Competitive analysis of a dispatch policy for a dynamic multi-period routing problem

We analyze an on-line algorithm (dispatch policy) for a dynamic multi-period routing problem. The objective is to minimize the total cost over all periods. We show that the competitive ratio of this policy for instances with customers located on the non-negative real line is .     

A dynamic multi-objective location-allocation model for search and rescue assets

This paper presents a dynamic multi-objective mixed integer linear programming model to optimize the location and allocation of search and rescue (SAR) boats and helicopters to enhance the performance of maritime SAR missions. Our model incorporates simulated incident scenarios to account for demand uncertainty and allows relocation of vessels seasonally. We define three objectives as responding to incidents within a critical time, generating a balanced workload distribution among vessels of various types, and minimizing costs associated with operations and vessel relocations. Implementing a goal programming approach, we solve the problem for various objective function term weights and compare the performance of each solution with respect to 10 different metrics. Using historical incident datasets for the Aegean Sea, we show that the proposed model and solution approach can significantly improve the SAR performance and provide decision support for planners in developing effective and efficient resource location-allocation schemes.     

The \alpha -cost minimization model for capacitated facility location-allocation problem with uncertain demands

Facility location-allocation problem aims at determining the locations of some facilities to serve a set of spatially distributed customers and the allocation of each customer to the facilities such that the total transportation cost is minimized. In real life, the facility location-allocation problem often comes with uncertainty for lack of the information about the customers’ demands. Within the framework of uncertainty theory, this paper proposes an uncertain facility location-allocation model by means of chance-constraints, in which the customers’ demands are assumed to be uncertain variables. An equivalent crisp model is obtained via the \(\alpha \) -optimistic criterion of the total transportation cost. Besides, a hybrid intelligent algorithm is designed to solve the uncertain facility location-allocation problem, and its viability and effectiveness are illustrated by a numerical example.     

Optimal transport and a bilevel location-allocation problem

In this paper a two-stage optimization model is studied to find the optimal location of new facilities and the optimal partition of the consumers (location-allocation problem). The social planner minimizes the social costs, i.e. the fixed costs plus the waiting time costs, taking into account that the citizens are partitioned in the region according to minimizing the capacity costs plus the distribution costs in the service regions. By using optimal transport tools, existence results of solutions to the location-allocation problem are presented together with some examples.     

Queueing network model for a single-operator machine interference problem with external operations

Machine interference is a significant problem in many manufacturing systems. Prior research shows that machine interference may be as high as 10% of machine time. This paper proposes a queueing network model for a single-operator, machine interference problem with external operations, i.e., those tasks that can be completed while the machine is running. The interactions for part/machine and machine/operator are modeled as an open and a closed queueing network, respectively. In the open network, part inter-arrival time follows an exponential distribution. In both networks, service times follow a general distribution that is characterized by their first two moments. An iterative procedure is developed to solve the proposed model. Solution quality is justified by an industry-based case study. Data were collected from the integrated circuit (IC) ink-marking machines of a leading IC packaging company in Taiwan that allowed the construction of an experimental design for computational tests that encompassed a wide range of production scenarios. Empirical results show promise for the proposed methodology in helping to solve industrial problems. Model limitations as well as future research opportunities are discussed.     

A location-allocation problem in a large Belgian brewery

This paper discusses the depot location problem of a large Belgian brewery. Emphasis is on practical problems encountered in the course of the study (e.g. data gathering, estimating distances, etc.). Both a discrete location model (Dualoc) and a continuous model developed in-house (GRAVLOC) were used to perform the analysis. Both models indicated substantial savings to be obtained by relocating some depots and by reallocating customers to depots.     

Heuristic algorithms for a multi-period multi-stop transportation planning problem

We consider a multi-period multi-stop transportation planning problem (MPMSTP) in a one-warehouse multi-retailer distribution system where a fleet of homogeneous vehicles delivers products from a warehouse to retailers. The objective of the MPMSTP is to minimize the total transportation distance for product delivery over the planning horizon while satisfying demands of the retailers. We suggest two heuristic algorithms based on the column generation method and the simulated annealing algorithm. Computational experiments on randomly generated test problems showed that the suggested algorithms gave better solutions than an algorithm currently used in practice and algorithms modified from existing algorithms for vehicle routing problems.     

Constructive heuristics for the uncapacitated continuous location-allocation problem

The multisource location-allocation problem in continuous space is investigated. Two constructive heuristic techniques are proposed to solve this problem. Both methods are based on designing suitable schemes for the generation of the initial solutions. The first considers the furthest distance rule and is enhanced by schemes borrowed from tabu search such as constructing the forbidden regions and freeing strategy. The second considers the discrete solutions found when solving the p-median problem. Some results on existing test problems are presented.     

价格数量折扣下多阶段报童问题的在线策略

价格数量折扣可以提高订购量, 是库存决策中的一个重要因素. 特别地, 当订购量达到一定水平时, 价格折扣才会发生. 应用理论计算机科学兴起的弱集成算法, 研究具有这种价格数量折扣的多阶段报童问题的在线策略. 弱集成算法是一种在线序列决策算法, 其主要特点是不对未来输入做任何统计假设, 克服了报童问题研究中需要对需求做概率假设的困难. 主要将弱集成算法应用到固定订购量的专家策略, 给出了价格数量折扣下多阶段报童问题的具体在线策略;得到了该在线策略相对于最优专家策略的理论保证. 进一步将回收价值和缺货损失费引入, 给出了推广的在线策略及其理论结果. 最后应用数值算例说明了给出的在线策略具有较好的竞争性能.     

An optimal birth control problem for a dynamical population model with size-structure

This work is concerned with an optimal control problem for a size-structured population model, which takes fertility as the control variable. The existence and uniqueness of solutions to the basic state system and the dual system are proven via the Banach fixed point theorem. Necessary optimality conditions of first order are established in the form of an Euler-Lagrange system by the use of tangent-normal cone technique. The existence of a unique optimal controller is established by means of Ekeland’s variational principle. An example and some comments are presented.     

An efficient heuristic approach for a multi-period logistics network redesign problem

In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities, product flows between facilities in the same echelon, direct shipments to customers, and facility relocation. A two-phase heuristic approach is proposed to obtain high-quality feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first phase of the heuristic, a linear programming rounding strategy is applied to find initial values for the binary location variables. The second phase of the heuristic uses local search to correct the initial variable choices when a feasible solution is not identified, or to improve the initial feasible solution when its quality does not meet given criteria. The results of a computational study are reported for randomly generated instances comprising a variety of logistics networks.     

Numerical method for solving an inverse problem for a population model

The inverse problem of determining the growth rate coefficient of biological objects from additional information on their time-dependent density is considered. Two nonlinear integral equations are derived for the unknown coefficient, which is determined on part of its domain from one equation and on the remaining part from the other equation. The nonlinear integral equations are solved by iterative methods. The convergence conditions for the iterative methods are formulated, and results of numerical experiments are presented.     

Model and algorithms for multi-period sea cargo mix problem

In this paper, we consider the sea cargo mix problem in international ocean container shipping industry. We describe the characteristics of the cargo mix problem for the carrier in a multi-period planning horizon, and formulate it as a multi-dimensional multiple knapsack problem (MDMKP). In particular, the MDMKP is an optimization model that maximizes the total profit generated by all freight bookings accepted in a multi-period planning horizon subject to the limited shipping capacities. We propose two heuristic algorithms that can solve large scale problems with tens of thousands of decision variables in a short time. Finally, numerical experiments on a wide range of randomly generated problem instances are conducted to demonstrate the efficiency of the algorithms.     

An analytic solution for multi-period uncertain portfolio selection problem

Fuzzy Optimization and Decision Making - The return rates of risky assets in financial markets are usually assumed as random variables or fuzzy variables. For the ever-changing real asset market,...     

Hopf bifurcation in a size-structured population dynamic model with random growth

This paper is devoted to the study of a size-structured model with Ricker type birth function as well as random fluctuation in the growth process. The complete model takes the form of a reaction-diffusion equation with a nonlinear and nonlocal boundary condition. We study some dynamical properties of the model by using the theory of integrated semigroups. It is shown that Hopf bifurcation occurs at a positive steady state of the model. This problem is new and is related to the center manifold theory developed recently in [P. Magal, S. Ruan, Center manifold theorem for semilinear equations with non-dense domain and applications to Hopf bifurcation in age-structured models, Mem. Amer. Math. Soc., in press] for semilinear equation with non-densely defined operators.     

An approximation-based approach for fuzzy multi-period production planning problem with credibility objective

This paper develops a fuzzy multi-period production planning and sourcing problem with credibility objective, in which a manufacturer has a number of plants or subcontractors. According to the credibility service levels set by customers in advance, the manufacturer has to satisfy different product demands. In the proposed production problem, production cost, inventory cost and product demands are uncertain and characterized by fuzzy variables. The problem is to determine when and how many products are manufactured so as to maximize the credibility of the fuzzy costs not exceeding a given allowable invested capital, and this credibility can be regarded as the investment risk criteria in fuzzy decision systems. In the case when the fuzzy parameters are mutually independent gamma distributions, we can turn the service level constraints into their equivalent deterministic forms. However, in this situation the exact analytical expression for the credibility objective is unavailable, thus conventional optimization algorithms cannot be used to solve our production planning problems. To overcome this obstacle, we adopt an approximation scheme to compute the credibility objective, and deal with the convergence about the computational method. Furthermore, we develop two heuristic solution methods. The first is a combination of the approximation method and a particle swarm optimization (PSO) algorithm, and the second is a hybrid algorithm by integrating the approximation method, a neural network (NN), and the PSO algorithm. Finally, we consider one 6-product source, 6-period production planning problem, and compare the effectiveness of two algorithms via numerical experiments.     

A multi-period network design problem for cellular telecommunication systems

Mathematical Programming models for multi-period network design problems, which arise in cellular telecommunication systems are presented. The underlying network topologies range from a simple star to complex multi-layer Steiner-like networks. Linear programming, Lagrangian relaxation, and branch-and-cut heuristics are proposed and a polynomial-bounded heuristic based on an interior point linear programming implementation is described. Extensive computational results are presented on a number of randomly generated problem sets and the performance of the heuristic(s) are compared with an optimal branch-and-bound algorithm.     

An algorithm for solving the multi-period online fulfillment assignment problem

This paper develops an optimal solution procedure for the multi-period online fulfillment assignment problem to determine how many and which of a retailer/e-tailer’s capacitated regional warehouse locations should be set up to handle online sales over a finite planning horizon. To reduce the number of candidate solutions in each period, dominance rules from the facility location literature are extended to handle the nonlinear holding and backorder cost implications of our problem. Computational results indicate that multi-period considerations can play a major role in determining the optimal set of online fulfillment locations. In 92% of our test problems, the multi-period solution incorporated fewer openings and closings than myopic single period solutions. To illustrate the use of the model under changing demands, the multi-period solution yielded different supply chain configurations than the myopic single period solution in over 37% of the periods.     

A multi-period inventory model with multi-dimensional procurement bidding

We consider a multi-period inventory model with raw material procurements carried out via a reverse auction. Bids are multi-dimensional, and they consist of supplier information of price, shortage quantity and lead time. This work is an extension of our earlier work that has focused on multi-dimensional procurement auctions in single-period inventory models, to multi-period settings. The new model is based on a hybrid approach combining stochastic dynamic programming and simulation.