A Greedy Heuristic for a Three-Level Multi-Period Single-Sourcing Problem

In this paper we consider a model for integrating transportation and inventory decisions in a three-level logistics network consisting of plants, warehouses, and retailers (or customers). Our model includes production and throughout capacity constraints, and minimizes production, holding, and tansportation costs in a dynamic environment. We show that the problem can be reformulated as a certain type of assignment problem with convex objective function. Based on this observation, we propose a greedy heuristic for the problem, and illustrate its behaviour on a class of randomly generated problem instances. These experiments suggest that the heuristic may be asymptotically feasible and optimal with probability one in the number of customers

Routing trains through railway stations: complexity issues

In this paper we consider the problem of routing trains through railway stations. This problem occurs as a subproblem in the project DONS that is currently being carried out under the supervision of Railned and Netherlands Railways. The project DONS involves the determination of the required future capacity of the Dutch railway infrastructure. In this paper we focus on the computational complexity of the problem of routing trains through railway stations. After an extensive description of the problem, we show that only a subset of the sections and routes of a railway station needs to be taken into account. Then we show that the routing problem is NP-complete as soon as each train has three routing possibilities. However, if each train has only two routing possibilities, then the problem can be solved in an amount of time that is polynomial in the number of trains. Furthermore, if the layout of the railway station is fixed, then the latter is also the case for the problem of finding an assignment of a maximum number of trains to routes that is feasible from a safety point of view. This result can be extended to the case where coupling and uncoupling of trains, certain service considerations, and a cyclic timetable have to be taken into account

Mitigating the Cost of Anarchy in Supply Chain Systems

In a decentralized two-stage supply chain where a supplier serves a retailer who, in turn, serves end customers, operations decisions based on local incentives often lead to suboptimal system performance. Operating decisions based on local incentives may in such cases lead to a degree of system disorder or anarchy, wherein one party's decisions put the other party and/or the system at a disadvantage. While models and mechanisms for such problem classes have been considered in the literature, little work to date has considered such problems under nonstationary demands and fixed replenishment order costs. This paper models such two-stage problems as a class of Stackelberg games where the supplier announces a set of time-phased ordering costs to the retailer over a discrete time horizon of finite length, and the retailer then creates an order plan, which then serves as the supplier's demand. We provide metrics for characterizing the degree of efficiency (and anarchy) associated with a solution, and provide a set of easily understood and implemented mechanisms that can increase this efficiency and reduce the negative impacts of anarchic decisions

Polynomial Time Algorithms For Some Multi-Level Lot-Sizing Problems With Production Capacities

We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated, in the presence of production capacities and for different transportation cost functions. The model we study is a generalization of the traditional single-item economic lot-sizing model, adding stationary production capacities at the manufacturer, as well as multiple intermediate storage levels (including the retailer level), and transportation between these levels. Allowing for general concave production costs and linear holding costs, we provide polynomialtime algorithms for the cases where the transportation costs are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. The running times of the algorithms are remarkably insensitive to the number of levels in the supply chain

Integrated market selection and production planning: complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier's ability to in°uence demand characteristics can lead to an improved match between supply and demand. This paper presents a new class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is NP-complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very effcient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances

Routing Trains through railway stations: model formulation and algorithms

In this paper we consider the problem of routing trains through railway stations. This problem occurs as a subproblem in a project which the authors are carrying out in cooperation with the Dutch railways. The project involves the analysis of future infrastructural capacity requirements in the Dutch railway network, Part of this project is the automatic generation and evaluation of timetables. To generate a timetable a hierarchical approach is followed: at the upper level in the hierarchy a tentative timetable is generated, taking into account the specific scheduling problems of the trains at the railway stations at an aggregate level. At the lower level in the hierarchy it is checked whether the tentative timetable is feasible with respect to the safety rules and the connection requirements at the stations. To carry out this consistency cheek, detailed schedules for the trains at the railway yards have to be generated. In this paper we present a mathematical model formulation for this detailed scheduling problem, based on the Node Packing Problem (NPP). Furthermore, we describe a solution procedure for the problem, based on a branch-and-cut approach. The approach is tested in an empirical study with data from the station of Zwolle in The Netherlands

A branch and price algorithm for the multi-period single-sourcing problem

In this paper we propose a Branch and Price algorithm for solving multi-period single-sourcing problems. In particular, we generalize a Branch and Price algorithm that was developed for the Generalized Assignment Problem (GAP) to a class of convex assignment problems. We then identify an important subclass of problems, containing many variants of the multi-period single-sourcing problem (MPSSP), as well as variants of the GAP, for which we derive an efficient solution procedure for the pricing problem, a critical factor in the efficiency of the Branch and Price algorithm. We execute an extensive numerical comparison between the performances of the Branch and Price algorithm and the MIP solver of CPLEX for a particular variant of the MPSSP

A Branch and Price Algorithm for the Multi-Period Single-Sourcing Problem

In this paper we propose a Branch and Price algorithm for solving multi-period single-sourcing problems. In particular, we generalize a Branch and Price algorithm that was developed for the Generalized Assignment Problem (GAP) to a class of convex assignment problems. We then identify an important subclass of problems, containing many variants of the multi-period single-sourcing problem (MPSSP), as well as variants of the GAP, for which we derive an efficient solution procedure for the pricing problem, a critical factor in the efficiency of the Branch and Price algorithm. We execute an extensive numerical comparison between the performances of the Branch and Price algorithm and the MIP solver of CPLEX for a particular variant of the MPSSP

Simulated annealing for constrained global optimization

Hide-and-Seek is a powerful yet simple and easily implemented continuous simulated annealing algorithm for finding the maximum of a continuous function over an arbitrary closed, bounded and full-dimensional body. The function may be nondifferentiable and the feasible region may be nonconvex or even disconnected. The algorithm begins with any feasible interior point. In each iteration it generates a candidate successor point by generating a uniformly distributed point along a direction chosen at random from the current iteration point. In contrast to the discrete case, a single step of this algorithm may generate any point in the feasible region as a candidate point. The candidate point is then accepted as the next iteration point according to the Metropolis criterion parametrized by an adaptive cooling schedule. Again in contrast to discrete simulated annealing, the sequence of iteration points converges in probability to a global optimum regardless of how rapidly the temperatures converge to zero. Empirical comparisons with other algorithms suggest competitive performance by Hide-and-Seek.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44934/1/10898_2005_Article_BF01100688.pd