Showing papers in "Operations Research in 1993"
TL;DR: What manufacturing managers at Hewlett-Packard Company (HP) see as the needs for model support in managing material flows in their supply chains are described and the initial development of such a model for supply chains that are not under complete centralized control is reported on.
Abstract: A supply chain is a network of facilities that performs the functions of procurement of material, transformation of material to intermediate and finished products, and distribution of finished products to customers. Often, organizational barriers between these facilities exist, and information flows can be restricted such that complete centralized control of material flows in a supply chain may not be feasible or desirable. Consequently, most companies use decentralized control in managing the different facilities at a supply chain. In this paper, we describe what manufacturing managers at Hewlett-Packard Company (HP) see as the needs for model support in managing material flows in their supply chains. These needs motivate our initial development of such a model for supply chains that are not under complete centralized control. We report on our experiences of applying such a model in a new product development project of the DeskJet printer supply chain at HP. Finally, we discuss avenues to develop better ...
817 citations
TL;DR: This paper describes some of the approaches used in exploratory modeling, and suggests some technological innovations needed to facilitate it.
Abstract: Exploratory modeling is using computational experiments to assist in reasoning about systems where there is significant uncertainty. While frequently confused with the use of models to consolidate knowledge into a package that is used to predict system behavior, exploratory modeling is a very different kind of use, requiring a different methodology for model development. This paper distinguishes these two broad classes of model use describes some of the approaches used in exploratory modeling, and suggests some technological innovations needed to facilitate it.
673 citations
TL;DR: It is shown for the first time that there is a variational inequality formulation of dynamic user equilibrium with simultaneous route choice and departure time decisions which, when appropriate regularity conditions hold, preserves the first in, first out queue discipline.
Abstract: In the present paper we are concerned with developing more realistic dynamic models of route choice and departure time decisions of transportation network users than have been proposed in the literature heretofore. We briefly review one class of models that is a dynamic generalization of the static Wardropian user equilibrium, the so-called Boston traffic equilibrium. In contrast, we then propose a new class of models that is also a dynamic generalization of the static Wardropian user equilibrium. In particular, we show for the first time that there is a variational inequality formulation of dynamic user equilibrium with simultaneous route choice and departure time decisions which, when appropriate regularity conditions hold, preserves the first in, first out queue discipline.
661 citations
TL;DR: This algorithm solves the uncapacitated minimum cost flow problem as a sequence of On log n shortest path problems on networks with n nodes and m arcs and runs in On log nm + n log n time.
Abstract: In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of On log n shortest path problems on networks with n nodes and m arcs and runs in On log nm + n log n time. Using a standard transformation, this approach yields an Om log nm + n log n algorithm for the capacitated minimum cost flow problem. This algorithm improves the best previous strongly polynomial time algorithm, due to Z. Galil and E. Tardos, by a factor of n2/m. Our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds, say m', is much less than m. In this case, the running time of the algorithm is Om' + n log nm + n log n.
487 citations
TL;DR: This work describes the empty container allocation problem, and introduces two dynamic deterministic formulations for the single and multicommodity cases, which offer a general modeling framework for this class of problems.
Abstract: The empty container allocation problem occurs in the context of the management of the land distribution and transportation operations of international maritime shipping companies. It involves dispatching empty containers of various types in response to requests by export customers and repositioning other containers to storage depots or ports in anticipation of future demands. We describe the problem and identify its basic structure and main characteristics. We then introduce two dynamic deterministic formulations for the single and multicommodity cases, which offer a general modeling framework for this class of problems, and which account for its specific characteristics: the space and time dependency of events, substitutions among container types, relationships with partner companies, imports and exports, massive equilibration flows, etc. Finally, we provide a mathematical formulation for handling, in the single commodity case, the uncertainty of demand and supply data that is characteristic of container...
387 citations
TL;DR: In this paper, the authors present an inventory model where the demand rate varies with an underlying state-of-the-world variable, and derive some basic characteristics of optimal policies and develop algorithms for computing them.
Abstract: We present an inventory model, where the demand rate varies with an underlying state-of-the-world variable. This variable can represent economic fluctuations, or stages in the product life-cycle, for example. We derive some basic characteristics of optimal policies and develop algorithms for computing them. In addition, we show that certain monotonicity patterns in the problem data are reflected in the optimal policies.
379 citations
TL;DR: This paper shows that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array, and shows how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lots size problems.
Abstract: Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by A. S. Manne (1958) and by H. M. Wagner and T. M. Whitin (1958). The Manne-Wagner-Whitin model and its variants have been studied widely in the operations research and management science communities, and a large number of algorithms have been proposed for solving various problems expressed in terms of this model, most of which assume concave costs and rely on dynamic programming. In this paper, we show that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array. We then show how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems. We focus on uncapacitated problems, i.e., problems without bounds on production, inventory, or backlogging; capacitated problem...
349 citations
TL;DR: It is shown that a fixed-limit booking policy that maximizes expected revenue can be characterized by a simple set of conditions on the subdifferential of the expected revenue function.
Abstract: This paper addresses the problem of determining optimal booking policies for multiple fare classes that share the same seating pool on one leg of an airline flight when seats are booked in a nested fashion and when lower fare classes book before higher ones. We show that a fixed-limit booking policy that maximizes expected revenue can be characterized by a simple set of conditions on the subdifferential of the expected revenue function. These conditions are appropriate for either the discrete or continuous demand cases. These conditions are further simplified to a set of conditions that relate the probability distributions of demand for the various fare classes to their respective fares. The latter conditions are guaranteed to have a solution when the joint probability distribution of demand is continuous. Characterization of the problem as a series of monotone optimal stopping problems proves optimality of the fixed-limit policy over all admissible policies. A comparison is made of the optimal solutions ...
346 citations
TL;DR: This paper investigates the application of a new class of neighborhood search algorithms—cyclic transfers—to multivehicle routing and scheduling problems and shows that cyclic transfer methods are either comparable to or better than the best published heuristic algorithms for several complex and important vehicle routing and schedules problems.
Abstract: This paper investigates the application of a new class of neighborhood search algorithms—cyclic transfers—to multivehicle routing and scheduling problems. These algorithms exploit the two-faceted decision structure inherent to this problem class: First, assigning demands to vehicles and, second, routing each vehicle through its assigned demand stops. We describe the application of cyclic transfers to vehicle routing and scheduling problems. Then we determine the worst-case performance of these algorithms for several classes of vehicle routing and scheduling problems. Next, we develop computationally efficient methods for finding negative cost cyclic transfers. Finally, we present computational results for three diverse vehicle routing and scheduling problems, which collectively incorporate a variety of constraint and objective function structures. Our results show that cyclic transfer methods are either comparable to or better than the best published heuristic algorithms for several complex and important ...
306 citations
TL;DR: This paper analyzes the problem of m identical vehicles with unlimited capacity and shows that in heavy traffic the system time is reduced by a factor of 1/m2 over the single-server case and considers the case in which each vehicle can serve at most q customers before returning to a depot.
Abstract: In 1991, D. J. Bertsimas and G. van Ryzin introduced and analyzed a model for stochastic and dynamic vehicle routing in which a single, uncapacitated vehicle traveling at a constant velocity in a Euclidean region must service demands whose time of arrival, location and on-site service are stochastic. The objective is to find a policy to service demands over an infinite horizon that minimizes the expected system time (wait plus service) of the demands. This paper extends our analysis in several directions. First, we analyze the problem of m identical vehicles with unlimited capacity and show that in heavy traffic the system time is reduced by a factor of 1/m2 over the single-server case. One of these policies improves by a factor of two on the best known system time for the single-server case. We then consider the case in which each vehicle can serve at most q customers before returning to a depot. We show that the stability condition in this case depends strongly on the geometry of the region. Several pol...
292 citations
TL;DR: This article proposes a reliability model for emergency service vehicle location, based on a reliability bound on the probability of system failure, and derives a 0-1 integer programming ( IP ) optimization model, and proposes the augmentation of the IP using certain valid inequalities as a preprocessing technique, and solves theIP using a branch-and-bound procedure.
Abstract: This article proposes a reliability model for emergency service vehicle location. Emergency services planners must solve the strategic problem of where to locate emergency services stations and the tactical problem of the number of vehicles to place in each station. We view the problem from a system reliability perspective, where system failure is interpreted as the inability of a vehicle to respond to a demand call within an acceptable amount of time. Our model handles the stochastic problem aspects in a more explicit way than previous models in the literature. Based on a reliability bound on the probability of system failure, we derive a 0-1 integer programming (IP) optimization model. We propose the augmentation of the IP using certain valid inequalities as a preprocessing technique, and solve the IP using a branch-and-bound procedure. Our computational results show that the preprocessing technique is highly effective. Also, sensitivity studies show that the planner can produce a variety of different d...
TL;DR: It is significant that the well known insensitivity property of the stationary M/G/∞ model does not hold for the nonstationary Mt/G/, and the time-dependent mean function m depends on the service-time distribution beyond its mean.
Abstract: We establish some general structural results and derive some simple formulas describing the time-dependent performance of the Mt/G/∞ queue (with a nonhomogeneous Poisson arrival process). We know that, for appropriate initial conditions, the number of busy servers at time t has a Poisson distribution for each t. Our results show how the time-dependent mean function m depends on the time-dependent arrival-rate function λ and the service-time distribution. For example, when λ is quadratic, the mean m(t) coincides with the pointwise stationary approximation λ(t)E[S], where S is a service time, except for a time lag and a space shift. It is significant that the well known insensitivity property of the stationary M/G/∞ model does not hold for the nonstationary Mt/G/∞ model; the time-dependent mean function m depends on the service-time distribution beyond its mean. The service-time stationary-excess distribution plays an important role. When λ is decreasing before time t, m(t) is increasing in the service-time...
TL;DR: Using the optimal control theory approach, two new DUO traffic assignment models for a congested transportation network are formulated, including new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model.
Abstract: The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. In this paper, we introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solutions of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first-order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints...
TL;DR: This paper shows how a recursive procedure derived for determining the policy costs for an average item in case of one-for-one replenishment policies can be used for the exact or approximate evaluation of more general policies where both the retailers and the warehouse order in batches.
Abstract: We consider a two-level inventory system with one warehouse and N identical retailers. Lead times (transportation times) are constant and the retailers face independent Poisson demand. In a previous paper, we derived a recursive procedure for determining the policy costs for an average item in case of one-for-one replenishment policies. In this paper, we show how these results can be used for the exact or approximate evaluation of more general policies where both the retailers and the warehouse order in batches. We compare our methods to the method recently suggested by A. Svoronos and P. Zipkin.
TL;DR: This paper demonstrates that the computational effort required to develop numerical solutions to continuous-state dynamic programs can be reduced significantly when cubic piecewise polynomial functions, rather than tensor product linear interpolants, are used to approximate the value function.
Abstract: This paper demonstrates that the computational effort required to develop numerical solutions to continuous-state dynamic programs can be reduced significantly when cubic piecewise polynomial functions, rather than tensor product linear interpolants, are used to approximate the value function. Tensor product cubic splines, represented in either piecewise polynomial or B-spline form, and multivariate Hermite polynomials are considered. Computational savings are possible because of the improved accuracy of higher-order functions and because the smoothness of higher-order functions allows efficient quasi-Newton methods to be used to compute optimal decisions. The use of the more efficient piecewise polynomial form of the spline was slightly superior to the use of Hermite polynomials for the test problem and easier to program. In comparison to linear interpolation, use of splines in piecewise polynomial form reduced the CPU time to obtain results of equivalent accuracy by a factor of 250–330 for a stochastic ...
TL;DR: Demand Driven Dispatch is an operating concept that addresses the assignment of airplane capacity to flight schedules to meet fluctuating market needs by dynamically assigned to flights to better match the predicted final demands.
Abstract: A major problem for the airline industry is the assignment of airplane capacity to flight schedules to meet fluctuating market needs. Demand Driven Dispatch (D3) is an operating concept that addresses this problem. Utilizing a demand forecast which improves as flight departure approaches, aircraft are dynamically assigned to flights to better match the predicted final demands. The result, demonstrated in studies of actual airline systems, is an increase in passenger loads and revenues with simultaneously reduced costs for a net of 1–5% improvement in operating profits. Concept implementation is simplified by the prevalence of yield management systems which provide the forecasting capability, and the emergence of airplane families which provide the necessary operational flexibility. Implementation also requires frequent solution of extremely large aircraft assignment problems. These problems, which can be formulated in terms of a multicommodity network flow, can be solved with heuristic algorithms shown to...
TL;DR: New integer linear programminig formulations are provided, and results on the matroidal structure of a class of combinatorial problems are developed that can solve to optimality problems involving up to 60 vertices.
Abstract: Given a complete directed graph G = V, A, the delivery man problem DMP consists of determining a Hamiltonian circuit minimizing the sum of distances along the circuit from a given vertex v1, to every vertex of V, including v1 itself. There exists a number of applications of the DMP in the fields of distribution and machine scheduling. The DMP is NP-hard. The objective of this paper is to develop new theoretical results and an exact algorithm for the problem. A new, integer linear programming formulation is provided, and results on the matroidal structure of a class of combinatorial problems are developed. These are used to derive lower bounds for the DMP. These bounds are embedded into an enumerative algorithm. The largest problems solved to optimality with the proposed algorithm involve 60 vertices. This compares favorably with previously published methods.
TL;DR: An overview of basic models and solution algorithms for the lot streaming problem is presented, including models with continuous and discrete sublot sizes, models with and without intermittent idling of machines, and models with consistent and variable sublots.
Abstract: We present an overview of basic models and solution algorithms for the lot streaming problem. We include models with continuous and discrete sublot sizes, models with and without intermittent idling of machines, and models with consistent and variable sublots. We also introduce a model with limited transporter capacity. First we present solutions for two machines, then generalize to three machines and, where possible, to several machines. We synthesize previous research and introduce several new results.
TL;DR: It is hypothesized that a ‘natural drift’ has occurred, i.e., that old-style OR has remained underdeveloped relative to its more purely theoretical and practical counterparts, and the extent to which this natural drift would be truly natural is explored.
Abstract: “Crisis? What crisis?” could also have been an appropriate title for this paper. The OR/MS literature contains more than enough papers addressing the crisis in OR/MS to take the matter seriously, but it is not always clear exactly what is meant by crisis. The complaints usually concern the perceived gap between theory and practice, pointing out that there are too many theoretical and too few practice-oriented papers. This may well be true, but we suggest a slightly different view of the crisis, by hypothesizing that a ‘natural drift’ has occurred, i.e., that old-style OR has remained underdeveloped relative to its more purely theoretical and practical counterparts. To explain how this hypothesis arose, we provide an overview of the debate on professional concerns in OR/MS, and contrast it with Harvard Business Review papers providing a managerial perspective. We also explore the extent to which such a natural drift would be truly natural, by comparing the development of OR/MS to that of other professions....
TL;DR: This paper presents an analysis of the fundamental case in which flights from many origins must be scheduled for arrival at a single, congested airport and describes a set of approaches for addressing a deterministic and a stochastic version of the problem.
Abstract: One of the most important functions of air traffic management systems is the assignment of ground-holding times to flights, i.e., the determination of whether and by how much the take-off of a particular aircraft headed for a congested part of the ATC system should be postponed to reduce the likelihood and extent of airborne delays. In this paper, we will present an analysis of the fundamental case in which flights from many origins must be scheduled for arrival at a single, congested airport. We will describe a set of approaches for addressing a deterministic and a stochastic version of the problem. A minimum cost flow algorithm can be used for the deterministic problem. Under a particular natural assumption regarding the functional form of delay costs, a very efficient, simple algorithm is also available. For the stochastic version, an exact dynamic programming formulation turns out to be impractical for typical instances of the problem and we present a number of heuristic approaches to it. The models a...
TL;DR: It is shown under mild probabilistic assumptions that the generated solutions and bounds come asymptotically within a few percentage points of optimality (within the considered class of strategies) for problems of moderate size.
Abstract: We consider distribution systems with a single depot and many retailers each of which faces external demands for a single item that occurs at a specific deterministic demand rate. All stock enters the systems through the depot where it can be stored and then picked up and distributed to the retailers by a fleet of vehicles, combining deliveries into efficient routes. We extend earlier methods for obtaining low complexity lower bounds and heuristics for systems without central stock. We show under mild probabilistic assumptions that the generated solutions and bounds come asymptotically within a few percentage points of optimality (within the considered class of strategies). A numerical study exhibits the performance of these heuristics and bounds for problems of moderate size. W e consider distribution systems with a single Al [depot and many retailers with external demands for a single item that occur at a specific constant (but retailer-dependent) deterministic rate. The depot places orders with an outside supplier. Goods are distributed from the depot to the retailers by a fleet of identical vehicles, combining deliveries into efficient routes. In an earlier paper, Anily and Federgruen (1990a) analyze a model where the depot serves as a mere coordinator of the replenishment process or alternatively as a transshipment point in which no inventory can be kept. In such systems, one has to determine replenishment policies for all retailers, as well as matching efficient routing patterns. In this paper, we extend the analysis to the case where central inventories may be kept in the warehouse. As a consequence, the above problems are compounded by that of determining a replenishment strategy for the warehouse, optimally coordinated with that of each retailer and synchronized with the transportation schedules. We assume that at each outlet, customer demands occur at a constant, deterministic but outlet specific rate. These demanid rates are assumed to be rational, so that after appropriate scaling they are even integers. An outlet may thus be viewed as the aggregate of an integer number of demand points, each of which faces a demand rate of two. Inventory carrying costs are incurred at a constant rate per unit of time, and per unit stored. (This rate is identical for all retailers, but is different at the warehouse.) The transportation costs include a fixed (leasing or renting) cost per route driven by one of the vehicles and variable costs proportional to the total (Euclidean) distance on all routes (but no unloading costs). As in most standard inventory models we assume that the cost of an order from the outside supplier is fixed-plus-linear.
TL;DR: This paper details solution methodologies for the static routing problem in which demand assignment of the AGVs are known; the focus is to obtain an implementable solution within a reasonable amount of computer time.
Abstract: Automated guided vehicles AGVs are a highly sophisticated and increasingly popular type of material handling device in flexible manufacturing systems. This paper details solution methodologies for the static routing problem in which demand assignment of the AGVs are known; the focus is to obtain an implementable solution within a reasonable amount of computer time. The objective is to minimize the makespan, while routing AGVs on a bidirectional network in a conflict-free manner. This problem is solved via column generation. The master problem in this column generation procedure has the makespan and vehicle interference constraints. Columns in the master problem are routes iteratively generated for each AGV. The subproblem is a constrained shortest path problem with time-dependent costs on the edges. An improvement procedure is developed to better the solution obtained at the end of the master-subproblem interactions. Several methods of iterating between the master and subproblem are experimented with in-depth computational experiments. Our empirical results indicate that the procedure as a whole usually generates solutions that are within a few percent of a proposed bound, within reasonable computer time.
TL;DR: It is shown that decomposition methods can be classified according to three main approaches, and one of these approaches is of special interest because it offers a symmetrical view of the decomposition.
Abstract: Queueing networks with blocking are useful for modeling and analyzing discrete event systems, especially manufacturing systems. Most analysis methods for queueing networks with blocking are approximation methods that involve a decomposition of the network into a set of subsystems. This paper presents some insight into these decomposition methods as well as new results. Attention is mainly restricted to the case of tandem queueing networks with exponential service times and blocking-after-service. This type of blocking is especially encountered in manufacturing systems. The first aim of this paper is to improve the understanding and present a unified view of the decomposition methods. We show that decomposition methods can be classified according to three main approaches. One of these approaches is of special interest because it offers a symmetrical view of the decomposition. The second aim of the paper is to provide properties pertaining to these decomposition methods in the case of exponential characterizations of subsystems. We prove the existence and uniqueness of the solution. Moreover, we prove the convergence of the computational algorithm associated with the symmetrical approach.
TL;DR: This paper extends the definition of an influence diagram by introducing a new representation for its conditional probability distributions, which allows one to clearly and efficiently represent asymmetric decision problems and provides an attractive alternative to both the decision tree and conventional influence diagram representations.
Abstract: An influence diagram is a graphical representation of a decision problem that is at once a formal description of a decision problem that can be treated by computers and a representation that is easily understood by decision makers who may be unskilled in the art of complex probabilistic modeling. The power of an influence diagram, both as an analysis tool and a communication tool, lies in its ability to concisely summarize the structure of a decision problem. However, when confronted with highly asymmetric problems in which particular acts or events lead to very different possibilities, many analysts prefer decision trees to influence diagrams. In this paper, we extend the definition of an influence diagram by introducing a new representation for its conditional probability distributions. This extended influence diagram representation, combining elements of the decision tree and influence diagram representations, allows one to clearly and efficiently represent asymmetric decision problems and provides an attractive alternative to both the decision tree and conventional influence diagram representations.
TL;DR: This work examines shortest path problems in acyclic networks in which arc costs are known functions of certain environment variables at network nodes and develops two recursive procedures for the individual arc case and a dynamic programming procedure that solves the corresponding problem.
Abstract: We examine shortest path problems in acyclic networks in which arc costs are known functions of certain environment variables at network nodes. Each of these variables evolves according to an independent Markov process. The vehicle can wait at a node (at a cost) in anticipation of more favorable arc costs. We first develop two recursive procedures for the individual arc case, one based on successive approximations, and the other on policy iteration. We also solve the same problem via parametric linear programming. We show that the optimal policy essentially classifies the state of the environment variable at a node into two categories: green states for which the optimal action is to immediately traverse the arc, and red states for which the optimal action is to wait. We then extend these concepts for the entire network by developing a dynamic programming procedure that solves the corresponding problem. The complexity of this method is shown to be O(n2K + nK3), where n is the number of network nodes and K ...
TL;DR: An algorithm is developed that systematically solves the dynamic scheduling problem by solving a sequence of linear programs and recovers the priority index set that is optimal for the corresponding discrete queueing model, generally known as Klimov's problem.
Abstract: A fluid network is a deterministic network model in which dynamic continuous flows are circulated and processed among a set of stations. A fluid network often describes the asymptotic behavior of a stochastic queueing network via functional strong law of large numbers. We study the dynamic scheduling of multiple classes of fluid traffic in such a network. An algorithm is developed that systematically solves the dynamic scheduling problem by solving a sequence of linear programs. It generates a policy, in the form of dynamic capacity allocation at each station among all fluid classes, that consists of a finite set of linear "pieces" over the entire time horizon. In a single-station, or equivalently, single-server, network, this solution procedure recovers the priority index set that is optimal for the corresponding discrete queueing model, generally known as Klimov's problem.
TL;DR: A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
Abstract: Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions (L, W) is supplied. There are n types of demanded rectangles r1, r2, …, rn, with the ith type having length li, width wi, value vi, and demand constraint bi. It is required to produce, from the stock rectangle S, ai copies of ri, 1 ≤ i ≤ n, to maximize a1v1 + a2v2 + · + anvn subject to the constraints ai ≤ bi. Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
TL;DR: The heuristic approach for handling the delivery dispatching problem is adopted, based in part on a decomposition of the problem by customer, where customer subproblems generate penalty functions that are applied in a master dispatches problem.
Abstract: We describe a dynamic and stochastic vehicle dispatching problem called the delivery dispatching problem. This problem is modeled as a Markov decision process. Because exact solution of this model is impractical, we adopt a heuristic approach for handling the problem. The heuristic is based in part on a decomposition of the problem by customer, where customer subproblems generate penalty functions that are applied in a master dispatching problem. We describe how to compute bounds on the algorithm's performance, and apply it to several examples with good results.
TL;DR: The procedure developed describes a systematic approach that allows decision makers to resolve system-inherent infeasibilities, and a heuristic based on rounding to develop good feasible solutions to the model.
Abstract: The resident scheduling problem is a specific case of the multiperiod staff assignment problem where individuals are assigned to a variety of tasks over multiple time periods. As in many staffing and training situations, numerous limitations and requirements may be placed on those assignments. This paper presents a procedure for addressing two major problems inherent in the determination of a solution to this type of problem: infeasibilities that naturally occur in the scheduling environment but are obscured by complexity; and the intractable nature of large-scale models with this structure. The procedure developed describes a systematic approach that allows decision makers to resolve system-inherent infeasibilities, and a heuristic based on rounding to develop good feasible solutions to the model. The procedure is illustrated via a case example of resident assignments for teaching and training modules in a university affiliated teaching hospital.
TL;DR: For congested networks on which flows vary over time, system marginal costs, user perceived costs and user externality costs are derived, for each arc and path, and a set of optimal congestion tolls and flow controls are obtained.
Abstract: For congested networks on which flows vary over time, we derive system marginal costs, user perceived costs and user externality costs, for each arc and path. We also obtain a set of optimal congestion tolls and flow controls which may be used to shift the user determined flows toward a socially preferred pattern. An important way in which our results differ from the usual static analysis is that the social cost externality depends not only on the level of congestion, but also on the rate of increase or decrease of congestion. This is intuitively explicable as follows. Consider users delayed on an arc. Their delays will be further compounded or multiplied if congestion has increased during the time they are delayed. On the other hand, their delays will be reduced if congestion has declined during the time they are delayed. This multiplier effect is such that the resultant dynamic externalities can easily be a few times larger, or smaller, than the externalities derived in the usual static analysis. As a r...