A heuristic approach for big bucket multi-level production planning problems

Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems

An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions

Airline planning benchmark problems—Part II : passenger groups, utility and demand allocation

This paper is the second of two papers entitled “Airline Planning Benchmark Problems”, aimed at developing benchmark data that can be used to stimulate innovation in airline planning, in particular, in flight schedule design and fleet assignment. The former has, to date, been under-represented in the optimisation literature, due in part to the difficulty of obtaining data that adequately reflects passenger choice, and hence schedule revenue. Revenue models in airline planning optimisation only roughly approximate the passenger decision process. However, there is a growing body of literature giving empirical insights into airline passenger choice. Here we propose a new paradigm for passenger modelling, that enriches our representation of passenger revenue, in a form designed to be useful for optimisation. We divide the market demand into market segments, or passenger groups, according to characteristics that differentiate behaviour in terms of airline product selection. Each passenger group has an origin, destination, size (number of passengers), departure time window, and departure time utility curve, indicating willingness to pay for departure in time sub-windows. Taking as input market demand for each origin–destination pair, we describe a process by which we construct realistic passenger group data, based on the analysis of empirical airline data collected by our industry partner. We give the results of that analysis, and describe 33 benchmark instances produced

A theoretical study of two-period relaxations for lot-sizing problems with big-bucket capacities

In this paper, we study two-period subproblems proposed by Akartunali et al. (2015) for lot-sizing problems with big-bucket capacities and nonzero setup times, complementing our previous work investigating the special case of zero setup times. In particular, we study the polyhedral structure of the mixed integer sets related to various two-period relaxations. We derive several families of valid inequalities and investigate their facet-defining conditions. We also discuss the separation problems associated with these valid inequalities

Network models and biproportional rounding for fair seat allocations in the UK elections

Systems for allocating seats in an election offer a number of socially and mathematically interesting problems. We discuss how to model the allocation process as a network flow problem, and propose a wide choice of objective functions and allocation schemes. Biproportional rounding, which is an instance of the network flow problem, is used in some European countries with multi-seat constituencies. We discuss its application to single seat constituencies and the inevitable consequence that seats are allocated to candidates with little local support. However, we show that variants can be selected, such as regional apportionment, to mitigate this problem. In particular, we introduce a parameter based family of methods, which we call Balanced Majority Voting, that can be tuned to meet the public's demand for local and global ``fairness''. Using data from the 2010 and 2015 UK General Elections, we study a variety of network models and implementations of biproportional rounding, and address conditions of existence and uniqueness

A hybrid constraint integer programming approach to solve nurse scheduling problems

The Nurse Scheduling Problem can be simply defined as assigning a series of shift sequences (schedules) to several nurses over a planning horizon according to some constraints and preferences. The inherent benefits of having higher-quality and more flexible schedules are a reduction in outsourcing costs and an increase of job satisfaction in health organizations. In this paper, we present a novel systematic hybrid algorithm, which combines Integer Programming (IP) and Constraint Programming (CP) to efficiently solve highly-constrained Nurse Scheduling Problems. Our focus is to exploit the problem-specific information to improve the performance of the algorithm, and therefore obtain high-quality solutions as well as strong lower bounds. We test our algorithm based on some real-world benchmark instances. Very competitive results are reported compared to the state-of-the-art algorithms from the recent literature, showing that the proposed algorithm is able to solve a wide variety of real-world instances with different complex structures

Cost-effectiveness of a nurse-led ORIF ankle care programme

In response to current outdated models of outpatient fracture care, a nurse-led ankle care protocol was implemented by Glasgow Royal Infirmary’s (GRI) fracture clinic. Its aim was to standardise post- surgery care for Open Reduction Internal Fixation (ORIF) ankle fractures, while maintaining patient reported outcomes. The demand for evaluation across healthcare in the UK is exponentially increasing and although the protocol has been widely accepted throughout the clinic, no evidence existed to confirm its cost-effectiveness. This study fills that gap in knowledge through a thorough cost-evaluation using Discrete Event Simulation (DES), a widely recognised and powerful modelling tool within healthcare evaluation. It was found that the difference between the total number of appointments attended patients between the two groups was not significant (p>0.05). However, results of the cost-modelling clearly show that a 28.12% saving can be achieved when comparing total staffing costs and X-ray costs between the two groups

A Computational Analysis of Lower Bounds for Big Bucket Production Planning Problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multilevel production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provides valuable insights on why these problems are hard to solve. We conclude with computational results from widely used test sets and discussion of future research

A hybrid integer programming and variable neighborhood search algorithm to solve Nurse Rostering Problems

The Nurse Rostering Problem (NRP) is defined as assigning a number of nurses to different shifts during a specified planning period, considering some regulations and preferences. This is often very difficult to solve in practice particularly by applying a sole approach. In this paper, we propose a novel hybrid algorithm combining the strengths of Integer Programming (IP) and Variable Neighbourhood Search (VNS) algorithms to design a hybrid method for solving the NRP. After generating the initial solution using a greedy heuristic, the solution is further improved by employing a Variable Neighbourhood Descent algorithm. Then IP, deeply embedded in the VNS algorithm, is employed within a ruin-and-recreate framework to assist the search process. Finally, IP is called again to further refine the solution during the remaining time. We utilize the strength of IP not only to diversify the search process, but also to intensify the search efforts. To identify the quality of the current solution, we use a new generic scoring scheme to mark the low-penalty parts of the solution. Based on the computational tests with 24 instances recently introduced in the literature, we obtain better results with our proposed algorithm, where the hybrid algorithm outperforms two state-of-the-art algorithms and Gurobi in most of the instances. Furthermore, we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm, and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes

A hybrid integer and constraint programming approach to solve nurse rostering problems

The Nurse Rostering Problem can be defined as assigning a series of shift sequences (schedules) to several nurses over a planning horizon according to some limitations and preferences. The inherent benefits of generating higher-quality schedules are a reduction in outsourcing costs and an increase in job satisfaction of employees. In this paper, we present a hybrid algorithm, which combines Integer Programming and Constraint Programming to efficiently solve the highly-constrained Nurse Rostering Problem. We exploit the strength of IP in obtaining lower-bounds and finding an optimal solution with the capability of CP in finding feasible solutions in a co-operative manner. To improve the performance of the algorithm, and therefore, to obtain high-quality solutions as well as strong lower-bounds for a relatively short time, we apply some innovative ways to extract useful information such as the computational difficulty of in- stances and constraints to adaptively set the search parameters. We test our algorithm using two different datasets consisting of various problem instances, and report competitive results benchmarked with the state-of-the-art algorithms from the recent literature as well as standard IP and CP solvers, showing that the proposed algorithm is able to solve a wide variety of instances effectively