Exact Solution Algorithm Research Articles

Optimal decision-making for a single-stage manufacturing system with rework options

ABSTRACTThis study investigates a manufacturing system with a single-stage production system that sometimes produces imperfect items. In this system, we assume that the rework process can start after the regular production process (immediate rework) or when the inventory of perfect goods is equal to zero (delayed rework). Also, we assumed non-zero set-up time for rework. Two models are presented for manufacturing systems with re-workable goods. The first model deals with non-zero set-up time for immediate rework and the second model deals with non-zero set-up times for delayed rework. We also investigate special cases associated with these models wherein the set-up times are zero. A general and aggregated model that included those two models is considered. The novelty of this research lies in selecting for a decision-maker the best approach based on system conditions and solutions. This paper provides a framework for rework policies to minimise the total cost of the system, which includes the cost of manufacturing cost, set-up cost for rework and regular production, holding cost for perfect and imperfect items, and the cost of rework. Finally, we solve the aggregated model by using an exact solution algorithm, and the optimal value of production in each period is obtained.

Integrated production, inventory, and batch delivery scheduling with due date assignment and two competing agents

AbstractThis paper considers several integrated production, inventory, and batch delivery scheduling problems on a single machine with due date assignment and two competing agents, each of which seeks to optimize its own performance. All the jobs of the first agent have a common due date, which is a decision variable to be determined by the decision maker, whereas the due dates of the jobs of the second agent are exogenously given. The jobs of the same agent are processed sequentially in batches and the batch processing time is equal to the total processing time of the jobs in the batch, where the batch size can be either bounded or unbounded. A batch is available only when all the jobs in it are completed. An available batch is delivered to its agent immediately, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. Finished jobs are kept in inventory, if necessary, incurring an additional holding cost. The first agent wishes to find a job sequence, a common due date, and a dispatch date for each of its jobs that jointly minimize the total cost comprising the earliness, weighted number of tardy jobs, job holding, due date assignment, and batch delivery costs, while the second agent seeks to minimize one of the following criteria plus the batch delivery cost: the maximum value of a regular scheduling criterion, total completion time, and weighted number of tardy jobs. The overall objective is to minimize the objective value of the first agent, subject to the objective value of the second agent not exceeding a given threshold. For each of the problems considered, we study its computational complexity and develop exact and/or approximation solution algorithms.

A hybrid recourse policy for the vehicle routing problem with stochastic demands

In this paper, we propose a new recourse policy for the vehicle routing problem with stochastic demands (VRPSD). In this routing problem, customer demands are characterized by known probability distributions. The actual demand values are only revealed upon arriving at a customer location. The objective of the problem is to plan routes minimizing the travel cost and the expect recourse cost. The latter cost is a result of a predetermined recourse policy designed to handle route failures. Given the planned routes, such failures may occur in the event where a vehicle has insufficient capacity to serve the current customer or the next customer. In the relevant literature, there are three types of recourse policies: (i) classical, where failures at customers are handled by return trips to the depot, (ii) optimal restocking, where preventive restocking trips to the depot are performed based on optimized customer-specific thresholds, and failures are handled by return trips to the depot, and (iii) rule-based policies, where preventive restocking trips are performed based on thresholds established by preset rules, and failures are handled by performing return trips to the depot. While the first type is rather myopic, the last two types of recourse policies use simplistic comparisons of the vehicle’s residual capacity to trigger recourse actions. In this paper, we propose a more advanced rule-based recourse policy, which does not solely depend on the vehicle’s residual capacity. To do so, we first propose a taxonomy that groups rule-based policies into three classes, we then propose the first hybrid recourse policy, which simultaneously combines two of these classes, namely risk and distance. We develop an exact solution algorithm for the VRPSD with this hybrid recourse policy and conduct a broad range of computational experiments. The algorithm is able to solve instances with up to 60 customers, and for certain experimental configurations, the exact algorithm solves to optimality up to 79% of the instances. Finally, we show that when the optimal routes of the hybrid policy are operated under the optimal restocking policy they yield a marginal average cost difference.

A Branch & Price algorithm for the minimum cost clique cover problem in max-point tolerance graphs

A point-interval $$(I_v, p_v)$$ is a pair constituted by an interval $$I_v$$ of $${\mathbb {R}}$$ and a point $$p_v \in I_v$$ . A graph $$G=(V,E)$$ is a Max-Point-Tolerance (MPT) graph if each vertex $$v\in V$$ can be mapped to a point-interval in such a way that (u, v) is an edge of G iff $$I_u \cap I_v \supseteq \{p_u, p_v\}$$ . MPT graphs constitute a superclass of interval graphs and naturally arise in genetic analysis as a way to represent specific relationships among DNA fragments extracted from a population of individuals. One of the most important applications of MPT graphs concerns the search for an association between major human diseases and chromosome regions from patients that exhibit loss of heterozygosity events. This task can be formulated as a minimum cost clique cover problem in a MPT graph and gives rise to a $${{\mathcal {N}}}{{\mathcal {P}}}$$ -hard combinatorial optimization problem known in the literature as the Parsimonious Loss of Heterozygosity Problem (PLOHP). In this article, we investigate ways to speed up the best known exact solution algorithm for the PLOHP as well as techniques to enlarge the size of the instances that can be optimally solved. In particular, we present a Branch&Price algorithm for the PLOHP and we develop a number of preprocessing techniques and decomposition strategies to dramatically reduce the size of its instances. Computational experiments show that the proposed approach is 10–30 $$\times $$ faster than previous approaches described in the literature, and suggest new directions for the development of future exact solution approaches that may prove of fundamental assistance in practice.

Viable Algorithmic Options for Designing Reactive Robot Swarms

A central problem in swarm robotics is to design a controller that will allow the member robots of the swarm to collectively perform a given task. Of particular interest in massively distributed applications are reactive controllers with severely limited computational and sensory abilities. In this article, we give the results of the first computational complexity analysis of the reactive swarm design problem. Our core results are derived relative to a generalization of what is arguably the simplest possible type of reactive controller, the so-called computation-free controller proposed by Gauci et al., which operates in grid-based environments in a noncontinuous manner. We show that the design of a generalized computation-free swarm for an arbitrary given task in an arbitrary given environment is not polynomial-time solvable either in general or by the most desirable types of approximation algorithms (including evolutionary algorithms with high probabilities of producing correct solutions) but is solvable in effectively polynomial time relative to several types of restrictions on swarms, environments, and tasks. All of our results hold for the design of several more complex types of generalized computation-free swarms. Moreover, all of our intractability and inapproximability results hold for the design of any type of reactive swarm (including those based on the popular feed-forward neural network and Brooks-style subsumption controllers) operating in grid-based environments in a noncontinuous manner whose member robots satisfy two simple conditions. As such, our results give the first theoretical survey of the types of efficient exact and approximate solution algorithms that are and are not possible for designing several types of reactive swarms.

Robust optimization approaches for the equitable and effective distribution of donated food

Motivated by our eight-year partnership with a local food bank, we present two robust optimization models to support the equitable and effective distribution of donated food over the food bank's service area. Our first model addresses uncertainty in the amount of donated food counties can effectively receive and distribute, which depends on local factors such as budget and workforce that are unknown to the food bank. Assuming that the capacity of each county varies within a range, the model seeks to maximize total food distribution while enforcing a user-specified level of robustness. Our second model uses robust optimization in a nontraditional manner, treating the upper bound on the level of allowed inequity as an uncertain parameter and limiting total deviation from a perfectly equitable distribution over all counties while maximizing total food shipment. We derive structural properties of both models and develop efficient exact solution algorithms. We illustrate our models using historical data obtained from our food bank partner, summarize the policy implications of our results and examine the impact of uncertainty on outcomes and decision making.

How Uncertain Information on Service Capacity Influences the Intermodal Routing Decision: A Fuzzy Programming Perspective

Capacity uncertainty is a common issue in the transportation planning field. However, few studies discuss the intermodal routing problem with service capacity uncertainty. Based on our previous study on the intermodal routing under deterministic capacity consideration, we systematically explore how service capacity uncertainty influences the intermodal routing decision. First of all, we adopt trapezoidal fuzzy numbers to describe the uncertain information of the service capacity, and further transform the deterministic capacity constraint into a fuzzy chance constraint based on fuzzy credibility measure. We then integrate such fuzzy chance constraint into the mixed-integer linear programming (MILP) model proposed in our previous study to develop a fuzzy chance-constrained programming model. To enable the improved model to be effectively programmed in the standard mathematical programming software and solved by exact solution algorithms, a crisp equivalent linear reformulation of the fuzzy chance constraint is generated. Finally, we modify the empirical case presented in our previous study by replacing the deterministic service capacities with trapezoidal fuzzy ones. Using the modified empirical case, we utilize sensitivity analysis and fuzzy simulation to analyze the influence of service capacity uncertainty on the intermodal routing decision, and summarize some interesting insights that are helpful for decision makers.

Generation of optimal persistent formations for heterogeneous multi-agent systems with a leader constraint**Project supported by the National Natural Science Foundation of China (Grant Nos. 71671059, 71401048, 71521001, 71690230, 71690235, and 71472058) and the Anhui Provincial Natural Science Foundation, China (Grant No. 1508085MG140).

In this study, we consider the generation of optimal persistent formations for heterogeneous multi-agent systems, with the leader constraint that only specific agents can act as leaders. We analyze three modes to control the optimal persistent formations in two-dimensional space, thereby establishing a model for their constrained generation. Then, we propose an algorithm for generating the optimal persistent formation for heterogeneous multi-agent systems with a leader constraint (LC-HMAS-OPFGA), which is the exact solution algorithm of the model, and we theoretically prove its validity. This algorithm includes two kernel sub-algorithms, which are optimal persistent graph generating algorithm based on a minimum cost arborescence and the shortest path (MCA-SP-OPGGA), and the optimal persistent graph adjusting algorithm based on the shortest path (SP-OPGAA). Under a given agent formation shape and leader constraint, LC-HMAS-OPFGA first generates the network topology and its optimal rigid graph corresponding to this formation shape. Then, LC-HMAS-OPFGA uses MCA-SP-OPGGA to direct the optimal rigid graph to generate the optimal persistent graph. Finally, LC-HMAS-OPFGA uses SP-OPGAA to adjust the optimal persistent graph until it satisfies the leader constraint. We also demonstrate the algorithm, LC-HMAS-OPFGA, with an example and verify its effectiveness.

Stability Analysis of Cost Allocation Methods for Inventory Routing

This paper considers the Inventory Routing Problem under two different inventory replenishment policies, namely the Maximum Level replenishment policy and the Order-up-to Level policy. The distribution cost under both replenishment policies is determined and allocated over the retailers that are served by the supplier. The distribution cost is obtained through an exact solution algorithm by Archetti et al. (2004). Various allocation methods, like proportional rules, methods based on separable and non-separable cost and game theoretic allocation concepts (Shapley value, nucleolus, pre-nucleolus), are used to allocate the cost over the retailers. Once the distribution cost and the cost allocations are obtained, the objective is to quantify and analyze the stability or instability of the cost allocation resulting from the various allocation methods.

A Time‐Dependent Fuzzy Programming Approach for the Green Multimodal Routing Problem with Rail Service Capacity Uncertainty and Road Traffic Congestion

This study explores an operational‐level container routing problem in the road‐rail multimodal service network. In response to the demand for an environmentally friendly transportation, we extend the problem into a green version by using both emission charging method and bi‐objective optimization to optimize the CO2 emissions in the routing. Two uncertain factors, including capacity uncertainty of rail services and travel time uncertainty of road services, are formulated in order to improve the reliability of the routes. By using the triangular fuzzy numbers and time‐dependent travel time to separately model the capacity uncertainty and travel time uncertainty, we establish a fuzzy chance‐constrained mixed integer nonlinear programming model. A linearization‐based exact solution strategy is designed, so that the problem can be effectively solved by any exact solution algorithm on any mathematical programming software. An empirical case is presented to demonstrate the feasibility of the proposed methods. In the case discussion, sensitivity analysis and bi‐objective optimization analysis are used to find that the bi‐objective optimization method is more effective than the emission charging method in lowering the CO2 emissions for the given case. Then, we combine sensitivity analysis and fuzzy simulation to identify the best confidence value in the fuzzy chance constraint. All the discussion will help decision makers to better organize the green multimodal transportation.

Service location grouping and pricing in transportation: Application in air cargo

It is a common practice for transportation firms to group together a set of locations that they serve and price their services based on the group that the origin and destination of a service belong to rather than point-to-point. Proper grouping of service locations and correct pricing under this policy is essential to the financial success of firms. In this research, we develop a novel model for transportation firms to simultaneously group service locations and determine group-to-group pricing by considering the price elasticity of customers’ demand. We formulate the problem as a mixed-integer nonlinear programming and propose two exact solution algorithms based on decomposition principles. The performances of our algorithms are evaluated using computational experiments and results show that proposed methods are effective.

An implicit enumeration algorithm for the hub interdiction median problem with fortification

Hubs are intermediate facilities that play a pivotal role in efficient functioning of transportation and telecommunication systems. Like any other service infrastructure, hub facilities can be subject to natural or man-made disruptions after installation. In this paper, we address the problem of optimally allocating protective resources among a set of p existing hub facilities in such a manner that the damage inflicted by an intentional strike against the service system is minimized. Casting the problem as a Stackelberg game, the leader (i.e., the network protector or defender) fortifies q of the p operating hubs in order to minimize the impact of the upcoming strike, whereas the follower (i.e., the attacker) tries to identify and interdict r of the p−q unprotected hubs that their loss would diminish the network performance the most. A bilevel programming formulation is presented to model the problem and using a min-max approach the model is reduced to a single level mixed integer programming (MIP) model. Furthermore, an efficient exact solution algorithm based on implicit enumeration is proposed for solving the problem. Extensive computational experiments show the capability of the proposed algorithm to obtain the optimal solutions in short computational times. Some managerial insights are also derived based on the obtained numerical results.

Nurse Scheduling with Opposition-Based Parallel Harmony Search Algorithm

Abstract One of the advances made in the management of human resources for the effective implementation of service delivery is the creation of personnel schedules. In this context, especially in terms of the majority of health-care systems, creating nurse schedules comes to the fore. Nurse scheduling problem (NSP) is a complex optimization problem that allows for the preparation of an appropriate schedule for nurses and, in doing so, considers the system constraints such as legal regulations, nurses’ preferences, and hospital policies and requirements. There are many studies in the literature that use exact solution algorithms, heuristics, and meta-heuristics approaches. Especially in large-scale problems, for which deterministic methods may require too much time and cost to reach a solution, heuristics and meta-heuristic approaches come to the fore instead of exact methods. In the first phase of the study, harmony search algorithm (HSA), which has shown progress recently and can be adapted to many problems is applied for a dataset in the literature, and the algorithm’s performance is evaluated by comparing the results with other heuristics which is applied to the same dataset. As a result of the evaluation, the performance of the classical HSA is inadequate when compared to other heuristics. In the second phase of our study, by considering new approaches proposed by the literature for HSA, the effects on the algorithm’s performance of these approaches are investigated and we tried to improve the performance of the algorithm. With the results, it has been determined that the improved algorithm, which is called opposition-based parallel HSA, can be used effectively for NSPs.

A Demand Estimator Based on a Nested Logit Model

The importance of historical travel demand has been well recognized by transportation researchers and practitioners. This paper presents a new nonlinear demand estimator that can be applied in both ground and air transportation. The estimator is formulated such that the distribution of the estimated demand follows a nested logit model. To solve the demand estimator, we develop an exact solution algorithm, which maximizes its dual problem sequentially along unit directions and keeps some of the first-order optimality conditions satisfied for the estimator. We investigate the convergence of the algorithm. We prove that all of the accumulation points produced by the solution algorithm satisfy some optimality conditions. A large example (a real U.S. network), which contains 66,767 origin-destination pairs, is presented.

The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints

The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisfy short-range—within the next three days—aircraft maintenance requirements. While maintenance plans commonly span multiple days, the methods used to compute tail assignments for the given plans can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by using solutions from the one-day routes aircraft maintenance routing approach as input. The daily tail assignment problem is solved with an objective to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A computational study will be performed to assess the performance of exact and heuristic solution algorithms that modify the input lines-of-flight to reduce maintenance misalignments. The daily tail assignment problem and the developed algorithms are demonstrated to compute solutions that effectively satisfy maintenance requirements when evaluated using input data collected from three different airlines.

A new exact solution algorithm for a novel generalized redundancy allocation problem

The traditional redundancy allocation problem (RAP) aims to determine a system structure that strikes an appropriate balance between series and parallel components and that maximizes reliability by using redundant components in parallel, thus satisfying resource consumption constraints. The RAP is a well-known NP-hard problem and has been an active area of research for the past four decades. By extending the series–parallel structure to a more general network structure, this paper proposes a novel RAP called the generalized RAP (GRAP). To reduce the computational burden in solving this intractable GRAP, a new algorithm, called the hybrid swarm optimization (HSO), is proposed. The HSO combines concepts from simplified swarm optimization (SSO), particle swarm optimization (PSO), simulated annealing, and network reliability methods. The paper presents designed experiments and computational studies that demonstrate the potential of using the proposed HSO for the GRAP instead of using the genetic algorithm, PSO, or SSO.

A simple algorithm for exact solutions of systems of linear and nonlinear integro-differential equations

A Simple algorithm is used to achieve exact solutions of systems of linear and nonlinear integro- differential equations arising in many scientific and engineering applications. The algorithm does not need to find the Adomain Polynomials to overcome the nonlinear terms in Adomain Decomposition Method (ADM). It does not need to create a homotopy with an embedding parameter as in Homotopy Perturbation Method (HPM) and Optimal Homotopy Asymptotic Method (OHAM). Unlike VIM, it does not need to find Lagrange Multiplier. In this manuscript no restrictive assumptions are taken for nonlinear terms. The applied algorithm consists of a single series in which the unknown constants are determined by the simple means described in the manuscript. The outcomes gained by this algorithm are in excellent concurrence with the exact solution and hence proved that this algorithm is effective and easy. Four systems of linear and nonlinear integro-differential equations are solved to prove the above claims and the outcomes are compared with the exact solutions as well as with the outcomes gained by already existing methods.

Two-Way Bounded Dynamic Programming Approach for Operations Planning in Transshipment Yards

We propose a two-way bounded dynamic programming (TBDP) approach to deal with situations, when it takes a long time to evaluate the value function in the state graph of dynamic programming. TBDP provides sharp bounds early in the solution process and identifies critical subproblems, i.e., states and transition arcs, for which the value function has to be estimated. Based on the TBDP framework, we develop a heuristic and an exact algorithm for the static crane scheduling problem (SCSP). The SCSP refers to simultaneous yard partitioning into single-crane areas and job sequencing at railway container transshipment yards, where both rail-rail and rail-road transshipments are present and rail-rail moves are short. The designed exact solution algorithm solves instances of practically relevant size within acceptable time limits. The proposed heuristic finds optimal solutions in 90% of the cases. We recommend using the heuristic algorithm for planning very large transshipment yards, with more than five tracks and a large number of container moves per crane.

Cheapest paths in dynamic networks

Flows over time problems relate to finding optimal flows over a capacitated network where transit times on network arcs are explicitly considered. In this article, we study the problem of determining a minimum cost origin‐destination path where the cost and the travel time of each arc depend on the time taken to travel from the origin to that particular arc along the path. We provide computational complexity results for this problem and an exact solution algorithm based on an enumeration scheme on the corresponding time expanded network. Finally, we show the efficiency of our approach through a number of experimental tests. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 23–32 2017

Resequencing with parallel queues to minimize the maximum number of items in the overflow area

AbstractThis article treats an elementary optimization problem, where an inbound stream of successive items is to be resequenced with the help of multiple parallel queues in order to restore an intended target sequence. Whenever early items block the one item to be currently released into the target sequence, they are withdrawn from their queue and intermediately stored in an overflow area until their actual release is reached. We aim to minimize the maximum number of items simultaneously stored in the overflow area during the complete resequencing process. We met this problem in industry practice at a large German automobile producer, who has to resequence containers with car seats prior to the assembly process. We formalize the resulting resequencing problem and provide suited exact and heuristic solution algorithms. In our computational study, we also address managerial aspects such as how to properly avoid the negative effects of sequence alterations. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 401–415, 2016