Yiyong Xiao

Development of a fuel consumption optimization model for the capacitated vehicle routing problem

Fuel consumption accounts for a large and increasing part of transportation costs. In this paper, the Fuel Consumption Rate (FCR), a factor considered as a load dependant function, is added to the classical capacitated vehicle routing problem (CVRP) to extend traditional studies on CVRP with the objective of minimizing fuel consumption. We present a mathematical optimization model to formally characterize the FCR considered CVRP (FCVRP) as well as a string based version for calculation. A simulated annealing algorithm with a hybrid exchange rule is developed to solve FCVRP and shows good performance on both the traditional CVRP and the FCVRP in substantial computation experiments. The results of the experiments show that the FCVRP model can reduce fuel consumption by 5% on average compared to the CVRP model. Factors causing the variation in fuel consumption are also identified and discussed in this study.

Deterministic EOQ with partial backordering and correlated demand caused by cross-selling

There has been much work regarding the deterministic EOQ with partial backordering. The majority of these studies assume no correlation in sales, so independent demands across items is applied in the models. However, it is generally recognized that cross-selling effects between items often appear in real contexts. Thus, incorporating such effects in the inventory model in the form of correlated demands makes it of more practical relevance. In this paper, the authors address a two-item inventory system where the demand of a minor item is correlated to that of a major item because of cross-selling. We firstly present a two-item EOQ model with identical order cycles, where the unmet demand of the major item can be partially backordered with lost sales whereas the demand of the minor item must be met without stockouts. This model is further extended to fit a more practical case where the order cycle of the major item is an integer multiple of that of the minor item. The optimal solutions of the two models, as well as the inventory decision procedures, are also developed. Comparative analysis on these two EOQ models has been drawn in the computational study which presents some insights into the parameter effect on the optimal inventory policy.

The activity-based aggregate production planning with capacity expansion in manufacturing systems

This paper builds a mixed integer linear programming (MILP) model to mathematically characterize the problem of aggregate production planning (APP) with capacity expansion in a manufacturing system including multiple activity centers. We use the heuristic based on capacity shifting with linear relaxation to solve the model. Two linear relaxations, i.e., a complete linear relaxation (CLR) on all the integer variables and a partial linear relaxation (PLR) on part of the integer variables are investigated and compared in computational experiments. The computational results show that the heuristic based on the capacity shifting with CLR is very fast but yields low-quality solution whereas the capacity shifting with PLR provides high-quality solutions but at the cost of considerable computational time. As a result, we develop a hybrid heuristic combining beam search with capacity shifting, which is capable of producing a high-quality solution within reasonable computational time. The computational experiment on large-scale problems suggests that when solving a practical activity-based APP model with capacity expansion at the industrial level, the capacity shifting with CLR is preferable, and the beam search heuristic could be subsequently utilized as an alternative if the relaxation gap is larger than the acceptable deviation.

Non-permutation flow shop scheduling with order acceptance and weighted tardiness

Model the problem of non-permutation flow shop scheduling with order acceptance.The model is transformed to linear MIP that is optimally solved by commercial solver.Theorems that are favorable for developing algorithms are presented.An efficient two-phase genetic algorithm (TP-GA) is proposed.The heuristic yields high quality non-permutation solutions. This paper studies the non-permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness (FSS-OAWT). We formulate the problem as a linear mixed integer programming (LMIP) model that can be optimally solved by AMPL/CPLEX for small-sized problems. In addition, a non-linear integer programming (NIP) model is presented to design heuristic algorithms. A two-phase genetic algorithm (TP-GA) is developed to solve the problem of medium and large sizes based on the NIP model. The properties of FSS-OAWT are investigated and several theorems for permutation and non-permutation optimum are provided. The performance of the TP-GA is studied through rigorous computational experiments using a large number of numeric instances. The LMIP model is used to demonstrate the differences between permutation and non-permutation solutions to the FSS-OAWT problem. The results show that a considerably large portion of the instances have only an optimal non-permutation schedule (e.g., 43.3% for small-sized), and the proposed TP-GA algorithms are effective in solving the FSS-OAWT problems of various scales (small, medium, and large) with both permutation and non-permutation solutions.

A simulating annealing algorithm to solve the green vehicle routing & scheduling problem with hierarchical objectives and weighted tardiness

A new mathematical model is developed to reduce CO2 emissions for vehicle routing.A simulating annealing algorithm is introduced to solve large-sized problems.CO2 emissions can be reduced by taking traffic congestion into account in vehicle routes.Distance/time-based schedules do not always reduce emissions under varying traffic conditions.The proposed model is tested on simulated real-life cases. We present a green vehicle routing and scheduling problem (GVRSP) considering general time-dependent traffic conditions with the primary objective of minimizing CO2 emissions and weighted tardiness. A new mathematical formulation is proposed to describe the GVRSP with hierarchical objectives and weighted tardiness. The proposed formulation is an alternative formulation of the GVRSP in the way that a vehicle is allowed to travel an arc in multiple time periods. The schedule of a vehicle is determined based on the actual distance that the vehicle travels each arc in each time period instead of the time point when the vehicle departs from each node. Thereby, more general time dependent traffic patterns can be considered in the model. The proposed formulation is studied using various objectives functions, such as minimizing the total CO2 emissions, the total travel distance, and the total travel time. Computational results show that up to 50% reduction in CO2 emissions can be achieved with average reductions of 12% and 28% compared to distance-oriented solutions and travel-time-oriented solutions, respectively. In addition, a simulated annealing (SA) algorithm is introduced to solve large-sized problem instances. To reduce the search space, the SA algorithm searches only for vehicle routes and rough schedules, and a straightforward heuristic procedure is used to determine near-optimal detailed schedules for a given set of routes. The performance of the SA algorithm is tested on large-sized problems with up to 100 nodes and 10 time periods.

Variable neighbourhood simulated annealing algorithm for capacitated vehicle routing problems

This article presents the variable neighbourhood simulated annealing (VNSA) algorithm, a variant of the variable neighbourhood search (VNS) combined with simulated annealing (SA), for efficiently solving capacitated vehicle routing problems (CVRPs). In the new algorithm, the deterministic ‘Move or not’ criterion of the original VNS algorithm regarding the incumbent replacement is replaced by an SA probability, and the neighbourhood shifting of the original VNS (from near to far by k← k+1) is replaced by a neighbourhood shaking procedure following a specified rule. The geographical neighbourhood structure is introduced in constructing the neighbourhood structures for the CVRP of the string model. The proposed algorithm is tested against 39 well-known benchmark CVRP instances of different scales (small/middle, large, very large). The results show that the VNSA algorithm outperforms most existing algorithms in terms of computational effectiveness and efficiency, showing good performance in solving large and very large CVRPs.

A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems

In this study, we improved the variable neighborhood search (VNS) algorithm for solving uncapacitated multilevel lot-sizing (MLLS) problems. The improvement is twofold. First, we developed an effective local search method known as the Ancestors Depth-first Traversal Search (ADTS), which can be embedded in the VNS to significantly improve the solution quality. Second, we proposed a common and efficient approach for the rapid calculation of the cost change for the VNS and other generate-and-test algorithms. The new VNS algorithm was tested against 176 benchmark problems of different scales (small, medium, and large). The experimental results show that the new VNS algorithm outperforms all of the existing algorithms in the literature for solving uncapacitated MLLS problems because it was able to find all optimal solutions (100%) for 96 small-sized problems and new best-known solutions for 5 of 40 medium-sized problems and for 30 of 40 large-sized problems.

Neighborhood search techniques for solving uncapacitated multilevel lot-sizing problems

In this paper, several neighborhood search techniques for solving uncapacitated multilevel lot-sizing problems are investigated. We introduce three indexes: distance, changing range, and changing level that have great influence on the searching efficacy of neighborhood search techniques. These insights can help develop more efficient heuristic algorithms. As a result, we have developed an iterated neighborhood search (INS) algorithm that is very simple but that demonstrates good performance when tested against 176 benchmark instances under different scales (small, medium, and large), with 25 instances having been updated with new best known solutions in the computing experiments.

The Deterministic Annealing Algorithms for Vehicle Routing Problems

Two direction guided annealing modifications to the traditional simulated annealing algorithm for solving the Vehicle Routing Problems (VRP) are proposed in this paper. The aim is to avoid searching solution space where the optimal solutions are not likely to be in. The string model of the VRP is adopted in these algorithms. The first approach is called the probability-based guided annealing algorithm, in which guide coefficients are formulated as probabilities for breaking and establishing connections between nodes. Based on these coefficients, a formulation is proposed to decide whether a stochastically generated exchange request between nodes is accepted for further computation or not. A detailed description of the algorithm is given. The algorithm is then implemented to solve a 100 shops capacitated VRP(CVRP). Three commonly used exchange rules are used for testing the performance of the algorithm: 1 to 1, random-insert, and 2-opt. Both computation time and distribution of the optimization cost function are measured and compared among the three exchange rules. Comparisons are also made with the traditional simulated annealing algorithm to contrast the superior efficiency of the new algorithm. Another guided annealing algorithm introduced in the paper is the pair-wise competitive annealing algorithm. The top N distances measured from each customer to surrounding nodes are chosen for the purpose of generating new solution states by the 2-opt exchange rule. The effective search space is decreased by only examining a smaller array containing the distance relationships for potentially shorter routes, when compared to straight-forward implementation of the traditional simulated annealing. A detailed listing of the algorithm is given, which is then implemented to solve the CVRP computationally. Similar experimental setups to the probability-based guided annealing algorithm are used. The given results show that the algorithm yields better solutions than that of the traditional simulated annealing, and with a much reduced computation time. Considerations and justifications on choosing the parameter N are also given.

The establishment of a preventive maintenance period optimum model

Based on analysis of the reliability of weapons system under the conditions of variable maintenance period, the number of maintenance and failure under the conditions of the minimum acceptable reliability, and the relationship between the preventive maintenance cost and the corrective maintenance cost, an optimization model of equipment maintenance period is established. A computational experiment shows that this model provides a rational approach to determine reasonable maintenance period and maintenance management decision-making.