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In this report we consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served. We showed that the optimal sequence of modes is ordered by rate of cost decrease. However, queues are not necessarily emptied. We propose a dynamic programming approach for solving the problem, which reduces the multiparametric QP (mpQP) to a series of problems that can be solved readily.

We present a case study based on a multi-terminal container operation in Antwerp, Belgium, where a set of cyclically calling container vessels is processed. The operator faces the problem of strategically allocating a terminal, a berthing interval, and a variable number of quay cranes to the vessels in the set. Restricting properties are terminal quay lengths, number of quay cranes and storage capacities. Currently, the operator's objective is to satisfy the preferences of the vessel lines, with respect to a terminal and berthing time, as much as possible. We are interested in the benefit of modifying a given allocation, i.e. the potential crane and inter-terminal costs savings if specific changes to a given allocation are allowed. An MILP is implemented in a two-step optimization, which enables us to efficiently investigate the benefit of modification. Experimental results suggest that small changes in a given allocation may lead to significant cost savings.

The objective of this report is to develop a method to control a manufacturing system using feedback control. The manufacturing system of interest is a three machine multi-product flow line with stochastic process times, producing eight different product types in large quantities. The performance of the feedback controlled flow line is compared to the performance of the flow line controlled by several common control methods: push, pull, conwip, and POLCA control. The main performance criteria for the flow line are assumed to be the throughput of the system and the inventory level.

In this report we will present three approaches to model manufacturing systems in an aggregate way leading to fast and effective (i.e., scalable) simulations that allow the development of simulation tools for rapid exploration of different production scenarios in a factory as well as in a whole supply chain. We will present the main ideas and show some validation studies. Fundamental references are given for more detailed studies.

In this paper we consider a port consisting of a cluster of inter-related terminals, where container vessels arrive cyclically. The problem is to strategically assign a terminal and a time interval of berthing to each of the vessels in the cycle. Restricting properties are terminal quay lengths and quay crane capacity. Conflicting objectives are i) minimizing the number of required quay cranes, ii) minimizing the amount of inter-terminal traffic and iii) minimizing the total weighted deviation from desired berthing intervals. We formulate both a straightforward and an alternative mixed integer linear program to model this system. Results show that the alternative model is much faster solvable and enables to optimize real-life problems within a couple of hours.

The dynamics of manufacturing systems has been a subject of study for several decades. Over the last years, manufacturing systems have become more and more complex. A good understanding of the dynamics of manufacturing systems has therefore become even more important. The goal of this report is to introduce a large variety of models that have been used for modeling manufacturing systems. By means of examples it is illustrated how certain modeling techniques can be used to derive models that can be used for analysis and/or control. Also, references are provided that can be used as a starting point for getting more details. Furthermore, recent developments in the modeling, analysis and control of manufacturing systems are presented.

In this paper we study the control of switching servers, which can for example be found in manufacturing industry. In general, these systems are discrete event systems. A server processes multiple job types. Switching between the job types takes time and during that time, no jobs can be processed, so capacity is lost. How should a server switch between the job types in an efficient way? In this paper we derive the optimal process cycle with respect to work in process levels for a server with two job types and finite buffer capacities. The analysis is performed using a hybrid fluid model approximation. After the optimal process cycle has been defined, a state feedback controller is proposed that steers the trajectory of the system to this optimal cycle. Workstations are often placed in series to form a flowline of servers. Our goal is to control flowlines of switching servers in a way that the work in process level is minimized. In a flowline, only the most downstream workstation influences the work in process level of the system, since upstream workstations simply move jobs from one server to the other. If it is possible to have the most downstream workstation process in its optimal cycle and the other workstations can make this happen, then optimal work in process levels are achieved. This paper investigates under which conditions the upstream workstations can make the most downstream workstation work optimally. Conditions on the upstream workstations are derived and the class of flowlines is characterized for which the optimal process cycle of an isolated downstream workstation can become the optimal process cycle for the flowline. For a flowline consisting of two workstations, a state feedback controller is proposed and convergence to the optimal process cycle is proved mathematically. An extensive case study demonstrates how the controller performs, for both the hybrid fluid model and in a discrete event implementation with stochastic inter-arrival and process times.

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We consider the distribution of goods from manufacturers to customers by a logistics provider, where manufacturers' supplies and customers' demands are given and cannot be controlled. The goods may temporarily be stored in warehouses to compensate for the stochastic behavior of the supplies and demands. Manufacturers, warehouses and customers are geographically connected by transportation links, e.g. roads, railways, waterways. The problem of a logistics provider is to determine which of these links to use and how much to ship through them, such that total costs are minimized and demands are met. This paper presents a method for designing close to optimal network topologies for this type of problem. We introduce a two-layer optimization procedure, which finds a cost-effective topology with a very limited number of links for a set of stochastic supplies and demands. In addition, we show that the obtained topology is only sensitive to changes in the first moments of supply and demand distributions. Hence, with only information about the individual means, a close to optimal topology can be determined based on a constructed set of stochastic time series of supplies and demands.

In every-day life, people and goods have to be transported from one place to another by different kinds of resources, e.g. buses, trains, airplanes and ships, but also transport belts, cranes, elevators and robots. A group of these resources linked together with the purpose of transporting people and/or goods from one place to the other forms a logistics network. Such a network is usually run by a number of logistics providers, some of which control the links while others control the nodes of that network. Each provider faces the problem of delivering the right amount of items in the right place at the right time. To satisfy these goals at minimal costs, a provider has to make combined decisions at three levels: strategic, tactical and operational. Due to the ever-growing complexity of the combined decisions, more often a provider requires efficient decision tools (mathematical models) that solve the problems for him. During the last decades, the number of people and goods to be transported has grown that large that even intelligent decision support tools cannot solve the combined decisions at once. A possible approach is to separate the overall problem into several subproblems, which are then solved step by step, or if possible alternatingly. In this dissertation we propose, develop and test multi-step optimization methods to support logistics providers in their decision making process in two particular logistics networks: i) a distribution network and ii) a multi-terminal container operation as node in a network. The separation of the combined problems into several subproblems is chosen such that each individual subproblem is practically interesting in its own right and can be solved within the time allowed at the considered decision making level(s). Although existing theoretical studies have already investigated several parts of the considered logistics networks, the separations chosen in this dissertation are unique and result from specific problems faced in practice. The research in this dissertation is supported by the Koninklijke Frans Maas Groep (taken over by DSV) and the terminal operator PSA HNN in Antwerp Belgium, who both provided us with interesting, practical problems and data to test our methods. The study concerning the distribution network discusses the joint problem at the tactical and operational level faced by a third party logistics services provider. The objective is to construct a consistent and efficient network topology (i.e. where to establish line hauls between suppliers, warehouses and retailers), that still enables just in time delivery at the operational level. A procedure is proposed that iteratively deletes network line hauls based on the operational performance of the present topology. An extensive number of experiments suggest that the proposed alternating procedure is very fast and finds quite accurate solutions. As expected, the constructed network topology is sensitive to the averages of supply and demand. Interestingly, the constructed network topology appears to be robust to changes in second and higher orders of supply and demand distributions. With respect to the multi-terminal container operation, we consider one terminal operator, who is responsible for multiple terminals in one container port. The combined problems at strategic, tactical and operational levels in this multi-terminal container operation are separated into four main problems. The first subproblem investigates whether the same number of vessel lines can be operated with a smaller amount of crane capacity and at the same time the amount of container transport between the different terminals can be reduced. The proposed approach aims to spread the vessels over the terminals and over time such that the workload is balanced and the inter-terminal transport is minimized. Although we guarantee that quay and crane capacities are never exceeded, the specific berth positions and crane allocations are still to be determined. Results of a case study in a representative data set suggest that a significant amount of crane capacity can be saved and at the same time the amount of inter-terminal transport can substantially be reduced. Once the various vessel lines have been allocated to a terminal for a certain amount of time, the second subproblem is to construct a refined schedule per terminal, which is robust to disturbances on vessel arrivals. In our definition a schedule is robust if for all arrival scenarios within an arrival window, feasible solutions exist and the maximally required crane capacity in the worst case scenario is minimal. A window-based model is proposed that allows slight modifications in the allocations from the first subproblem to increase the robustness of the terminals’ schedules. Again, we allocate quay and quay crane capacities, while the specific berth positions and crane allocations are not constructed yet. As expected, the window-based plan requires slightly more crane capacity than the nominal window-ignoring plan for zero or relatively small arrival disturbances. However, the window-based plan is much more robust to larger realistic disturbances that are still within the arrival window bounds. Given the schedules, the third subproblem allocates berth positions for the vessel lines at the quay and stack positions for the containers in the yard. These combined decisions determine the total travel distance, that has to be covered by straddle carriers moving containers from quay to yard and vice versa. A procedure is developed that alternatingly allocates i) berth positions, guaranteeing non-overlapping and ii) container blocks, ensuring that block capacities are never exceeded, such that the total straddle carrier distance is minimized. The alternating procedure appears to be very fast, but the result heavily depends on the initial condition. A second model is proposed that turns out to find a proper initial guess for the alternating procedure. Results suggest that the straddle carrier distance in a representative allocation can significantly be reduced by applying the proposed method. Recently, results of this procedure have been implemented in a terminal operated by PSA HNN. The results of the first three subproblems construct tactical schedules, berth positions and yard design. The fourth subproblem addresses the online operational decision making if the system is disrupted from this tactical timetable. A rolling horizon approach is proposed that takes forecasts on arrivals, load compositions and resource activities into account to construct decisions on the current operations. Subsequently, the vessels’ i) time allocation, ii) berth position allocation, and iii) crane allocation under disturbances are addressed. The three subproblems can be solved within the time allowed at this operational level. Experiments suggest that explicitly taking the forecasts of specific parameters into account can substantially reduce the operational costs. Hence, we think the proposed procedure can properly serve as a decision support tool for a terminal operator. This research clearly shows that the proposed methods can be very valuable for logistics providers. The actual implementation of one of the results into a terminal operated by PSA HNN is already a confirmation of the method’s suitability. Although the approaches in this dissertation may not take all specific managerial decisions into account, at least we are able to quantify the additional costs induced by these decisions.