Showing papers in "OR Spectrum in 2010"
TL;DR: This paper reviews quantitative operations management approaches to food distribution management, and relates this to challenges faced by the industry, with main focus on three aspects: food quality, food safety, and sustainability.
Abstract: The management of food distribution networks is receiving more and more attention, both in practice and in the scientific literature. In this paper, we review quantitative operations management approaches to food distribution management, and relate this to challenges faced by the industry. Here, our main focus is on three aspects: food quality, food safety, and sustainability. We discuss the literature on three decision levels: strategic network design, tactical network planning, and operational transportation planning. For each of these, we survey the research contributions, discuss the state of the art, and identify challenges for future research.
463 citations
TL;DR: A review of four decades of research on dynamic lot-sizing with capacity constraints shows that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice.
Abstract: This paper presents a review of four decades of research on dynamic lot-sizing with capacity constraints. We discuss both different modeling approaches to the optimization problems and different algorithmic solution approaches. The focus is on research that separates the lot-sizing problem from the detailed sequencing and scheduling problem. Our conceptional point of reference is the multi-level capacitated lot-sizing problem (MLCLSP). We show how different streams of research emerged over time. One result is that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice. Our review also shows that currently mathematical programing and the use of metaheuristics are particularly popular among researchers in a vivid and flourishing field of research.
270 citations
TL;DR: Results show that the heuristic procedure proposed is capable of handling the dynamic aspect of the problem and of providing high-quality solutions and succeeded in reducing waiting times for patients while using fewer vehicles.
Abstract: This study analyzes and solves a patient transportation problem arising in large hospitals. The aim is to provide an efficient and timely transport service to patients between several locations in a hospital campus. Transportation requests arrive in a dynamic fashion and the solution methodology must therefore be capable of quickly inserting new requests in the current vehicle routes. Contrary to standard dial-a-ride problems, the problem under study includes several complicating constraints which are specific to a hospital context. The study provides a detailed description of the problem and proposes a two-phase heuristic procedure capable of handling its many features. In the first phase a simple insertion scheme is used to generate a feasible solution, which is improved in the second phase with a tabu search algorithm. The heuristic procedure was extensively tested on real data provided by a German hospital. Results show that the algorithm is capable of handling the dynamic aspect of the problem and of providing high-quality solutions. In particular, it succeeded in reducing waiting times for patients while using fewer vehicles.
204 citations
TL;DR: In this article, a base model for scheduling trucks at cross docking terminals is introduced, which relies on a set of simplifying assumptions in order to derive fundamental insights into the underlying problem's structure.
Abstract: At cross docking terminals, shipments from inbound trucks are unloaded, sorted and moved to dispatch points where they are directly loaded onto outbound trucks for an immediate delivery elsewhere in the distribution system. This warehouse management concept aims at realizing economies in transportation cost by consolidating divergent shipments to full truckloads without requiring excessive inventory at the cross dock. The efficient operation of such a system requires an appropriate coordination of inbound and outbound trucks, e.g. by computerized scheduling procedures.This work introduces a base model for scheduling trucks at cross docking terminals, which relies on a set of simplifying assumptions in order to derive fundamental insights into the underlying problem’s structure, i.e. its complexity, and to develop a building block solution procedure, which might be employed to solve more complex real-world truck scheduling problems.
192 citations
TL;DR: This work considers the problem of simultaneously scheduling IT-projects and assigning multi-skilled internal and external human resources with resource-specific efficiencies to the project work to minimize labor costs and shows the benefit of applying the MIP compared to simple heuristics used in practice in terms of obtaining feasible and low-cost solutions.
Abstract: We consider the problem of simultaneously scheduling IT-projects and assigning multi-skilled internal and external human resources with resource-specific efficiencies to the project work. The objective is to minimize labor costs. The problem is modeled as a mixed-integer linear program (MIP) with a tight LP-bound. The performance of the model w.r.t. solution gap and computation time is assessed and managerial insight is given concerning different problem parameters such as the time window size of projects, the number of skills of human resources, and the workload. Furthermore, we show the benefit of applying the MIP compared to simple heuristics used in practice in terms of obtaining feasible and low-cost solutions. Finally, we provide insight into the benefit of applying the MIP in case of central compared to decentral planning.
188 citations
TL;DR: The modified window partition based solution method in Wang and Regan is modified so that its computation time is reduced greatly and the quality of solutions is relatively high for the m-TSPTW.
Abstract: A truck scheduling problem for container transportation in a local area with multiple depots and multiple terminals including containers as a resource for transportation is addressed. Four types of movements of containers as inbound full, outbound full, inbound empty and outbound empty movements as well as the time windows at both the origin and the destination are considered. The total operating time of all trucks in operation is taken as the optimization criterion that has to be minimized. The problem is mathematically modeled based on a preparative graph formulation and falls into an extension of the multiple traveling salesman problem with time windows (m-TSPTW). The window partition based solution method for the m-TSPTW in Wang and Regan (Transp Res Part B: Methodol 36:97–112, 2002) is modified so that its computation time is reduced greatly. The experiments based on a number of randomly generated instances indicate that the modified method is quite fast and the quality of solutions is relatively high for the m-TSPTW. These experiments also demonstrate that our approach is able to generate high-quality results for the equivalent truck scheduling and inland container movement problem in container drayage operations.
139 citations
TL;DR: Empirical results validate the necessity of utilizing panel data and reveal that considerable waste exists in container port production, which provides a basis for assessing the competitiveness of container ports, for benchmarking best practice and identifying specific sources or causes of inefficiency.
Abstract: Applications of Data Envelopment Analysis (DEA) to container port production have been largely restricted to standard DEA models using cross-sectional data. The efficiency results derived may be biased; for instance, as the result of random effects or a recent investment in future production. In overcoming this problem, panel data on container port production may be more suitable for medium- to long-term efficiency analysis. This paper evaluates available DEA panel data approaches by applying them to a sample of 25 leading container ports. Empirical results validate the necessity of utilizing panel data and reveal that considerable waste exists in container port production. It also provides a basis for assessing the competitiveness of container ports, for benchmarking best practice and identifying specific sources or causes of inefficiency.
112 citations
TL;DR: A method to determine dynamic order quantities for perishable products with limited shelf-life, positive lead time, FIFO or LIFO issuing policy, and multiple service level constraints is presented.
Abstract: Food retail inventory management faces major challenges by uncertain demand, perishability, and high customer service level requirements. In this paper, we present a method to determine dynamic order quantities for perishable products with limited shelf-life, positive lead time, FIFO or LIFO issuing policy, and multiple service level constraints. In a numerical study, we illustrate the superiority of the proposed method over commonly suggested order-up-to-policies. We show that a constant-order policy might provide good results under stationary demand, short shelf-life, and LIFO inventory depletion.
108 citations
TL;DR: A so-called block planning approach is presented which establishes cyclical production patterns based on the definition of setup families which minimizes total production and transportation costs.
Abstract: In the fast moving consumer goods industry there is an ongoing trend towards an increased product variety and shorter replenishment cycle times. Hence, manufacturers seek a better coordination of production and distribution activities. In this paper, a so-called block planning approach is presented which establishes cyclical production patterns based on the definition of setup families. For the delivery of final goods from the plants to distribution centres two transportation modes are considered, full truckload and less than truckload. The proposed mixed-integer linear optimization model minimizes total production and transportation costs. Numerical results demonstrate the practical applicability of the proposed block planning approach. In particular, a rigid and a flexible block planning approach are compared which differ by their degree of flexibility in the scheduling of the production lots.
103 citations
TL;DR: This paper investigates two concepts to increase efficiency and compares them to several benchmark algorithms, using a discrete-event simulation tool and found that the trade-off between stacking further away in the terminal versus stacking close by the exit points and accepting more reshuffles leads to improvements over the benchmark.
Abstract: Container stacking rules are an important factor in container terminal efficiency. In this paper, we investigate two concepts to increase efficiency and compare them to several benchmark algorithms, using a discrete-event simulation tool. The first concept is to use knowledge about container departure times, in order to limit the number of reshuffles. We stack containers leaving shortly before each other on top of each other. The second concept is the trade-off between stacking further away in the terminal versus stacking close to the exit points and accepting more reshuffles. It is concluded that even the use of imperfect or imprecise departure time information leads to significant improvements in efficiency. Minimizing the difference in departure times proved to be important. It was also found that the trade-off between stacking further away in the terminal versus stacking close by the exit points and accepting more reshuffles leads to improvements over the benchmark.
91 citations
TL;DR: The method solves an online optimisation problem by constructing a new crane schedule for a certain planning horizon whenever a new job arrives or a job is completed, leading to a productivity gain of more than 20%.
Abstract: We describe an approach for scheduling triple cross-over stacking cranes in an automated container storage block with asynchronous hand over at the transfer areas at both block front ends. The problem is characterised by frequent long crane moves that make job assignment and crane routing particularly challenging, as an intricate synchronisation between the cranes is required. The main objective is to maximise the productivity of the crane system under peak load while preventing delays in the transport of import and export containers from and to the transfer areas. Our method solves an online optimisation problem by constructing a new crane schedule for a certain planning horizon whenever a new job arrives or a job is completed. We report on extensive simulation studies for evaluating the scheduling strategy. The results show that the method performs significantly better than commonly used heuristics, leading to a productivity gain of more than 20%.
TL;DR: In this article, the authors consider a container terminal operator who faces the problem of constructing a cyclic berth plan, which defines the arrival and departure times of each cyclically calling vessel on a terminal, taking into account the expected number of containers to be handled and the necessary quay and crane capacity.
Abstract: We consider a container terminal operator who faces the problem of constructing a cyclic berth plan. Such a plan defines the arrival and departure times of each cyclically calling vessel on a terminal, taking into account the expected number of containers to be handled and the necessary quay and crane capacity to do so. Con- ventional berth planning methods ignore the fact that, in practice, container terminal operator and shipping line agree upon an arrival window rather than an arrival time: if a vessel arrives within that window then a certain vessel productivity and hence departure time is guaranteed. The contributions of this paper are twofold. We not only minimize the peak loading of quay cranes in a port, but also explicitly take into account the arrival window agreements between the terminal operator and shipping lines. We present a robust optimization model for cyclic berth planning. Computational results on a real-world scenario for a container terminal in Antwerp show that the robust
TL;DR: A new interactive learning-oriented method called Pareto navigator for nonlinear multiobjective optimization that is applicable also for problems with three or more objective functions, and in fact it is best suited for such problems.
Abstract: We describe a new interactive learning-oriented method called Pareto navigator for nonlinear multiobjective optimization. In the method, first a polyhedral approximation of the Pareto optimal set is formed in the objective function space using a relatively small set of Pareto optimal solutions representing the Pareto optimal set. Then the decision maker can navigate around the polyhedral approximation and direct the search for promising regions where the most preferred solution could be located. In this way, the decision maker can learn about the interdependencies between the conflicting objectives and possibly adjust one’s preferences. Once an interesting region has been identified, the polyhedral approximation can be made more accurate in that region or the decision maker can ask for the closest counterpart in the actual Pareto optimal set. If desired, (s)he can continue with another interactive method from the solution obtained. Pareto navigator can be seen as a nonlinear extension of the linear Pareto race method. After the representative set of Pareto optimal solutions has been generated, Pareto navigator is computationally efficient because the computations are performed in the polyhedral approximation and for that reason function evaluations of the actual objective functions are not needed. Thus, the method is well suited especially for problems with computationally costly functions. Furthermore, thanks to the visualization technique used, the method is applicable also for problems with three or more objective functions, and in fact it is best suited for such problems. After introducing the method in more detail, we illustrate it and the underlying ideas with an example.
TL;DR: In this article, a framework for considering resource transfers in single and multi-project environments is developed, which includes managerial approaches to handle resource transfers, a classification of resource transfer types and new roles that resources can take in these transfers.
Abstract: Most approaches to multi-project scheduling are based on the assumption that resources can be transferred between projects without any expense in time and cost. As this assumption often is not realistic, we generalise the multi-project scheduling problem (RCMPSP) by additionally including transfer times and cost. To integrate this aspect, in a first step, we develop a framework for considering resource transfers in single- and multi-project environments. It includes managerial approaches to handle resource transfers, a classification of resource transfer types and new roles that resources can take in these transfers. Afterwards, we define the multi-project scheduling problem with transfer times (RCMPPTT) and formulate it in a basic and an extended version as integer linear programmes. Eventually, it is supplemented for the first time by cost considerations and introduced as resource constrained multi-project scheduling problem with transfer times and cost (RCMPSPTTC). Computational experiments compare the presented managerial approaches and prove the necessity of explicitly considering transfer times in project scheduling already during the planning phase. Moreover, the experiments evaluate the presented MIP models and show that specialised solution procedures are vital.
TL;DR: Simulation experiments show that the waiting times of AGVs and external trucks are significantly reduced due to the increased utilization through cooperation and the workload of the two RMGs can be better balanced and interference can be more easily avoided, thereby maximizing crane utilization.
Abstract: This paper proposes heuristic-based and local-search-based real-time scheduling methods for twin rail-mounted gantry (RMG) cranes working in a block at an automated container terminal. The methods reschedule the cranes in real time for a given fixed-length look-ahead horizon whenever an RMG finishes a job. One difficulty with this problem is that sometimes additional rehandling of containers needs to be carried out in order to complete a requested job, especially when other containers are stacked on top of the target container. These rehandlings are the main cause of the delay of the crane operations, leading to extended waiting of automated guided vehicles (AGVs) or external trucks that co-work with the cranes. By treating the rehandling operations as independent jobs in our solution methods, we can greatly facilitate the cooperation between the two RMGs. Through this cooperation, the workload of the two RMGs can be better balanced and interference can be more easily avoided, thereby maximizing crane utilization. Simulation experiments show that the waiting times of AGVs and external trucks are significantly reduced due to the increased utilization through cooperation.
TL;DR: Computational tests prove that the consideration of internal reshuffles leads to a further shortening of vessel handling times compared to a sole application of crane double cycling.
Abstract: Fast handling of vessels is one of the most important goals in container terminal operations planning. In recent studies, quay crane double cycling has been investigated to accelerate the service of vessels. In our paper, we show that the service process can be further accelerated by changing the treatment of so-called reshuffle containers. Reshuffle containers have to be removed from their position in the vessel only to gain access to containers stacked below them. Our approach enables to reposition reshuffle containers directly within the bay of a vessel, referred to as internal reshuffles, instead of temporarily unloading them. A mathematical problem formulation and a heuristic solution method, namely a greedy randomized adaptive search procedure, are provided for planning crane operations under internal reshuffles. Computational tests prove that the consideration of internal reshuffles leads to a further shortening of vessel handling times compared to a sole application of crane double cycling.
TL;DR: A quantitative arrival scheduling simulation is presented to analyze contrasting APS, in order to identify promising strategy design directions for central and decentral strategies, under high and low fuel price regimes.
Abstract: In maritime container transport, the random nature of vessel arrival and terminal service processes often lead to significant handling delays and/or resource underutilization. Arrival planning strategies (APS) promise to mitigate such undesirable effects by managing the variance of the terminal arrival process, taking different cost components and situational dynamics into account. We present a quantitative arrival scheduling simulation to analyze contrasting APS, in order to identify promising strategy design directions. Results are presented for central and decentral strategies, under high and low fuel price regimes. The analysis results in significant quantitative and qualitative differences between the strategies.
TL;DR: In this study, a model with respect to the leasing and purchasing of containers is developed and a hybrid GA is proposed to reduce the computation time while still obtaining an acceptable result.
Abstract: With the recent development of container transportation, the imbalance of empty containers among ports has become more serious. We consider the problem of positioning empty containers. The goal of this study is to propose a plan for transporting empty containers between container ports (terminals) to reduce the imbalance. There is currently a demand at each port and any backlog of containers is not permitted. The objective is to minimize the total relevant costs such as transportation cost, handling cost, and holding cost, etc. In this study, we develop a model with respect to the leasing and purchasing of containers. Mixed integer programming and genetic algorithms are used to solve the model. A hybrid GA is also proposed to reduce the computation time while still obtaining an acceptable result.
TL;DR: A simulation-based optimization model is presented for this wider modeling problem with the objective of finding the schedule which optimizes a classical objective function.
Abstract: The discharge/loading process of a single container ship by multiple quay cranes and shuttle vehicles moving back and forth from the quay to the yard and vice versa is focused in this paper. The core problem of this major operational issue reduces to finding the optimal assignment and optimal sequencing (schedule) of bays (jobs) processed by a fixed number of available cranes (machines). Under the classical assumption that machines have no release time and that their processing occurs with continuity, at a constant rate, in literature it has been tackled as a deterministic machine scheduling problem and formulated by integer programming as the quay crane scheduling problem (QCSP). Here, instead, the QCSP is viewed as a decisional step within an uncertain and dynamic logistic process where the quay cranes are the resources to be managed at the best, i.e., by minimizing the time spent waiting for each other due to conflicts, as well as the time wasted for blocking and starvation phenomena due to congestion occurring along the path from the quay area and to the stacking yard and vice versa. We present a simulation-based optimization (SO) model for this wider modeling problem with the objective of finding the schedule which optimizes a classical objective function. The search process for the optimal schedule is accomplished by a simulated annealing (SA) algorithm, while performance estimation of the overall container discharge/loading process is provided by the simulation framework as a whole. Numerical experiments on a real instance are presented for tuning purposes of the SA procedure implemented within the simulator.
TL;DR: This paper seeks to address the dispatching problem for vehicles (or prime movers) in a transshipment hub by considering the quay cranes and yard cranes capacity by developing two heuristics based on genetic algorithm and minimum cost flow network model.
Abstract: This paper seeks to address the dispatching problem for vehicles (or prime movers) in a transshipment hub by considering the quay cranes and yard cranes capacity. The objective of this paper is to minimize the makespan time at the quay side. This issue is particularly important for a port which uses information technology in making real time decision because the port can exploit information technology to make full use of the data in making good decision. A mixed integer programming (MIP) model is developed to formulate the problem. As the existing solver cannot solve the MIP model in reasonable time, we develop two heuristics to tackle the problem. The first method is based on the neighborhood search, while the second method is based on genetic algorithm (GA) and minimum cost flow (MCF) network model. Unlike the typical GA which usually represents the chromosome using job sequence, we use the ready time for jobs as the representation of the chromosome, and MCF model is then used to decode the chromosome to determine the job sequence for prime movers. The experiment results indicate the superiority of the GA–MCF-based algorithm over the neighborhood search algorithm.
TL;DR: This paper is developing a production and distribution planning model for food supply chains and presents heuristics for solving the resulting mixed-integer linear programming model and demonstrates the effectiveness of the developed methodology in a numerical investigation.
Abstract: After a number of food safety crises, the design and implementation of traceability systems became an important tool for managing safety risks in the food industry. In the literature, numerous studies deal with traceability from the viewpoint of information system and technology development. However, traceability and its implications for food safety receive less attention in literature on production and distribution planning. From the viewpoint of operations management, an efficient management of food safety risks requires the consideration of the amounts of potentially recalled products, affected regions/customers, and logistics efforts connected to solving the safety problem. In this paper we are developing a production and distribution planning model for food supply chains to address these issues. We also present heuristics for solving the resulting mixed-integer linear programming model and demonstrate the effectiveness of the developed methodology in a numerical investigation.
TL;DR: An integer linear program for planning the layout of container yards is introduced and a variable neighborhood descent (VND) heuristic for solving non-rectangular instances is developed.
Abstract: In this paper, we introduce an integer linear program for planning the layout of container yards. We concentrate on a special layout class of container yards which we call yard layout with transfer lanes. For those layouts typically rubber tired gantry cranes are used for stacking operations and trucks for horizontal transports. We show that the optimization model can be formulated as a special type of a resource constrained shortest path problem for which the LP relaxation always has at least one integer optimal solution. This model is restricted to a rectangular storage yard which allows a linear formulation. For an arbitrary shaped container yard we adopt the model and develop a variable neighborhood descent (VND) heuristic for solving non-rectangular instances. Concerning the rectangular case, we show that the VND heuristic achieves optimal solutions for 38% of the realistic test instances.
TL;DR: An important feature of these approaches is a new compound perturbation operator that consists of many unitary moves that allows trains to be shifted feasibly and more easily within the solution.
Abstract: Train scheduling is a complex and time consuming task of vital importance. To schedule trains more accurately and efficiently than permitted by current techniques a novel hybrid job shop approach has been proposed and implemented. Unique characteristics of train scheduling are first incorporated into a disjunctive graph model of train operations. A constructive algorithm that utilises this model is then developed. The constructive algorithm is a general procedure that constructs a schedule using insertion, backtracking and dynamic route selection mechanisms. It provides a significant search capability and is valid for any objective criteria. Simulated Annealing and Local Search meta-heuristic improvement algorithms are also adapted and extended. An important feature of these approaches is a new compound perturbation operator that consists of many unitary moves that allows trains to be shifted feasibly and more easily within the solution. A numerical investigation and case study is provided and demonstrates that high quality solutions are obtainable on real sized applications.
TL;DR: The effect of the stochastic demand on the coordinated plans is analysed and it shows that due to information asymmetry and double marginalisation, costs considerably exceed the cost minimum of the whole transportation chain.
Abstract: Very few research efforts have been spent on the coordination of plans and operations of independent service providers in an intermodal transportation chain. The impact of the lack of collaboration and coordination is pointed out in a setting considering overseas transports. It shows that due to information asymmetry and double marginalisation, costs considerably exceed the cost minimum of the whole transportation chain. In order to reduce these inefficiencies, a coordination scheme is elaborated which is able to identify significant improvements and which allows the service providers involved to keep their private planning domain with no disclosure of critical data. Due to the time lag in maritime transportation, uncertainties about future requests exist that could make the improvements achieved from coordination invalid. Hence, the effect of the stochastic demand on the coordinated plans is analysed.
TL;DR: It is shown how a seaport container terminal’s long-run average quay crane rate depends on the system that automatically assigns yard trucks to container transportation jobs in the terminal in real time.
Abstract: We show how a seaport container terminal’s long-run average quay crane rate depends on the system that automatically assigns yard trucks to container transportation jobs in the terminal in real time. Several real-time, dual-load yard truck control systems are proposed and evaluated by a fully-integrated, discrete event simulation model of a vessel-to-vessel transshipment terminal. The model is designed to reproduce the microscopic, stochastic, real-time environment at a multiple-berth facility. Overall, the literature still lacks a comprehensive analysis that (1) considers different methods for controlling dual-load vehicles in real time within a fully-integrated, stochastic container terminal environment and (2) compares them in terms of an absolute global performance measure such as average quay crane rate. This paper provides such an analysis.
TL;DR: An interesting discovery is that re-modelling a set of integer variables into multiple binary variables improve the run time tremendously, and in some cases, outperform the relaxed original model.
Abstract: Different terminals, with their unique combinations of liner services, yard layouts and equipment configurations, may find that different yard planning strategies work better for their scenarios. While an optimum yard plan can be found for each yard planning strategy, it is interesting to know which strategy gives the best plan. In designing an IT-based search engine to discover the best yard planning strategy and/or scenario, having a generic specification and solver is important, so that the whole solution space could be represented and searched. We design a generic problem specification with parameterised scenarios and yard planning strategies, and formulate a generic mathematical model that solves for the optimum weekly yard plan template for that given problem. A good run time of this generic model is extremely important as the model will be executed hundreds of times in the search engine. Experiments are conducted with the model. An interesting discovery is that re-modelling a set of integer variables into multiple binary variables improve the run time tremendously, and in some cases, outperform the relaxed original model. We also find that the strategy which allows sharing of yard space between services yield better utilization for yard space and rail mounted gantry handling capacity.
TL;DR: The numerical results indicate that the presented approach works best for medium-sized and large contact centers with skills-based routing of customers for which stochastic queueing models are rarely applicable.
Abstract: This paper presents a profit-oriented shift scheduling approach for inbound contact centers. The focus is on systems in which multiple agent classes with different qualifications serve multiple customer classes with different needs. We assume that customers are impatient, abandon if they have to wait, and that they may retry. A discrete-time modeling approach is used to capture the dynamics of the system due to time-dependent arrival rates. Staffing levels and shift schedules are simultaneously optimized over a set of different approximate realizations of the underlying stochastic processes to consider the randomness of the system. The numerical results indicate that the presented approach works best for medium-sized and large contact centers with skills-based routing of customers for which stochastic queueing models are rarely applicable.
TL;DR: A pricing and scheduling strategy based on dynamic programming where not only the direct costs of a job insertion are taken into account, but also the impact on future opportunities is proposed.
Abstract: In this paper we consider a dynamic full truckload pickup and delivery problem with time-windows. Jobs arrive over time and are offered in a second-price auction. Individual vehicles bid on these jobs and maintain a schedule of the jobs they have won. We propose a pricing and scheduling strategy based on dynamic programming where not only the direct costs of a job insertion are taken into account, but also the impact on future opportunities. Simulation is used to evaluate the benefits of pricing opportunities compared to simple pricing strategies in various market settings. Numerical results show that the proposed approach provides high quality solutions, in terms of profits, capacity utilization, and delivery reliability.
TL;DR: An empirical study shows that, for smaller investment volumes, transaction costs dominate risk costs so that optimal portfolios contain only a very small number of assets, compared to alternative vehicles, particularly index certificates and exchange-traded funds.
Abstract: A direct application of classical portfolio selection theory is problematic for the small investor because of transaction costs in the form of bank and broker fees. In particular, minimum fees force the investor to choose a comparatively rather small selection of assets. The existence of transaction costs leads to an optimization problem that juxtaposes those costs against the risk costs that arise with portfolios consisting of only a few assets. Despite the non-convex and, thus, complex optimization, an algorithmic solution turns out to be very fast and precise. An empirical study shows that, for smaller investment volumes, transaction costs dominate risk costs so that optimal portfolios contain only a very small number of assets. Based upon these results, the cost-effectiveness of direct investments is compared to alternative vehicles, particularly index certificates and exchange-traded funds, depending on the level of invested wealth.
TL;DR: In this article, the authors considered single-level uncapacitated and capacitated lot sizing problems with product substitution, where products may be substituted by certain other products to satisfy demand.
Abstract: We consider single-level uncapacitated and capacitated lot-sizing problems with product substitution, where products may be substituted by certain other products to satisfy demand. The models incorporate initial inventories and general substitution structures. We formulate the problems as mixed-integer linear programs and develop Simple Plant Location-based reformulations as well as new valid inequalities. Computational results on generated problem instances show that the reformulations are superior to the original formulations and those with valid inequalities added a priori, except for instances with multiple resources and downward substitution. In most cases, the running times of a mixed-integer programming solver on approximate extended formulations that only contain a subset of the disaggregated constraints were almost as good as on complete Simple Plant Location-based reformulations.