Large-scale Problem Instances Research Articles

Effect of replenishment and backroom on retail shelf-space planning

Shelf-space optimization models support retailers in making optimal shelf-space decisions. They determine the number of facings for each item included in an assortment. One common characteristic of these models is that they do not account for in-store replenishment processes. However, the two areas of shelf-space planning and in-store replenishment are strongly interrelated. Keeping more shelf stock of an item increases the demand for it due to higher visibility, permits decreased replenishment frequencies and increases inventory holding costs. However, because space is limited, it also requires the reduction of shelf space for other items, which then deplete faster and must be reordered and replenished more often. Furthermore, the possibility of keeping stock of certain items in the backroom instead of the showroom allows for more showroom shelf space for other items, but also generates additional replenishment costs for the items kept in the backroom. The joint optimization of both shelf-space decisions and replenishment processes has not been sufficiently addressed in the existing literature. To quantify the cost associated with the relevant in-store replenishment processes, we conducted a time and motion study for a German grocery retailer. Based on these insights, we propose an optimization model that addresses the mutual dependence of shelf-space decisions and replenishment processes. The model optimizes retail profits by determining the optimum number of facings, the optimum display orientation of items, and the optimum order frequencies, while accounting for space-elasticity effects as well as limited shelf and backroom space. Applying our model to the grocery retailer’s canned foods category, we found a profit potential of about 29%. We further apply our model to randomly generated data and show that it can be solved to optimality within very short run times, even for large-scale problem instances. Finally, we use the model to show the impact of backroom space availability and replenishment cost on retail profits and solution structures. Based on the insights gained from the application of our model, the grocery retailer has decided to change its current approach to shelf-space decisions and in-store replenishment planning.

Memetic algorithm with route decomposing for periodic capacitated arc routing problem

In this paper, the Periodic Capacitated Arc Routing Problem (PCARP) is investigated. PCARP is an extension of the well-known CARP from a single period to a multi-period horizon. In PCARP, two objectives are to be minimized. One is the number of required vehicles (nv), and the other is the total cost (tc). Due to the multi-period nature, given the same graph or road network, PCARP can have a much larger solution space than the single-period CARP counterpart. Furthermore, PCARP consists of an additional allocation sub-problem (of the days to serve the arcs), which is interdependent with the routing sub-problem. Although some attempts have been made for solving PCARP, more investigations are yet to be done to further improve their performance especially on large-scale problem instances. It has been shown that optimizing nv and tc separately (hierarchically) is a good way of dealing with the two objectives. In this paper, we further improve this strategy and propose a new Route Decomposition (RD) operator thereby. Then, the RD operator is integrated into a Memetic Algorithm (MA) framework for PCARP, in which novel crossover and local search operators are designed accordingly. In addition, to improve the search efficiency, a hybridized initialization is employed to generate an initial population consisting of both heuristic and random individuals. The MA with RD (MARD) was evaluated and compared with the state-of-the-art approaches on two benchmark sets of PCARP instances and a large data set which is based on a real-world road network. The experimental results suggest that MARD outperforms the compared state-of-the-art algorithms, and improves most of the best-known solutions. The advantage of MARD becomes more obvious when the problem size increases. Thus, MARD is particularly effective in solving large-scale PCARP instances. Moreover, the efficacy of the proposed RD operator in MARD has been empirically verified.

An efficient local search framework for the minimum weighted vertex cover problem

The minimum weighted vertex cover (MWVC) problem, an extension of the classical minimum vertex cover (MVC) problem, is an important NP-complete combinatorial optimization problem with a wide range of applications. The objective of this paper is to design an efficient local search algorithm to solve the MWVC problem. First, the weighted edge strategy is proposed to define the dynamic scoring strategy so that our algorithm can find different possible optimal solutions. Second, the weighted configuration checking (WCC) strategy is proposed to overcome the cycling problem in local search. By combining the WCC strategy with the scoring strategy, we design the vertex selection strategy to determine the vertex to be selected as a candidate solution component. Based on these strategies, a novel local search framework, namely diversion local search based on weighted configuration checking (DLSWCC), is presented. DLSWCC is evaluated against several state-of-the-art algorithms on various benchmark instances. Experimental results show that DLSWCC outperforms its competitors in terms of both solution quality and computational efficiency in most classical instances. Specifically, DLSWCC can obtain 22 new upper bounds of 71 moderate-scale problem instances, 5 new upper bounds of 15 large-scale problem instances, and 56 new upper bounds of 56 massive graph instances.

Quay crane scheduling problem with considering tidal impact and fuel consumption

This study investigates a quay crane scheduling problem with considering the impact of tides in a port and fuel consumption of ships. A mixed-integer nonlinear programming model is proposed. Some nonlinear parts in the model are linearized by approximation approaches. For solving the proposed model in large-scale problem instances, both a local branching based solution method and a particle swarm optimization based solution method are developed. Numerical experiments with some real-world like cases are conducted to validate the effectiveness of the proposed model and the efficiency of the proposed solution methods.

Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry

We study the Mean-SemiVariance Project (MSVP) portfolio selection problem, where the objective is to obtain the optimal risk-reward portfolio of non-divisible projects when the risk is measured by the semivariance of the portfolio׳s Net-Present Value (NPV) and the reward is measured by the portfolio׳s expected NPV. Similar to the well-known Mean-Variance portfolio selection problem, when integer variables are present (e.g., due to transaction costs, cardinality constraints, or asset illiquidity), the MSVP problem can be solved using Mixed-Integer Quadratic Programming (MIQP) techniques. However, conventional MIQP solvers may be unable to solve large-scale MSVP problem instances in a reasonable amount of time. In this paper, we propose two linear solution schemes to solve the MSVP problem; that is, the proposed schemes avoid the use of MIQP solvers and only require the use of Mixed-Integer Linear Programming (MILP) techniques. In particular, we show that the solution of a class of real-world MSVP problems, in which project returns are positively correlated, can be accurately approximated by solving a single MILP problem. In general, we show that the MSVP problem can be effectively solved by a sequence of MILP problems, which allow us to solve large-scale MSVP problem instances faster than using MIQP solvers. We illustrate our solution schemes by solving a real MSVP problem arising in a Latin American oil and gas company. Also, we solve instances of the MSVP problem that are constructed using data from the PSPLIB library of project scheduling problems.

A decomposition method for large scale MILPs, with performance guarantees and a power system application

Lagrangian duality in mixed integer optimization is a useful framework for problem decomposition and for producing tight lower bounds to the optimal objective. However, in contrast to the convex case, it is generally unable to produce optimal solutions directly. In fact, solutions recovered from the dual may not only be suboptimal, but even infeasible. In this paper we concentrate on large scale mixed-integer programs with a specific structure that appears in a variety of application domains such as power systems and supply chain management. We propose a solution method for these structures, in which the primal problem is modified in a certain way, guaranteeing that the solutions produced by the corresponding dual are feasible for the original unmodified primal problem. The modification is simple to implement and the method is amenable to distributed computation. We also demonstrate that the quality of the solutions recovered using our procedure improves as the problem size increases, making it particularly useful for large scale problem instances for which commercial solvers are inadequate. We illustrate the efficacy of our method with extensive experimentations on a problem stemming from power systems.

A learning and optimizing system for order acceptance and scheduling

Order acceptance and scheduling is an interesting scheduling problem when scheduling and acceptance decisions need to be handled simultaneously. The complexity of the problem causes difficulty for many solution methods. In this paper, we proposed a learning and optimizing system to deal with the order acceptance and scheduling problem with a single-machine and dependent setup times. The aim of this system is to combine the advantages of the hyper-heuristic for learning useful scheduling rules and the meta-heuristic for further refining the solutions from the obtained rules. The experiments show that the proposed system is very effective as compared to other heuristics proposed in the literature. The analyses also show the benefits of scheduling rules obtained by the hyper-heuristic, especially for large-scale problem instances.

Hybrid Symbiotic Organisms Search Algorithm for Solving 0-1 Knapsack Problem

We propose a new binary version of hybrid symbiotic organisms search algorithm based on harmony search with greedy strategy for solving 0-1 knapsack problems. A greedy strategy is employed to repair the infeasible solution and optimise the feasible solution. The experiments are carried out in small-scale and large-scale knapsack problem instances. We report on computational experiments which are compared with the results achieved with other state-of-the-art approaches. The results attest the performance of our approach.

Models on ship scheduling in transshipment hubs with considering bunker cost

This paper studies a decision problem for scheduling ships׳ starting operation time in a transshipment hub with considering the bunker cost and the transshipment cost of containers. Based on the information about the handing capacity of the container port in each period, the port operator makes a proper decision and informs the shipping companies about the start operation days of each liner route. The optimized decision may help shipping companies significantly reduce the cost. This study proposes a mixed integer programming model. The NP-hardness of the problem is proved. A local branching based solution method is also developed for solving the model. Extensive numerical experiments demonstrate the optimality of the solution by the proposed method is less than 3% for large-scale problem instances.

An efficient algorithm for capacitated assortment planning with stochastic demand and substitution

The ever increasing product variety in grocery retailing is in conflict with the limited shelf space. Managing the assortment and regular order quantity for perishable and non-perishable products is therefore a core task for retailers. Retailers want to maximize profit by considering potential revenues, purchase costs, diminishing profits for products and opportunity costs for unfulfilled demand when determining assortment sizes and order volume to meet stochastic consumer demand.We considered a newsvendor-based decision model that jointly optimizes assortment size and the associated order volumes for listed items. The model considers out-of-assortment (OOA) and out-of-stock (OOS) substitution effects. The model is a structural equivalent to the model described in Kök and Fisher (2007) and solved there via a heuristic procedure. We develop an optimal solution procedure and a time-efficient heuristic that solves the model. The heuristic suggested is applicable for practically relevant, large-scale problem instances. Numerical tests reveal that the heuristic procedure produces close-to-optimal solutions and outperforms the Kök and Fisher heuristic with regard to both computational time and solution quality. A simulation study with discrete demand justifies our approach with using continuous demand distributions. The numerical analyses show that considering substitution effects in a decision-based model has a significant impact on the total profit and solution structure. Further managerial insights are presented with regard to assortment heterogeneity when shelf size, substitution and demand variability are varied.

A two-agent single-machine scheduling problem with late work criteria

This paper addresses a two-agent scheduling problem where the objective is to minimize the total late work of the first agent, with the restriction that the maximum lateness of the second agent cannot exceed a given value. Two pseudo-polynomial dynamic programming algorithms are presented to find the optimal solutions for small-scale problem instances. For medium- to large-scale problem instances, a branch-and-bound algorithm incorporating the implementation of a lower bounding procedure, some dominance rules and a Tabu Search-based solution initialization, is developed to yield the optimal solution. Computational experiments are designed to examine the efficiency of the proposed algorithms and the impacts of all the relative parameters.

An incremental approach using local-search heuristic for inventory routing problem in industrial gases

In this paper we solve the inventory routing problem (IRP) occurring in industrial gas distribution where liquefied industrial gases are distributed to customers that have cryogenic tanks to store the gases on-site. We consider a multi-period inventory routing problem with multiple products assuming deterministic demand rates and the proposed model is formulated as a linear mixed-integer program. We propose an incremental approach based on decomposing the set of customers in the original problem into sub-problems. The smallest sub-problem consists of the customer that needs to be delivered most urgently along with a set of its neighbors. We solve each sub-problem with the number of customers growing successively by providing the solution of the previously solved sub-problem as an input. Each sub-problem is then solved with a randomized local-search heuristic method. We also propose an objective function that drives the local-search heuristics toward a long-term optimal solution. The main purpose of this paper is to develop a solution methodology appropriate for large-scale real-life problem instances particularly in industrial gas distribution.

A genetic algorithm-based decomposition approach to solve an integrated equipment-workforce-service planning problem

We develop a new genetic algorithm to solve an integrated Equipment-Workforce-Service Planning problem, which features extremely large scales and complex constraints. Compared with the canonical genetic algorithm, the new algorithm is innovative in four respects: (1) The new algorithm addresses epistasis of genes by decomposing the problem variables into evolutionary variables, which evolve with the genetic operators, and the optimization variables, which are derived by solving corresponding optimization problems. (2) The new algorithm introduces the concept of Capacity Threshold and calculates the Set of Efficient and Valid Equipment Assignments to preclude unpromising solution spaces, which allows the algorithm to search much narrowed but promising solution spaces in a more efficient way. (3) The new algorithm modifies the traditional genetic crossover and mutation operators to incorporate the gene dependency in the evolutionary procedure. (4) The new algorithm proposes a new genetic operator, self-evolution, to simulate the growth procedure of an individual in nature and use it for guided improvements of individuals. The new genetic algorithm design is proven very effective and robust in various numerical tests, compared to the integer programming algorithm and the canonical genetic algorithm. When the integer programming algorithm is unable to solve the large-scale problem instances or cannot provide good solutions in acceptable times, and the canonical genetic algorithm is incapable of handling the complex constraints of these instances, the new genetic algorithm obtains the optimal or close-to-optimal solutions within seconds for instances as large as 84 million integer variables and 82 thousand constraints.

A sample average approximation method for disassembly line balancing problem under uncertainty

This paper considers a Disassembly Line Balancing Problem (DLBP) under uncertainty. Disassembly task times are assumed to be random variables with known probability distributions. To deal with this uncertainty, a stochastic program is developed. It both chooses the best disassembly alternative for an end of life product and assigns the corresponding disassembly tasks to the workstations of the line with the aim to minimize the line cost. The latter includes the operation costs for workstations as well as penalty costs generated by the cycle time constraint violations. AND/OR precedence constraints among tasks are observed. A proposed solution algorithm is capable of providing high quality solutions even for large scale problem instances. It integrates Monte Carlo sampling techniques with the L-shaped algorithm.

Applying semi-synchronised task farming to large-scale computer vision problems

Distributed compute clusters allow the computing power of heterogeneous (and homogeneous) resources to be utilised to solve large-scale science and engineering problems. One class of problem that has attractive scalability properties, and is therefore often implemented using compute clusters, is task farming (or parameter sweep) applications. A typical characteristic of such applications is that no communication is needed between distributed subtasks during the overall computation. However, interesting large-scale task farming problem instances that do require global communication between subtask sets also exist. We propose a framework called semi-synchronised task farming in order to address problems requiring distributed formulations containing subtasks that alternate between independence and synchronisation. We apply this framework to several large-scale contemporary computer vision problems and present a detailed performance analysis to demonstrate framework scalability. Semi-synchronised task farming splits a given problem into a number of stages. Each stage involves firstly distributing independent subtasks to be completed in parallel. Following subtask set completion, a set of synchronised global decisions, based on information retrieved from the distributed results, is made. The results influence the following subtask distribution stage. This subtask distribution followed by result collation process is iterated until overall problem solutions are obtained. We construct a simplified Bulk Synchronous Parallel (BSP) model to formalise this framework and with this formalisation, we develop a predictive model for overall task completion time. We present experimental benchmark results comparing the performance observed by applying our framework to solve real-world problems on compute clusters with that of solving the tasks in a serial fashion. Furthermore by assessing the predicted time savings that our framework provides in simulation and validating these predictions on a range of complex problems drawn from real-world computer vision tasks, we are able to reliably predict the performance gain obtained when using a compute cluster to tackle resource intensive computer vision tasks.

A mixed integer linear programming model and variable neighborhood search for Maximally Balanced Connected Partition Problem

This paper deals with Maximally Balanced Connected Partition (MBCP) problem. It introduces a mixed integer linear programming (MILP) formulation of the problem with polynomial number of variables and constraints. Also, a variable neighborhood search (VNS) technique for solving this problem is presented. The VNS implements the suitable neighborhoods based on changing the component for an increasing number of vertices. An efficient implementation of the local search procedure yields a relatively short running time. The numerical experiments are made on instances known in the literature. Based on the MILP model, tests are run using two MILP solvers, CPLEX and Gurobi. It is shown that both solvers succeed in finding optimal solutions for all smaller and most of medium scale instances. Proposed VNS reaches most of the optimal solutions. The algorithm is also successfully tested on large scale problem instances for which optimal solutions are not known.

Electric Vehicle Routing Problem with Industry Constraints: Trends and Insights for Future Research

This paper presents and analyzes the one-to-many vehicle routing and scheduling problem with electric vehicles. Initially, focus is given on the problem formulation and the restrictions imposed in practice are examined. EVRP is NP-hard in the strong sense since it is natural extension of the well-known Capacitated Vehicle Routing Problem and requires substantial computational effort for determining optimal or near optimal solutions for medium and large scale problem instances. A comprehensive mathematical formulation is developed in order to model the EVRP and the multiple constraints appeared due to capacity limitations, time window restrictions and the predefined charging level of the vehicles. In addition, recent trends for the EVRP are analyzed producing valuable insights for future research regarding extra operational constraints, real-life data sets and solution frameworks that embody approximation algorithms for an efficient and effective search of the solution space.

Selecting Large Portfolios of Social Projects in Public Organizations

We address the portfolio selection of social projects in public organizations considering interdependencies (synergies) affecting project funds requirements and tasks. A mixed integer linear programming model is proposed incorporating the most relevant aspects of the problem found in the literature. The model supports both complete (all or nothing) and partial (a certain amount from a given interval of funding) resource allocation policies. Numerical results for large-scale problem instances are presented.

An arc-exchange decomposition method for multistage dynamic networks with random arc capacities

Multistage dynamic networks with random arc capacities (MDNRAC) have been successfully used for modeling various resource allocation problems in the transportation area. However, solving these problems is generally computationally intensive, and there is still a need to develop more efficient solution approaches. In this paper, we propose a new heuristic approach that solves the MDNRAC problem by decomposing the network at each stage into a series of subproblems with tree structures. Each subproblem can be solved efficiently. The main advantage is that this approach provides an efficient computational device to handle the large-scale problem instances with fairly good solution quality. We show that the objective value obtained from this decomposition approach is an upper bound for that of the MDNRAC problem. Numerical results demonstrate that our proposed approach works very well.

Balancing transfer lines using Benders decomposition and ant colony optimisation techniques

In this paper, we investigate a transfer line balancing problem in order to find the line configuration that minimises the non-productive time. The problem is defined at an auto manufacturing company where the cylinder head is manufactured. Technological restrictions among design features and manufacturing operations are taken into consideration. The problem is represented by an integer programming model that assigns design features and cutting tools to machining stations, and specifies the number of machines and production sequence in each station. Three algorithms are developed to efficiently solve the problem under study. The first algorithm uses Benders decomposition approach that decomposes the proposed model into an assignment problem and a sequencing problem. The second algorithm is a hybrid algorithm that mixes Benders decomposition approach with the ant colony optimisation technique. The third algorithm solves the problem using two nested ant colonies. Using 15 different problem dimensions, we compare results of the three algorithms in a computational study. The first algorithm finds optimal solutions of small problem instances only. Second and third algorithms demonstrate optimality gaps less than 4.04 and 3.8%, respectively, when compared to the optimal results given by the first algorithm. Moreover, the second and third algorithms are very promising in solving medium and large-scale problem instances.