Gerhard Sorger

Sequencing of parts and robot moves in a robotic cell

In this paper, we deal with the problem of sequencing parts and robot moves in a robotic cell where the robot is used to feed machines in the cell. The robotic cell, which produces a set of parts of the same or different types, is a flow-line manufacturing system. Our objective is to maximize the long-run average throughput of the system subject to the constraint that the parts are to be produced in proportion of their demand. The cycle time formulas are developed and analyzed for this purpose for cells producing a single part type using two or three machines. A state space approach is used to address the problem. Both necessary and sufficient conditions are obtained for various cycles to be optimal. Finally, in the case of many part types, the problem of scheduling parts for a specific sequence of robot moves in a two machine cell is formulated as a solvable case of the traveling salesman problem.

Competitive dynamic advertising: A modification of the Case game

Abstract In this paper, we consider a modified version of the advertising differential game of Case (1979). We derive non-cooperative Nash equilibria for open-loop controls as well as for feedback strategies. We consider finite and infinite planning horizons. The feedback equilibrium is shown to be robust against stochastic disturbances of the state equation.

On the Long-Run Distribution of Capital in the Ramsey Model

Abstract We study issues related to the long-run distribution of wealth in two variants of Ramseys model of optimal capital accumulation. First we show that, in the case where a government levies a progressive income tax, there exist infinitely many stationary equilibria in which all households own positive capital stocks. Moreover, it is demonstrated that non-stationary equilibria can exhibit complicated dynamics. Then we discuss the case where households exercise market power on the capital market and we show that this may also lead to equilibria in which all households own positive amounts of capital. Journal of Economic Literature Classification Numbers: E62, O41.

Ergodic Chaos in Optimal Growth Models with Low Discount Rates

SummaryWe show that for every discount factorρε(0,1) one can find infinitely many strictly concave discrete-time optimal growth models in reduced form which have optimal policy functions exhibiting ergodic chaos. These reduced form models are interpreted in a two-sector optimal growth setting with utility functions depending on consumption as well as on capital.

Capacity Allocation for Dynamic Process Improvement with Quality and Demand Considerations

Management of process improvement activities is an essential part of the manufacturing strategy of a firm to remain globally competitive in the long run. This paper considers a manufacturing environment where process improvement activities require use of the productive capacity of the firm in addition to other investments. Thus the firm must allocate its productive capacity between production activities and improvement activities. The output of production activities is used to meet customer demand. Process improvement activities improve the quality of the output, which in turn leads to lower quality related costs both internal and external and possibly lower per-unit production cost. It is assumed that the demand function is downward sloping and that revenue is a concave function of output. A continuous-time, finite-horizon, profit maximization, resource allocation model is developed to find an optimal time path for process improvement activities and production activities. Computational results are provided to study the effect of various problem parameters on the optimal decisions.

On the minimum rate of impatience for complicated optimal growth paths

The occurrence of complex dynamics in economic models has received wide attention by the economic profession during the last decade (see Boldrin and Woodford (1990) for a recent survey). One of the most interesting and surprising results obtained so far is the indeterminacy theorem of Boldrin and Montrucchio (1986b), which implies that virtually every dynamical behavior is fully compatible with the standard assumptions of decreasing returns, competitive markets, and perfect foresight. Deneckere and Pelikan (1986) have used a related approach to derive similar results for the special case of one-dimensional dynamics. Whereas the analysis in Boldrin and Montrucchio (1986b) and Deneckere and Pelikan (1986) is restricted to optimal growth models formulated in discrete time, an analogous result holds also for the continuous time case (see Montrucchio (1988) and Sorger (1990)). All of these indeterminacy theorems have been proved by a constructive approach which requires a sufficiently high rate of impatience on the side of the decision maker. In particular, to construct optimal growth models exhibiting some well known chaotic maps (like the logistic map, or the Henon map) as optimal policy functions, one needs time preference rates of more than 400%.

Analysis of Nash equilibria in a class of capital accumulation games

In a simple capital accumulation game we study existence and dynamic properties of the cooperative solution, two kinds of Markov perfect equilibria (MPE), and a trigger strategy equilibrium. In the cooperative solution the stock always converges towards a steady state. This property is shared by our first MPE, whereas the second type of MPE may result in complicated dynamics. A Pareto comparison of both MPE depends on the parameter specifications but can turn out either way. Finally, we show how the players can achieve the efficient payoffs of the cooperative solution as an equilibrium outcome by using trigger strategies.

On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots

SummaryWe consider a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous households. Under the standard assumptions of strictly concave and time-additive utility functionals and a strictly concave production function we show that perfect foresight equilibria can be non-unique, even locally non-unique (indeterminate), and periodic of arbitrary long periodp. Moreover, we prove that there can exist non-trivial rational expectations (sunspot) equilibria when the agents expectations about future factor prices depend on extrinsic uncertainty.

Adpuls in continuous time

Abstract Hermann Simon (1982) presented a formulation of the advertising sales relation for which pulsing is a long run optimal policy. His model, named Adpuls , explains wearout phenomena drawing on Helsons (1964) adaptation level theory. It is formulated in discrete time and the optimal policy alternates between high and low advertising effort from period to period. So the length of the model period determines the phase durations of pulsing. But the model period is predetermined. Practice, however, is interested in optimal durations of flights and pauses between them. In order to cope with this problem a continuous time version of Adpuls is proposed, for which optimal pulsing patterns are obtained numerically.

A DIFFERENTIAL GAME APPROACH TO EVOLUTIONARY EQUILIBRIUM SELECTION

The equilibrium selection model of Matsui and Matsuyama (1995), which is based on rational players who maximise their discounted future payoff, is analysed with the help of an associated differential game. Equilibrium selection results are derived for games with a ½-dominant equilibrium, for games with a potential function, and some simple supermodular games.