Location-transportation Problem Research Articles

A location–transportation problem under demand uncertainty for a pharmaceutical network in Brazil

We study the integrated location–transportation problem under uncertain demand, addressing the case of a pharmaceutical logistics network in Brazil. We propose a mathematical model with multi-time scales to make decisions accordingly with their timing. The model considers practical features, such as fleet sizing, safety constraints in cargo transportation, and tax issues. We address uncertainty in decision-making by developing a robust counterpart and present solution methods based on Fix-and-Optimize heuristics. We perform computational experiments using real data from a partner company and evaluate the impact of uncertainty on the problem. The heuristics outperform the MIP model by reducing the average of logistics costs and taxes by 40%. Demand uncertainty and variability significantly influence the problem decisions. Also, the robust model reduces expected solution costs. Thus, these models and solution methods can support the decision-making process on location–transportation problems in Logistics Network Planning in contexts similar to the pharmaceutical industry in Brazil.

An integrated location–transportation problem under value-added tax issues in pharmaceutical distribution planning

This paper focuses on a medium-term distribution plan for a pharmaceutical network, considering distribution center (DC) location and transportation decisions. The problem is characterized by low DC opening costs due to outsourced warehousing services. Therefore, transportation costs have a higher impact on location decisions and should be carefully evaluated. In addition, medicines vary widely in sales price and volume, demand behavior, and physical characteristics, which affects the distribution planning. This paper proposes a multi-product, multi-period, and multi-modal mathematical model integrating network design and distribution planning decisions, such as product flow, transportation modes, type of freight shipping, fleet sizing, and escorting services for high-value cargo. The mathematical formulation takes into consideration realistic features such as value-added tax, whose rate varies among locations. A Local Branching matheuristic taking advantage of the hierarchical problem structure is introduced. The result of tests using real-life data demonstrate the model’s effectiveness to support the trade-off between the location and transportation problem, corroborating the relevance of making these decisions simultaneously. A comparison of the results with a company shows opportunities to reduce overall logistics costs plus the total amount of chargeable taxes. Regarding computational running times, the proposed matheuristic outperformed CPLEX in 75% of instances.

Target-oriented robust location–transportation problem with service-level measure

We study a target-oriented, multi-period location–transportation problem where customer demands are uncertain. This problem is to determine the facility locations, production quantities, capacities, and shipment quantities, where the objective is to achieve the desired profit and fill rate to the full extent when it is impossible to reach both. To achieve the goal, we propose a target-oriented framework for the location–transportation problem, where a service-level measure is constructed to guarantee the desired fill rate and a hard constraint on profit is imposed to ensure a decent profit. This framework gets rid of the issues arising from estimating the weights of different objectives in a multi-objective optimization approach. To capture the characteristics of a multi-period decision-making process, an affine decision rule is introduced. Our method not only ensures that the transportation decisions of each period can adapt to realized demands wisely, but also prevents the high complexity of the model resulting from uncertainty and adaptation. Specifically, to tackle challenges of problem intractability, we reformulate the robust counterpart of the problem into a conservative approximation in the form of a mixed-integer quadratic program and propose a Benders decomposition approach to produce effective solutions. Finally, the performance of the target-oriented framework is assessed through computational experiments based on realistic instances.

Target-oriented Robust Location-transportation Problem with Service-level Measure

We study a target-oriented, multi-period location-transportation problem where customer demands are uncertain and transportation decisions are adaptative. This problem is meant to determine the facility locations, production quantities, capacities, and shipment quantities, with the objective of achieving the desired profit and fill rate to the full extend when reaching both is impossible. To realize that objective, we propose a target-oriented framework for location transportation problem, where service-level measure is constructed to guarantee desired fill rate, and a hard constraint on profit is imposed to ensure decent profit. This framework gets rid of the issues arising from estimating the weights of different objectives in a multi-objective optimization framework. Additionally, to incorporate the characteristics of a multi-period decision-making process, an affine decision rule is introduced, which not only ensures that the transportation decisions of each period can adapt to realized demands wisely, but also prevents the high complexity of the model due to the uncertainty and adaptation. That is to say, to tackle the intractability, we reformulate the robust counterpart into a conservative approximation which is a mixed-integer quadratic programming, and then effective solutions can be produced with Benders Decomposition algorithm. Finally, the performance of the target-oriented framework is assessed through computational experiments based on realistic instances.

A robust optimization model for location-transportation problem of disaster casualties with triage and uncertainty

Emergency medical services (EMS) are essential components for post-disaster rescue activities. Considering injury heterogeneity and deterioration over time of the casualties, the uncertainty in the number of the casualties can effectively improve the medical service performance. This paper develops a robust optimization model for combined facility location and casualty transportation under uncertainty in the number of casualties. We divide casualties into two types: mild casualties who are transported to on-site clinics with rescue vehicles and serious casualties who are transported to general hospitals with helicopters. Meanwhile, we consider the Injury Severity Score (ISS) increment to describe the injury deterioration of the casualties over time. The objective is to minimize the total weighted ISS increment of mild casualties and serious casualties. Then, we employ the robust optimization method to deal with the uncertainty and derive the robust counterpart of the proposed model in this paper. Case studies based on Yushu Earthquake show that the model can get the optimal emergency facility location and casualty transportation scheme to minimize the total weighted ISS increment. The total weighted ISS increment increases as the constraint violation probability decreases, which reflects the trade-off between performance and robustness. Sensitivity analyses show that the greater uncertainty of the casualty number is, the greater the impact on the total weighted ISS increment is, the more conservative the decision scheme is. The capacity of general hospitals has a greater effect on the objective value compared with the capacity of on-site clinics and the decision scheme of the robust optimization model has a greater optimality compared with the deterministic model when the problem size is magnified.

Multi-objective solid transportation-location problem with variable carbon emission in inventory management: a hybrid approach

The most important strategic issue for several industries is where to find facilities so as to discover a transportation path for optimizing the objectives at the same time. This paper acquaints a streamlining model with incorporate the facility location problem, solid transportation problem, and inventory management under multi-objective environment. The aims of the stated formulation are multi-fold: (i) to seek the optimum locations for potential facilities in Euclidean plane; (ii) to find the amount of distributed commodities; and (iii) to reduce the overall transportation cost, transportation time, and inventory cost along with the carbon emission cost. Here, variable carbon emission cost is taken into consideration because of the variable locations of facilities and the amount of distributed products. After that, a new hybrid approach is introduced dependent on an alternating locate-allocate heuristic and the intuitionistic fuzzy programming to get the Pareto-optimal solution of the proposed formulation. In fact, the performances of our findings are discussed with two numerical examples. Sensitivity analysis is executed to check the resiliency of the parameters. Ultimately, managerial insights, conclusions and avenues of future studies are offered at the end of this study.

A Robust Optimization Methodology for Multi-objective Location-transportation Problem in Disaster Response Phase under Uncertainty

This paper presents a multi-objective model for location-transportation problem under uncertainty that has been developed to respond to crisis. In the proposed model, humanitarian aid distribution centers (HADC), the number and location of them, the amount of relief goods stored in distribution centers, the amount of relief goods sent to the disaster zone, the number of injured people transferred to medical centers and the delivery of relief regarding the limits of capacity for transport, distribution centers and also available time and budget limits are all considered. This work aims at minimizing unfulfilled needs; that is meaning the number of people have not been transferred to medical centers. In order to take the inevitable uncertainty in some parameters into account, the primal deterministic model has been reformulated by applying the robust optimization approach. Also the performance of the both deterministic and robust models are investigated by solving a numerical example. The results of the study show that the robust counterpart of deterministic model will remain feasible with a high probability in reality.

Transportation-location problem with unknown number of facilities

The traditional transportation-location problem seeks to determine the location of m new capacitated facilities in continuous space and the level of interaction between these new facilities and existing facilities to minimize the total fixed and variable costs. This paper studies a variant of the transportation-location problem where the number of new facilities is also a decision variable. The problem has practical applications for designing large distribution networks. Several non-linear mixed integer formulations are presented in order to understand the intrinsic complexity of the problem. Given that the problem is NP-hard, a decomposition heuristic (DH) and a simulated annealing-based heuristic (SA) are developed based on the mathematical structure of the problem and compared via experimentation. It is found that both heuristics find the same solution for 40 internally generated problems. Three new benchmark problems are presented and an upper bound is provided.

The Value of Flexibility in Robust Location–Transportation Problems

This article studies a capacitated fixed-charge multiperiod location–transportation problem in which, while the location and capacity of each facility must be determined immediately, the determination of the final production and distribution of products can be delayed until actual orders are received in each period. In contexts where little is known about future demand, robust optimization, namely using a budgeted uncertainty set, becomes a natural method for identifying meaningful decisions. Unfortunately, it is well known that these types of multiperiod robust decision problems are computationally intractable. To overcome this difficulty, we propose a set of tractable conservative approximations for the problem that each exploit to a different extent the idea of reducing the flexibility of the delayed decisions. While all of these approximation models outperform previous approximation models that have been proposed for this problem, each also has the potential to reach a different level of compromise between efficiency of resolution and quality of the solution. A row generation algorithm is also presented to address problem instances of realistic size. We also demonstrate that full flexibility is often unnecessary to reach nearly, or even exact, optimal robust locations and capacities for the facilities. Finally, we illustrate our findings with an extensive numerical study where we evaluate the effect of the amount of uncertainty on the performance and structure of each approximate solution that can be obtained. The online appendix is available at https://doi.org/10.1287/trsc.2016.0728 .

A COMPARISON OF PARALLEL BRANCH AND BOUND ALGORITHMS FOR LOCATION-TRANSPORTATION PROBLEMS IN HUMANITARIAN RELIEF

This paper studies the effect of branching rules (BR) and heuristic algorithms (HA) to findfeasible solutions for a branch and bound (BB) algorithm used to solve sub-problems in a parallel two-phasebranch and bound (PTBB) approach. The nine PTBB algorithms, which are developed by varying 32combinations of BR and HA strategies, are tested on the facility location-transportation problem for disasterresponse (FLTDR). The mathematical model for the problem determines the number and location ofdistribution centres in a relief network, the amount of relief supplies to be stocked at each distribution centreand the vehicles to take the supplies in order to maximize the percentage of needs coverage of disaster victimsunder capacity restriction, transportation and budgetary constraints. To examine the performance of thealgorithms, computational experiments are conducted on the various sizes of generated problems. Threestrategies of BR and HA provided in the “intlinprog” function of MATLAB were applied for these problems.The objective function values and the computational times of all algorithms were collected and analyzed. Theresults showed that all PTBB algorithms can solve problem sizes of four candidate locations with fifteendemand points without premature termination by time. The PTBB algorithm using “maxfun” branching rulesand “rss” heuristic to find a feasible solution is recommended for FLTDR because of the least computationaltime usage.

Heuristic approaches for the multiperiod location-transportation problem with reuse of vehicles in emergency logistics

The coordination among the different actors in relief chains is crucial to provide effective and efficient response in emergency logistics. By recognizing this fact, we have developed two stochastic mixed-integer programming models to integrate and coordinate facility location, transportation and fleet sizing decisions in a multi-period, multi-commodity, and multi-modal context under uncertainty. One model even considers the option of reusing vehicles to cover extra routes within the same time period in an attempt to save overall resources and improve service levels. Typical uncertainty in victims׳ needs, incoming supply, inventory conditions, and roads availability are modeled through a set of scenarios representing plausible disaster impacts. To solve instances of practical size, we have devised relax-and-fix and fix-and-optimize heuristics based on decompositions by time, scenario, and stage. The proposed instances entail characteristics of the megadisaster in the Mountain Region of Rio de Janeiro State in Brazil. The results suggest that the integration of decisions in a multiperiod context and the option of reusing vehicles reduce total costs, thus improving the overall performance of the relief operations. Also, the time-decomposition fix-and-optimize heuristic outperforms the CPLEX solver in terms of elapsed times and optimality gaps, mainly in moderate-size instances. Finally, we show the importance to explicitly consider randomness instead of using simpler worst-case scenario approaches.

The impact of operations anticipations on the quality of stochastic location-allocation models

It is now a common practice to use optimization models, such as location-allocation models, to support the design of supply chain networks (SCN). The value creation potential of a SCN design must be evaluated in terms of capital expenditures, but also of the operating revenues and expenses incurred during the planning horizon considered. The design model used should therefore be formulated to anticipate these revenues and expenses (relatively) accurately over the planning horizon. In classical location-allocation models, the aggregate flow and throughput variables used yield very crude anticipations. It was never shown that they lead to the best SCN design that one should expect. This paper draws on the stochastic multi-period location-transportation problem (SMLTP) for studying the impact of various types of operations anticipations on the quality of the SCN designs obtained. Since accurate anticipations yield more complex models, solvability is also an issue. Several alternative SCN design models based on more detailed anticipations than the ones embedded in classical location-allocation models are proposed and tested. Accuracy-solvability trade-offs are explored and recommendations are made on the modeling strategy to use to get better SCN designs.

Applications of Parallel Computing for Facility Location-Transportation Problems for Disaster Response

This study extends the capability and increases the performance of a traditional Branch and Bound (BB) algorithm to solve Facility Location-Transportation problems for Disaster Response (FLTDR) using parallel computing. A Two-Stage Branch and Bound (TBB) algorithm was developed to support two parallel computing approaches. This algorithm divides problems into two small sub-problems, which are a facility location sub-problem and a transportation sub-problem. All possible numbers of distribution centers are determined. All possible locations relating to any number of distribution centers are explicitly explored. The transportation sub-problem corresponding to any selected location is then solved. Two parallel approaches for the TBB algorithm (PTBB) differ in partitioning the list of sub-problems. The first approach (PTBB1) solves both sub-problems in parallel. The other (PTBB2) explores the locations in sequence and solves only the transportation sub-problems in parallel. The numerical experiments were conducted on various sizes of generated problems. The quality of the solution and the computing time of both approaches were compared with a BB algorithm with premature termination by time. The experimental experiences showed that both PTBB1 and PTBB2 are more efficient and effective than a BB algorithm. However, the PTBB1 should be suggested for the FLTDR because of the least computational time usage.

A transportation-location problem model for pedestrian evacuation in chemical industrial parks disasters

A successful emergency management for chemical industrial parks (CIPs) accidents includes the route and shelter selection. Both of them are based on the collection of chemicals, atmosphere, geographic and population databases of CIPs. This decision process can be considered as a kind of transportation-location problem (TLP). In this paper, a conceptual model of emergency decision system for TLP of CIPs has been reported and a new multi-objective TLP model of pedestrian evacuation has also been proposed. The model includes sub-criteria, and the affected areas are categorized into a priority hierarchy based on human vulnerability model (HVM). The model can be used to design shelter places and guide the evacuation of the affected people. Besides, it can maximize the total time satisfaction level of evacuees combined with the routes passable probabilities. Finally, a case study shows that this model is flexible and applicable to various scenarios and risk measures.

An exact solution approach for multi-objective location–transportation problem for disaster response

This paper considers a three-objective location–transportation problem for disaster response. The location problem aims at determining the number, the position and the mission of required humanitarian aid distribution centers (HADC) within the disaster region. The transportation problem deals with the distribution of aid from HADCs to demand points. Three conflicting objectives are considered. The first objective minimizes the total transportation duration of needed products from the distribution centers to the demand points. The second objective minimizes the number of agents (first-aiders) needed to open and operate the selected distribution centers. The third objective minimizes the non-covered demand for all demand points within the affected area. We propose an epsilon-constraint method for this problem and prove that it generates the exact Pareto front. The proposed algorithm can be applied to any three-objective optimization problem provided that the problem involves at least two integer and conflicting objectives. The results obtained in our experimental study show that the computing time required by the proposed method may be large for some instances. A heuristic version of our algorithm yielded, however, good approximation of the Pareto front in relatively short computing times.

Solving two-stage robust optimization problems using a column-and-constraint generation method

In this paper, we present a column-and-constraint generation algorithm to solve two-stage robust optimization problems. Compared with existing Benders-style cutting plane methods, the column-and-constraint generation algorithm is a general procedure with a unified approach to deal with optimality and feasibility. A computational study on a two-stage robust location-transportation problem shows that it performs an order of magnitude faster.

Joint Location-Transportation Problem for Post-earthquake Initial Stage Based on Bi-level Programming

Joint Location-Transportation Problem for Post-earthquake Initial Stage Based on Bi-level Programming

Modeling approaches for the design of resilient supply networks under disruptions

This paper studies various modeling approaches to design resilient supply networks (SN) for the location–transportation problem under uncertainty. The future environment of the SN is shaped by random demands, and by disruptions perturbing depots capacity and ship-to-point demand processes. The paper proposes several stochastic programming models incorporating alternative resilience seeking formulations. A generic approach to model SN disruptions, and to elaborate and evaluate SN designs is also proposed. Experiments are made to compare the SN design models formulated, and recommendations are drawn on the approach to use to design effective and robust supply networks.

Robust location transportation problems under uncertain demands

In robust optimization, the multi-stage context (or dynamic decision-making) assumes that the information is revealed in stages. So, part of the decisions must be taken before knowing the real values of the uncertain parameters, and another part, called recourse decisions, is taken when the information is known. In this paper, we are interested in a robust version of the location transportation problem with an uncertain demand using a 2-stage formulation. The obtained robust formulation is a convex (not linear) program, and we apply a cutting plane algorithm to exactly solve the problem. At each iteration, we have to solve an NP-hard recourse problem in an exact way, which is time-consuming. Here, we go further in the analysis of the recourse problem of the location transportation problem. In particular, we propose a mixed integer program formulation to solve the quadratic recourse problem and we define a tight bound for this reformulation. We present an extensive computation analysis of the 2-stage robust location transportation problem. The proposed tight bound allows us to solve large size instances.

Recourse problem of the 2-stage robust location transportation problem

Abstract In this paper, we are interested in the recourse problem of the 2-stage robust location transportation problem. We propose a solution process using a mixed-integer formulation with an appropriate tight bound.