Incorporating supplier selection and order allocation into the vehicle routing and multi-cross-dock scheduling problem

In the vehicle routing problem with cross-docking (VRPCD), it is assumed that the selected suppliers and the quantity of the products purchased from each supplier are known. This paper presents an MILP model which incorporates supplier selection and order allocation into the VRPCD in a multi-cross-dock system minimising the total costs, including purchasing, transportation, cross-docking, inventory and early/tardy delivery penalty costs. The sensitivity of the model on the key parameters of the objective function is analysed and the supply decisions are evaluated when the coefficients of the distribution cost are changed. A two-stage solution algorithm (TSSA) is proposed and the results of the TSSA for small-sized instances are compared with the exact solutions. Finally, a large-sized real case of an urban freight transport is solved using the TSSA.     

A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.     

A mathematical model for vehicle routing problem under endogenous uncertainty

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.     

A coordinated algorithm for integrated production scheduling and vehicle routing problem

In this paper, the integrated production scheduling and vehicle routing problem is considered for a Make-to-Order manufacturer, who has a single machine for production and limited vehicles with capacity constraints for transportation. The objective is to determine production scheduling and vehicle routing, which are two interacted decisions, to minimise the maximum order delivery time. A property on optimal production sequence is proposed first, based on which backward and forward batching methods are developed and are embedded into a proposed genetic algorithm. The proposed genetic algorithm is capable of providing high-quality solutions by determining the two decisions simultaneously. For comparison purpose, a two-stage algorithm is developed, which decomposes the overall problem into two successively solved sub-problems. The experiments show that the proposed genetic algorithm can provide higher quality solutions than the proposed two-stage algorithm and two published algorithms studying related problems.     

Integrated multi-factory production and distribution scheduling applying vehicle routing approach

This paper introduces a new integrated multi-factory production and distribution scheduling problem in supply chain management. This supply chain consists of a number of factories joined together in a network configuration. The factories produce intermediate or finished products and supply them to other factories or to end customers that are distributed in various geographical zones. The problem consists of finding a production schedule together with a vehicle routing solution simultaneously to minimise the sum of tardiness cost and transportation cost. A mixed-integer programming model is developed to tackle the small-sized problems using CPLEX, optimally. Due to the NP-hardness, to deal with medium- and large-sized instances, this paper develops a novel Improved Imperialist Competitive Algorithm (IICA) employing a local search based on simulated annealing algorithm. Performance of the proposed IICA is compared with the optimal solution and also with four variants of population-based metaheuristics: Imperialist Competitive Algorithm, Genetic Algorithm, Particle Swarm Optimisation (PSO), and Improved PSO. Based on the computational results, it is statistically shown that quality of the IICA’s solutions is the same as optimal ones solving small problems. It also outperforms other algorithms in finding near-optimal solutions dealing with medium and large instances in a reasonably short running time.     

A cloud theory-based particle swarm optimization for multiple decision maker vehicle routing problems with fuzzy random time windows

This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.     

Cash transportation vehicle routing and scheduling under stochastic travel times

Stochastic disturbances occurring in real-world operations could have a significant influence on the planned routing and scheduling results of cash transportation vehicles. In this study, a time–space network flow technique is utilized to construct a cash transportation vehicle routing and scheduling model incorporating stochastic travel times. In addition, to help security carriers to formulate more flexible routes and schedules, a concept of the similarity of time and space for vehicle routing and scheduling is incorporated into the model. The test results show that the model could be useful for security carriers in actual practice.     

Multi-objective optimization for the multi-mode finance-based project scheduling problem

The finance-based scheduling problem (FBSP) is about scheduling project activities without exceeding a credit line financing limit. The FBSP is extended to consider different execution modes that result in the multi-mode FBSP (MMFBSP). Unfortunately, researchers have abandoned the development of exact models to solve the FBSP and its extensions. Instead, researchers have heavily relied on the use of heuristics and meta-heuristics, which do not guarantee solution optimality. No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP. CPLEX, which is an exact solver, has witnessed a significant decrease in its computation time. Moreover, its current version, CPLEX 12.9, solves multi-objective optimization problems. This study presents a mixed-integer linear programming model for the multi-objective MMFBSP. Using CPLEX 12.9, we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP. We test our model by solving several problems from the literature. We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases. The small increase in computation time compared with possible cost savings make exact models a must for practitioners. Moreover, the linear programming-relaxation of the model, which takes seconds, can provide an excellent lower bound.     

A fuzzy linear programming approach for municipal solid-waste management under uncertainty

In this study, a fuzzy linear programming (FLP) method is developed for dealing with uncertainties expressed as fuzzy sets that exist in the constraints’ left-hand and right-hand sides and the objective function. A direct transforming algorithm is advanced for solving the FLP model that improves upon the existing method through provision of a quantitative expression for uncertain relationships among a large number of fuzzy sets. The proposed solution method can greatly reduce computational requirements, which is particularly meaningful for the application of FLP to large-scale practical problems with many fuzzy sets. The developed FLP method is applied to a case of long-term waste-management planning. The results indicate that reasonable solutions have been obtained. They can be used for generating decision alternatives and to help managers identify desired policies for waste management under uncertainty. Compared with the conventional interval-parameter linear programming approach, FLP can provide more information for solutions, containing not only the lower and upper bounds but also the most possible value for decision variables and objective function.     

A mixed-integer programming approach to the parallel replacement problem under technological change

The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement policies for each asset in a group of assets that operate in parallel and are subject to fixed and variable purchase costs. We study the mixed-integer programming formulation of PRES under technological change by incorporating capacity gains into the model such that newer, technologically advanced assets have higher capacity than assets purchased earlier. We provide optimal solution characteristics and insights about the economics of the problem and derive associated cutting planes for optimising the problem. Computational experiments illustrate that the inequalities are quite effective in solving PRES under technological change instances.     

On the integer programming formulation of production scheduling optimisation algorithm for the hot rolling processes

This note is concerned with the formulation of scheduling of the hot rolling process (SHRP). Based on the capacitated vehicle routing problem (CVRP), Chen et al. (Chen, A.L., Yang, G.K., and Wu, Z.M., 2008. Production scheduling optimization algorithm for the hot rolling processes. International Journal of Production Research, 46 (7), 1955–1973) proposed a nonlinear integer programming formulation of SHRP. Due to some deficiencies in the formulation, Kim (Kim, B.-I., 2010. Some comments on Chen et al. ‘Production scheduling optimization algorithm for the hot rolling processes’. International Journal of Production Research, 48 (7), 2165–2167) very recently gave some correction to the model. However, even with the correction the model has flaws. The purpose of this note is to give a complete, also based on CVRP, corrected formulation with substantial number of variables reduced.     

A vehicle routing problem with time windows and stochastic demands

Abstract

This study presents an approach for considering a vehicle routing problem where customers’ pickup demands are uncertain and require serving within some settled time windows. Customers’ demands are assumed to follow given discrete probability distributions. This study proposes a nonlinear stochastic integer program with recourse to formulate the vehicle routing problem with stochastic demands and time windows (VRPTW‐SD, for short). The objective of the VRPTW‐SD is to minimize the total cost of the first‐stage solution and expected recourse cost of the second‐stage solution. The total cost of the first‐stage problem includes the total travel cost for all links and the total waiting cost at all nodes. When a vehicle capacity is attained or exceeded, recourse actions are needed and recourse costs incurred in order to finish the planned route schedules. Two categories of schedule failure are introduced in this work; the recourse costs derive from the variations in travel time travel time, waiting time, and penalties of late arrival for time windows. In addition, an optimization algorithm is developed for solving the VRPTW‐SD, according to the framework of the L‐shaped method. Numerical results are given to demonstrate its validity.     

Improved mixed-integer linear programming model and heuristics for bi-objective single-machine batch scheduling with energy cost consideration

This article addresses bi-objective single-machine batch scheduling under time-of-use electricity prices to minimize the total energy cost and the makespan. The lower and upper bounds on the number of formed batches are first derived and a continuous-time mixed-integer linear programming model is proposed, which improves an existing discrete-time model in the literature. Two improved heuristics are proposed based on the improved model. Computational experiments demonstrate that the improved model and heuristics can run hundreds of times faster than the existing ones for large-size instances.     

A robust scheduling for the multi-mode project scheduling problem with a given deadline under uncertainty of activity duration

The problem of this paper deals with the multi-mode project scheduling problem under uncertainty of activity duration where only the renewable resources are taken into account and a given deadline has to be met at the cost of recruiting additional resources. A heuristic algorithm is employed to solve this problem, and to maintain the robustness of the baseline schedule, the concept of critical chain project management (CCPM) is applied in which a new definition to resource buffer is considered. A simulation methodology is used to determine the size and location of resource buffers in the schedules in which three different buffer sizes and three different uncertainty levels are considered. Results and analysis of the simulation outcomes illustrate that resource buffers are useful and should be simulated by the CCPM schedules, as they help to decrease the total duration of the project during implementation and meet the deadline of the project with more assurance.     

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.     

A fuzzy goal programming model for the simple U-line balancing problem with multiple objectives

A fuzzy goal programming model for the simple U-line balancing (SULB) problem with multiple objectives is presented. In real life applications of the SULB problem with multiple objectives, it is difficult for the decision-maker(s) to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore a fuzzy goal programming model is developed for this purpose. The proposed model is the first fuzzy multi-objective decision-making approach to the SULB problem with multiple objectives which aims at simultaneously optimizing several conflicting goals. The proposed model is illustrated using an example. A computational study is conducted by solving a large number of test problems to investigate the relationship between the fuzzy goals and to compare them with the goal programming model proposed by Gökçen and A?pak (Gökçen, H. and A?pak, K., European Journal of Operational Research, 171, 577–585, 2006). The results of the computational study show that the proposed model is more realistic than the existing models for the SULB problem with multiple objectives and also provides increased flexibility for the decision-maker(s) to determine different alternatives.     

Study on the vehicle routing problem considering congestion and emission factors

To meet the requirement of greening transportation in poor traffic condition, vehicle routing problem (VRP) with consideration of fuel consumption and congestion is studied. We formulated a time-dependent green vehicle routing problem (TD-GVRP) model with minimised total cost as the objective function which includes fuel consumption cost, and the measurement of fuel consumption is based on the Comprehensive Modal Emissions Model (CMEM). In the model, the situation of waiting at customer nodes to avoid bad traffic is defined. To solve this model, a Response Surface Method (RSM)-based hybrid algorithm (HA) that combines genetic algorithm (GA) and particle swarm optimisation (PSO) is constructed. Finally, using instances from PRPLIB database, the following experiments are carried out and the corresponding conclusions are drawn. (i) Comparison of the proposed objective and traditional VRP objectives shows that fuel consumption can be greatly reduced by introducing fuel consumption factor into the objective function. (ii) Sensitivity analysis of congestion duration provides the influence of congestion duration on fuel consumption and travel time. (iii) Experiments based on different waiting time reveal that the optimisation of departure time can reduce fuel consumption and total cost to some extent.     

Field services design and management of natural gas distribution networks: a class of vehicle routing problem with time windows approach

Service operations management of metropolitan gas networks at operational level implies the optimisation of decisions related to logistic activities, taking into account multi-objectives and operational constraints. This paper proposes a metaheuristic approach for the operational planning of the daily logistic activities based on vehicle routing with time window model. Experimental results for a real planning case in a gas distribution network demonstrate the approach effectiveness.     

A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty

This article presents a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm for solving an inventory management problem for large-scale construction projects under a fuzzy random environment. By taking into account the purchasing behaviour and strategy under rules of international bidding, a multi-objective fuzzy random dynamic programming model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform fuzzy random parameters into fuzzy variables that are subsequently defuzzified by using an expected value operator with optimistic–pessimistic index. The iterative nature of the authors’ model motivates them to develop a DP-based PSO algorithm. More specifically, their approach treats the state variables as hidden parameters. This in turn eliminates many redundant feasibility checks during initialization and particle updates at each iteration. Results and sensitivity analysis are presented to highlight the performance of the authors’ optimization method, which is very effective as compared to the standard PSO algorithm.     

A mixed-integer programming formulation and Lagrangean relaxation for the cross-dock door assignment problem

In a cross-dock, goods are unloaded from incoming trucks, consolidated according to their destinations, and then, loaded into outgoing trucks with little or no storage in between. In this paper, we study the cross-dock door assignment problem in which the assignment of incoming trucks to strip doors, and outgoing trucks to stack doors is determined, with the objective of minimising the total material handling cost. We present a new mixed integer programming formulation which is embedded into a Lagrangean relaxation that exploits the special structure of the problem to obtain bounds on the optimal solution value. A primal heuristic is used at every iteration of the Lagrangean relaxation to obtain high quality feasible solutions. Computational results obtained on benchmark instances (with up to 20 origins and destinations, and 10 strip and stack doors) and on a new and more difficult set of instances (with up to 50 origins and destinations, and 30 strip and stack doors) confirm the efficiency of the algorithm.