Heuristic Solution Methods Research Articles

Optimal marketing policy for managing new generation products in the presence of forward-looking customers by considering product diffusion

PurposeThe effect of customers’ forward-looking behavior on firms’ profit has been highlighted by many researchers and practitioners. This study aims to develop a mathematical model for new generation products to analyze the optimal pricing and advertising policies in the presence of homogeneous forward-looking customers. A firm that produces and sells a new generation product was considered. This firm aimed to determine the optimal pricing and advertising expenditure by maximizing the total profit.Design/methodology/approachThe demand was presented as a diffusion model inspired by the Bass diffusion model. This paper used Pontryagin’s maximum principle to analyze the proposed model. The presented model was implemented in some numerical examples by proposing a heuristic solution method. Numerical examples confirmed the theoretical results.FindingsThis paper found a threshold on the optimal advertising policy depends on customers’ forward-looking behavior, advertising coefficient (both direct and word-of-mouth advertising) and discount rate. The funding showed that the optimal pricing path of the first generation was monotonically decreasing or increasing and, then, decreasing. Results revealed that, by increasing the customers’ forward-looking behavior, the firm should reduce the price and advertising expenditure. Also, the price was shown to be negatively affected by the discount rate and word-of-mouth advertising. The profitability will improve if the firm spends more budget on advertising by increasing the discount rate and advertising effectiveness. Further, when the word-of-mouth advertising effect is high, the firm should increase the advertising expenditure first and, then, decrease it.Originality/valueNowadays, forward-looking customers’ anticipation for releasing a new generation can harm the firms’ profit. In this regard, this research analyzed optimal pricing and advertising policies for a new generation product in a market populated by homogeneous forward-looking customers. To the best of the knowledge, this is the first study that investigated these two marketing policies jointly in the presence of forward-looking customers.

Procurement portfolio planning for a newsvendor with supplier delivery uncertainty

We consider the problem of allocating procurement quantities for a required input to multiple suppliers in advance of a selling season with uncertain demand. Planning complexity is compounded by uncertainty in whether each supplier will deliver on time, in addition to the existence of an option for reserving capacity with a perfectly reliable supplier and the presence of a spot market for the input with an uncertain price. We apply analytical methods including two-stage stochastic programming with recourse, nonlinear optimization, and exact and efficient model-based heuristic solution methods. We show that for a selected supplier, the newsvendor’s conditional service level, given that the supplier delivers on time, equals a critical ratio value determined by the supplier’s cost and reliability parameters. Post-optimality analysis reveals interesting insights on the way reliability and cost parameters interact to determine whether a supplier receives a positive order allocation, as well as the impact of payment schemes on supplier selection decisions. The analysis clarifies an insightful relationship between the conditional service level and a critical ratio value for each selected supplier. The results also sharpen insights on the way relative supplier reliability and cost parameter values interact to determine an optimal supply portfolio. Furthermore, the ability to interpret a perfectly reliable supplier with a capacity reservation cost as an equivalent unreliable supplier reveals additional insights on the relative value of capacity reservation and facilitates direct comparison among seemingly disparate supply options.

A Heuristic Solution Method of Mixed Problem of Materials' Cutting Plan Decision and Production Scheduling for Foundation Reinforcement Units Manufacturing

A Heuristic Solution Method of Mixed Problem of Materials' Cutting Plan Decision and Production Scheduling for Foundation Reinforcement Units Manufacturing

Optimizing Road Networks for Automated Vehicles with Dedicated Links, Dedicated Lanes, and Mixed-Traffic Subnetworks

This study focuses on network configurations to accommodate automated vehicles (AVs) on road networks during the transition period to full automation. The literature suggests that dedicated infrastructure for AVs and enhanced infrastructure for mixed traffic (i.e., AVs on the same lanes with conventional vehicles) are the main alternatives so far. We utilize both alternatives and propose a unified mathematical framework for optimizing road networks for AVs by simultaneous deployment of AV-ready subnetworks for mixed traffic, dedicated AV links, and dedicated AV lanes. We model the problem as a bilevel network design problem where the upper level represents road infrastructure adjustment decisions to deploy these concepts and the lower level includes a network equilibrium model representing the flows as a result of the travelers’ response to new network topologies. An efficient heuristic solution method is introduced to solve the formulated problem and find coherent network topologies. Applicability of the model on real road networks is demonstrated using a large-scale case study of the Amsterdam metropolitan region. Our results indicate that for low AV market penetration rates (MPRs), AV-ready subnetworks, which accommodate AVs in mixed traffic, are the most efficient configuration. However, after 30% MPR, dedicated AV lanes prove to be more beneficial. Additionally, road types can dictate the viable deployment plan for certain parts of road networks. These insights can be used to guide planners in developing their strategies regarding road network infrastructure during the transition period to full automation.

Hospital-wide surveillance-based antimicrobial treatments: A Monte-Carlo look-ahead method

Background and objectives. We present a heuristic solution method to the problem of choosing hospital-wide antimicrobial treatments that minimize the cumulative infected patient-days in the long run in a health care facility. Methods. Our solution method is a rollout algorithm. We rely on the stochastic version of a compartmental model to describe the spread of an infecting organism in the health care facility and the emergence and spread of resistance to two drugs. We assume that the parameters of the model are known. Treatments are chosen at the beginning of each period based on the count of patients with each health status, and on stochastic simulations of the future emergence and spread of antimicrobial resistance. The same treatment is then administered to all patients, including uninfected patients, during the period and cannot be adjusted until the next period. Results. In our simulations, our algorithm allows to reduce the average cumulative infected patient-days over two years by 47.0% compared to the best standard therapy, and by 32.2% compared to a similar heuristic algorithm not using surveillance data (significantly at the 95% threshold). Conclusion. Our heuristic solution method is simple yet flexible. We explain how it can be used either to perform online optimization, or to produce data for quantitative analysis. Its performance is illustrated using a relatively simple infectious disease transmission model, but it is compatible with more advanced epidemiological models.

A two-generation new product model by considering forward-looking customers: Dynamic pricing and advertising optimization

Nowadays, one of the challenges of the firm managing multi-generation products is the forward-looking behavior of customers. Anticipating the introduction of a newer generation affects the demand and sales volume of the current generation and next generation. In this research, we investigated how to efficiently structure the pricing and advertising strategies of a firm that launches a two-generation new product to a market populated by forward-looking customers. Two thresholds were determined on the advertising expenditure of Generations 1 and 2. Our analysis proposed that the optimal pricing path of Generation 1 was monotonically decreasing or increasing and, then, decreasing. The optimal pricing of Generation 2 followed a concave curve. A heuristic solution method was proposed to solve the numerical examples. Findings revealed that, with increasing the customers' forward-looking behavior, the firm's profit would decrease. In the presence of forward-looking customers, it is beneficial for the firm to reduce the price of Generation 1 and allocate more budget to advertise Generation 2. Among other results, the advertising expenditure was shown to be positively affected by the number of potential customers and advertising effectiveness. Also, the length of the planning horizon had a negative effect on the advertising expenditure. A higher discount rate could lead to lower price, while higher advertising effectiveness and length of the planning horizon would result in higher price. Further, the results showed that, with increasing the word-of-mouth advertising effectiveness, the firm should increase the advertising expenditure and decrease the price firstly and, afterwards, decrease the advertising effort and increase the price.

Bus scheduling considering trip‐varying travel times, vehicle availability and capacity

Bus scheduling is a well-known NP-hard problem, and it is addressed with the use of heuristic solution methods or graphical approaches. In this study, the author proposes an improved formulation of the bus scheduling problem that considers the vehicle availability, the vehicle capacity and the allowed headway variability among successive trip dispatches. His formulation expands the classic bus scheduling model formulation by including the aforementioned features. In his study, the bus scheduling problem is understood as the problem of setting the optimal dispatching times for a set of pre-determined daily trips of a particular bus line. His model facilitates the search of solutions that can improve the waiting times of passengers while meeting the operational requirements and avoiding overcrowding. His proposed mathematical program is proved to be non-convex, and it is solved with heuristic solution methods because numerical optimisation approaches cannot guarantee a globally optimal solution. The performance of his approach is tested in a case study using real operational data from bus line 302 in Singapore. A simulation-based evaluation demonstrates potential gains of up to 20% on average passenger waiting times and a major reduction in refused passenger boardings because of overcrowding.

Heuristic solution methods for the selective disassembly sequencing problem under sequence-dependent costs

The first Waste Framework Directive issued by the European Union dates back to the seventies but was drastically amended in the last decade to reduce environmental impacts of waste by encouraging reuse, recycling and remanufacturing. Product recovery starts with disassembly which results in high labor costs. Disassembly supports environmentally conscious choices like replacement of defective parts to extend the life span of products, removal of suitable components for reuse and extraction of hazardous substances to decontaminate materials for reprocessing. Besides, selective disassembly also accommodates maintenance and repairs. Optimizing the cost of disassembly is crucial to make this process an economically viable option. Due to change tools and parts reorientation, disassembly costs are sequence-dependent. Therefore minimizing the disassembly cost involves the search for an adequate sequence of disassembly tasks. Consequently, this paper addresses the disassembly sequencing problem for selective and sequential disassembly under sequence-dependent costs. As optimal formulations fail to handle real-world cases, we develop a randomized greedy algorithm (needing a very few number of parameters to be set and proving to be robust with respect to their value) and a matheuristic to solve efficiently medium to large-sized instances.

Exact and flexible solution approach to a critical chain project management problem

An important component in critical chain project management is a scheduling methodology to support resource constraints. Given task duration estimates and precedence relations along with resource designation for each task, one seeks to adhere to a target due date as well as to shorten the estimated makespan. Key are two types of time buffers to absorb potential delays accumulated from preceding tasks, and this makes the problem complex and hard to solve. The “good enough” strategy has been prevalent in research, focusing on the development of heuristic solution methods. There has been only one attempt to minimize estimated makespan, wherein discrete algebra is utilized. The method is, however, inflexible as you must compose a search space. Even the slightest extension requires a major recast of the approach. Hence, we develop a new approach to find an exact optimal solution in an efficient manner. Given a project instance, an optimization problem is constructed as a mixed-integer linear-program, for which an exact solution can be found using an off-the-shelf solver. While the problem is NP hard, larger-scale project instances, including up to 30 tasks, can be solved within a practical time standard. Extension with respect to resource assignment is easily accomplished. Experimental results highlight the significance of the developed framework.

The flow interception location model with congestion cost based on the number of facility users and its heuristic solution method

The flow interception location model with congestion cost based on the number of facility users and its heuristic solution method

Data-Driven Modeling and Optimization of the Order Consolidation Problem in E-Warehousing

We analyze data emanating from a major e-commerce warehouse and provided by a third-party warehouse logistics management company to replicate flow diagrams, assess order fulfillment efficiency, identify bottlenecks, and suggest improvement strategies. Without access to actual layouts and process-flow diagrams and purely based on data, we are able to describe the processes in detail and prescribe changes. By investigating the characteristics of orders, the wave-sorting operation, and the order-preparation process, we find that products from different orders are picked in batches for efficiency. Similar products are picked in small containers called totes. Totes are then stored in a buffer area and routed to be emptied of their contents at induction lines. Orders are then consolidated at the put wall, where each order is accumulated in a cubby. This order consolidation process depends on the sequence in which totes are processed and has a huge impact on order-completion time. We, therefore, present a generalization of the parallel machine–scheduling problem that we call the order consolidation problem to determine the tote-processing sequence that minimizes total order completion time. We provide mathematical formulations and devise heuristic and exact solution methods. We propose a fast simulated annealing metaheuristic and a branch-and-price approach in which the subproblems are variants of the single machine-scheduling problem and are solved using dynamic programming. We also devise a new branching rule, compare it against the literature, and test it on randomly generated and industry data. Applied to the data and the warehouse under study, optimizing the order consolidation is found to decrease the completion time of 75.66% of orders and achieve average improvements of up to 28.77% in order consolidation time and 21.92% in cubby usage.

Optimal Protection Coordination of Nonstandard Overcurrent Relays Using Hybrid QCQP Method

The optimal protection coordination (OPC) problem of directional overcurrent relays (OcR) in power system networks is a complex, highly constrained nonconvex optimization problem because of the nonlinear inverse nature of the OcR characteristics. Finding the best OcR settings by solving OPC is a challenging task because of its nonconvex nature. Although various heuristic, hybrid heuristic, and traditional optimization-based solution methods are suggested in the literature, such methods are just far enough to provide better optimal solutions to the OPC problem. Besides, the standard inverse characteristics of the OcRs with fixed characteristic coefficients limit the OPC problem from finding the best settings. As digital relaying technology has the feasibility to embed more relay settings, nonstandard relay characteristics can be developed to achieve minimum relay operating times. To find the best OcR operating times, a nonstandard characteristic based OPC problem is formulated in this work by parameterizing the OcR characteristic coefficients along with the OcR settings. By setting two variables of the proposed OPC using particle swarm optimization (PSO), the rest of OPC is formulated as a quadratic programming problem with quadratic constraints (QCQP). The proposed method is developed in MATLAB programming platform, and results are found to be satisfactory.

Inventory routing under stochastic supply and demand

It is well known that the integrated optimization of multiple and inter-related decisions in a supply chain can bring important benefits to companies. In this spirit, the inventory routing problem focuses on jointly optimizing inventory replenishment and vehicle routing decisions in a distribution context. In practice, the presence of uncertainty often further complicates the problem. We address a stochastic inventory routing problem under the consideration that both the product supply and the customer demands are uncertain. We propose a two-stage stochastic programming formulation, where routing decisions are made in the first stage, while delivery quantities, inventory levels and specific recourse actions are determined in the second stage. In this context, we analyze different recourse mechanisms such as lost sales, backlogging and an additional source for the product in a capacity reservation contract setting. We provide managerial insights from the results of computational experiments using instances based on a benchmark test set. In particular, we study the response mechanisms of the optimal solutions for different levels of uncertainty and cost configurations. Furthermore, we observe that supply and demand uncertainty have different effects on the value of taking the uncertainty into account. We also study the effect of incorporating a service level. Finally, we propose a heuristic solution method which is based on the progressive hedging algorithm and provides high-quality solutions within reasonable running times for problems with a large number of scenarios.

A Heuristic Solution Method for Multi-Depot Vehicle Routing-Based Waste Collection Problems

This paper addresses waste collection problems in which urban household and solid waste are brought from waste collection points to waste disposal plants. The collection of waste from the collection points herein is modeled as a multi-depot vehicle routing problem (MDVRP), aiming at minimizing the total transportation distance. In this study, we propose a heuristic solution method to address this problem. In this method, we firstly assign waste collection points to waste disposal plants according to the nearest distance, then each plant solves the single-vehicle routing problem (VRP) respectively, assigning customers to vehicles and planning the order in which customers are visited by vehicles. In the latter step, we propose the sector combination optimization (SCO) algorithm to generate multiple initial solutions, and then these initial solutions are improved using the merge-head and drop-tail (MHDT) strategy. After a certain number of iterations, the optimal solution in the last generation is reported. Computational experiments on benchmark instances showed that the initial solutions obtained by the sector combination optimization algorithm were more abundant and better than other iterative algorithms using only one solution for initialization, and the solutions with distance gap were obtained using the merge-head and drop-tail strategy in a lower CPU time compared to the Tabu search algorithm.

On the analysis of last-mile relief delivery on a tree network: Application to the 2015 Nepal earthquake

The last mile delivery in humanitarian relief supply often happens on a tree or an almost-tree network allowing split deliveries. We present a relief delivery model incorporating a tree network for last mile delivery. We developed a mixed integer programming (MIP) formulation with the goal of minimizing the unsatisfied demand of the population. For better computational performance, we reformulated the MIP exploiting the tree network structure and found that this gave an order of magnitude reduction in computational time. To further improve computational efficiency, we developed a heuristic solution method based on a decomposition scheme applied to the tree network formulation. This led to the Capacitated Vehicle Routing Problem on trees with split deliveries, for which we derived a closed-form solution. This decomposition scheme resulted in a further order of magnitude reduction in computation time. To demonstrate the application of our approach we applied our model to the humanitarian logistics relief operation encountered in the 2015 Nepal earthquake.

Modeling joint activity-travel patterns in pedestrian networks with use of Wi-Fi data

Abstract This paper proposes a new activity-based equilibrium model to solve a joint activity-travel pattern scheduling problem in pedestrian networks. A novel supernetwork platform, pedestrian-joint-activity-time-space, is proposed to capture the complex structure of pedestrian networks and intragroup interactions on joint activity choices of pedestrians. The joint activity-travel pattern scheduling problem is transformed into an extended static user equilibrium traffic assignment model with side constraints for group interactions. A heuristic solution method is proposed to solve the user equilibrium problem concerned. A simplified pedestrian network is used to illustrate the convergence of the proposed heuristic solution method. Furthermore, the use of Wi-Fi tracking data from mobile phones to generate the activity patterns of pedestrians and their interactions is also investigated with a real case study in a selected area of The Hong Kong Polytechnic University.

The Hybrid Electric Vehicle—Traveling Salesman Problem with time windows

In this paper, we extend the Hybrid Electric Vehicle – Traveling Salesman Problem (HEV-TSP) that deploys hybrid electric vehicles for customer delivery tours, by considering that customers must be served within given time windows. This feature makes the problem very difficult to solve. We developed a Variable Neighborhood Search based heuristic solution method, which is able to handle hybrid electric vehicle problems with a realistic number of customers. We introduce a large set of benchmark instances, representing typical delivery areas for small package shipping companies. Exact solutions for instances with a small number of customers are calculated by formulating the problem as an integer linear program and solving the instances with the standard solver CPLEX. The proposed heuristic achieves optimal solutions on the small and good quality solutions on larger instances. Furthermore, the results show that the profitability of hybrid electric vehicles highly depends on the structure of the delivery area and the number of customers to serve. Therefore, our heuristic does not only serve to support decision makers in the daily tour planning, but also in the evaluation of the profitability of hybrid electric vehicles for a specific delivery area structure.

Loading tow trains ergonomically for just-in-time part supply

Faced with an aging workforce, many manufacturing companies consider alleviating the ergonomic strain of material handling on their workers increasingly important. This is one of the reasons why frequent small-lot deliveries of parts to the assembly stations on the shop floor via small electric delivery vehicles – so-called tow trains – have become widespread in many industries. Deploying tow trains, however, does not automatically ease the ergonomic burden on logistics workers, but requires careful stowage planning in addition. In this paper, we consider the following problem. Given a set of bins of differing weight to be carried by tow train to a given set of stations on the shop floor, where should each bin be stowed on the tow train such that it can be unloaded efficiently from an economic perspective while also minimizing the ergonomic strain during loading and unloading? We investigate the physiological stress of handling bins on different levels of a tow train wagon by applying an established ergonomic evaluation method from the human factors engineering literature. We model the ensuing optimization problem as a special type of assignment problem and propose suitable exact and heuristic solution methods. In a computational study, our approaches are shown to perform well, delivering optimal solutions for instances of realistic size within fractions of a second in many cases. We show that optimal stowage plans can significantly ease the physiological burden on the workforce without compromising economic efficiency. We also derive some insights into the ideal layout of the tow train from an ergonomics perspective.

Adaptive Large Neighborhood Search for Multitrip Vehicle Routing with Time Windows

We consider a multitrip vehicle routing problem with time windows (MTVRPTW), in which each vehicle can perform several trips during its working shift. This problem is especially relevant in the context of city logistics. Heuristic solution methods for multitrip vehicle routing problems often separate routing and assignment phases to create trips and then assign them to the available vehicles. We show that this approach is outperformed by an integrated solution method in the presence of time windows. We use an automatic configuration tool to obtain efficient and contextualized implementations of our solution methods. We provide suitable instances for the MTVRPTW as well as an instance generator. Also, we discuss the relevance of two objective functions: the total duration and the total travel time. When minimizing the travel time, large increases in waiting time are incurred, which is not realistic in practice.

Modeling a production-inventory-routing problem of blood products using heuristic solution methods

Blood and blood products are vital resources for the surgery and the treatment of certain diseases. As a scarce and perishable resource, they require sophisticated management to minimize waste in order to address this challenge, the present study revolves around the idea of the management of the pr oduction, supply and distribution of blood products. In this research, two questions of robust and flexible have been investigated for the production, inventory and routing blood products. The flexibility is incorporated into the problem through introducing the possibility of sharing inventory among network entities by transferring blood products between hospitals and also the possibility of meeting a blood group’s need with another compatible blood type or replacement. The problem is then solved by heuristic (local search) and meta-heuristic (Adaptive Large Neighborhood Search (ALNS)) algorithms, which are the methods of choice in particular for NP-hard problems. Finally, the results obtained from the two algorithms are compared it is shown that the heuristic algorithm outperforms the Adaptive Large Neighborhood Search (ALNS) in both models, that can lead to reduction is cost and required transitions.