Compression/Expansion). The Grand Composite Curve has been used to determine the maximum portions of streams using Pinch Compression/Expansion. However, the pinch temperatures for hot streams (hot pinch) and cold streams (cold Pinch) are different. They were not well distinguished in previous studies. Based on a recent mathematical optimisation study by the authors on the topic of heat and work integration, it is concluded that the pinch identity (hot or cold) should be the same as the identity of the stream at the inlet of compression/expansion. This paper introduces the new insight with an illustrative example. The insight is then verified by thermodynamic and mathematical analyses of various cases. A simple application of the insight to the self-heat recuperation scheme is investigated. An alternative scheme has been proposed. The total work consumption is reduced by 17.7 % in a thermal process with butane. The new insight is an important addition to the methodologies for heat and work integration that are established in previous studies. Copyright © 2017, AIDIC Servizi S.r.l.

Simulation of the response time distribution of fault-tolerant multi-tier cloud services

We are considering the problem of obtaining the response time distribution of fault-tolerant multi-tier services. In the provision of software-as-a-service applications, the service provider is obliged to ensure a certain quality of service. Herein, we regard upper bounds on the response time. The services consist of multiple components with different functionality, which are prone to failures, and fail according to a certain failure time distribution. However, due to redundancy, a failure will not necessarily bring the service down, but rather increase the response time. A fundamental difficulty with estimating the response time distribution while considering failures is related to the disparity in the time scales of the time between failures and service times. To overcome this issue, we propose an approach based on a decomposition, which combines an analytic model of the failure process and a discrete event simulation model to sample the response time distribution. In an experimental study, we compare this simulation-based approach with an analytic approach, and illustrate how this approach can be utilised by service providers as decision support. We also show that in certain cases, the analytic approach might provide a safe bound on the response time

Adaptive large neighborhood search heuristics for multi-tier service deployment problems in clouds

This paper proposes adaptive large neighborhood search (ALNS) heuristics for two service deployment problems in a cloud computing context. The problems under study consider the deployment problem of a provider of softwareas- a-service applications, and include decisions related to the replication and placement of the provided services. A novel feature of the proposed algorithms is a local search layer on top of the destroy and repair operators. In addition, we use a mixed integer programming-based repair operator in conjunction with other faster heuristic operators. Because of the di erent time consumption of the repair operators, we need to account for the time usage in the scoring mechanism of the adaptive operator selection. The computational study investigates the benefits of implementing a local search operator on top of the standard ALNS framework. Moreover, we also compare the proposed algorithms with a branch and price (B&P) approach previously developed for the same problems. The results of our experiments show that the benefits of the local search operators increase with the problem size. We also observe that the ALNS with the local search operators outperforms the B&P on larger problems, but it is also comparable with the B&P on smaller problems with a short run time

Block scheduling at magnetic resonance imaging labs

This paper considers a tactical block scheduling problem at a major Norwegian hospital. Here, specific patient groups are reserved time blocks for scanning at a heterogeneous set of Magnetic Resonance Imaging (MRI) labs. The time blocks consist of several time slots, and one or more patients from the same group are scanned in a block. A total weekly number of time slots for each specific patient group is given through demand forecast and negotiations, and several restrictions apply to the allocation of time blocks. Only part of the week is allocated to blocks for the specific patient groups. The rest is classified as open time. Thus, the MRI block scheduling problem consists of finding a cyclic weekly plan where one or more time blocks are to be allocated to each specific patient group, by deciding the day, start time and length, to minimise unfavourable patient group allocations, as well as allocations of open time. For the problem, we propose an integer programming model with an objective function that combines penalties for allocating time blocks to patient groups at unfavourable time slots and labs, and rewards for advantageous positioning of open time slots. The aim of the optimisation model is to facilitate the coordination of the MRI resources between the hospital departments, that are responsible for the specific patient groups, to achieve a fair distribution of time slots to the specific patient groups and open time blocks. The computational study is based on the real problem as well as artificially generated instances. Real-sized instances for our case hospital can be solved in short time. We illustrate how the model can be used to produce Pareto optimal solutions, and how these solutions can provide the decision makers with managerial insight