Long-run Average Profit Research Articles

A Repair-Time Limit Replacement Policy With Estimation Error

In this article, we consider a repair-time limit replacement policy with estimation error. If a system fails, we estimate the repair time to recover the system failure. In reality, the estimation error occurs in the estimation of repair time. Considering the estimation error, we formulate the repair-time limit replacement policy and obtain analytically the long-run average profit rate and the total discounted profit. We obtain numerically the optimal repair-time limits to maximize the long-run average profit rate and the total discounted profit. Numerical examples are experimented to find trends of the optimal repair-time limit and the effect of model parameters on the optimal repair-time limit.

FIFO Versus LIFO Issuing Policies for Stochastic Perishable Inventory Systems

We consider an inventory system for perishable items in which the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by one of the items on the shelf, if available. A demand remains unsatisfied if it arrives at an empty shelf. The aim of this paper is to compare two issuing policies: under FIFO (‘first in, first out’) any demand is satisfied by the item with the currently longest shelf life, while under LIFO (‘last in, first out’) always the youngest item on the shelf is assigned first. We determine the long-run net average profit as a function of the system parameters under each of the two policies, taking into account the revenue earned from satisfied demands, the cost of shelf space, penalties for unsatisfied demands, and the purchase cost of incoming items. The analytical results are used in several numerical examples in which the optimal input rate and the maximum expected long-run average profit under FIFO and under LIFO are determined and compared. We also provide a sensitivity analysis of the optimal solution for varying parameter values.

Optimal static pricing for a service facility with holding costs

We study a service facility modelled as a single-server queueing system with Poisson arrivals and limited or unlimited buffer size. In systems with unlimited buffer size, the service times have general distributions, whereas in finite buffered systems service times are exponentially distributed. Arriving customers enter if there is room in the facility and if they are willing to pay the posted price. The same price is charged to all customers at all times (static pricing). The service provider is charged a holding cost proportional to the time that the customers spend in the system. We demonstrate that there is a unique optimal price that maximizes the long-run average profit per unit time. We also investigate how optimal prices vary as system parameters change. Finally, we consider buffer size as an additional decision variable and show that there is an optimal buffer size level that maximizes profit.

DYNAMIC PRICING AND INVENTORY CONTROL FOR A PRODUCTION SYSTEM WITH AVERAGE PROFIT CRITERION

In this article we study the joint optimization of finished goods inventory and pricing in a make-to-stock production system with long-run average profit criterion. The production time is random with controllable rate and the demand is Markovian with rate depending on the sale price. The objective is to dynamically adjust the production rate and the sale price to maximize the long-run average profit. We obtain the optimal dynamic pricing and production control policy and present an efficient bisection algorithm for computing the policy parameters.

Optimal price and pro rata decisions for combined warranty policies with different repair options

A repairable product under a non-renewing combined warranty policy that is subject to a displaced log-linear demand function of the product's price and pro rata period length is considered. Expressions for the manufacturer's long-run average profit per unit time under replacement, minimal and general repair options are obtained. In addition, expressions for the stationary points and second-order conditions of the profit function are presented. Numerical illustrations that demonstrate optimal product pricing, pro rata length determination, and repair option selection to maximize the manufacturers, profit are given.

A Capacitated Commodity Trading Model with Market Power

This Master Thesis proposes an analytical model of commodity trading in the presence of market power, which is new to the literature. We establish the rational behavior of traders between two markets and derive price spread dynamics based on the trading volumes. We consider two commodity markets that quote different prices for the same product, and a trader capable of purchasing in one market to resell in the other, within a trading capacity. For simplicity, we assume that the inventory present between the two markets is constant, i.e., the amount stored is fixed (and is directly linked to the trading capacity). We first establish the structure of the optimal trading policy. This policy determines, given a realization of the current price spread between the two markets, how much (if any) volume must be bought/sold from/at the first market and sold/bought at/from the second market, so that the long-run average profit is maximized. When optimizing, the trader takes into account its impact on future spreads. We then describe the parameters of the optimal policy and we apply our model to kerosene prices in New York and Los Angeles, and illustrate the insights derived.

Maximisation of long-run average profit through dynamic control of production and pricing in a manufacturing system

This paper concerns the joint management problem of production control and dynamic pricing to balance the finished goods inventory and market demand in a make-to-stock manufacturing system using a long-run average profit criterion. In the system, the production rate is random, with a controllable mean rate, and the demand is Markov, with a changeable mean rate which depends on the sale price. The management issue is how to dynamically adjust the production rate and the selling price to maximise the long-run average profit. We discover that the optimal policy of dynamic pricing and production control over an infinite horizon is a matter of thresholds. An effective algorithm is suggested.

Congestion-dependent pricing in a stochastic service system

We study a service facility modeled as a queueing system with finite or infinite capacity. Arriving customers enter if there is room in the facility and if they are willing to pay the price posted by the service provider. Customers belong to one of a finite number of classes that have different willingnesses-to-pay. Moreover, there is a penalty for congestion in the facility in the form of state-dependent holding costs. The service provider may advertise class-specific prices that may fluctuate over time. We show the existence of a unique optimal stationary pricing policy in a continuous and unbounded action space that maximizes the long-run average profit per unit time. We determine an expression for this policy under certain conditions. We also analyze the structure and the properties of this policy.

Congestion-dependent pricing in a stochastic service system

We study a service facility modeled as a queueing system with finite or infinite capacity. Arriving customers enter if there is room in the facility and if they are willing to pay the price posted by the service provider. Customers belong to one of a finite number of classes that have different willingnesses-to-pay. Moreover, there is a penalty for congestion in the facility in the form of state-dependent holding costs. The service provider may advertise class-specific prices that may fluctuate over time. We show the existence of a unique optimal stationary pricing policy in a continuous and unbounded action space that maximizes the long-run average profit per unit time. We determine an expression for this policy under certain conditions. We also analyze the structure and the properties of this policy.

Dynamic Pricing in e‐Services under Demand Uncertainty

High volatility of the e‐services market, due to increasing competition, low life cycle of products, and easy availability of information about competing service offerings to customers, makes the demand for service offerings quite uncertain. Revenue management in such markets calls for real‐time techniques to learn the demand and its dependence on both the price and the service level associated with the service offering. We assume firms reply on exploratory approaches for demand estimation, in which firms experiment with different service offerings in order to simultaneously learn the demand while doing business. Such exploration and learning process can be costly without supervision. As reported by Rothschild (Journal of Economic Theory, 9 185‐202, 1974), traditional Bayesian dynamic control approaches may conclude with suboptimal offerings. We propose a novel demand learning approach that is guaranteed to converge to the optimal offering. The approach combines simulated annealing algorithm with Bayesian learning. We further present intelligent techniques that adaptively reduce the effort of exploration on suboptimal service offerings so as to improve the long‐run average profit.

Random fuzzy EOQ model with imperfect quality items

This paper investigates an economic order quantity (EOQ) problem with imperfect quality items, where the percentage of imperfect quality items in each lot is characterized as a random fuzzy variable while the setup cost per lot, the holding cost of each unit item per day, and the inspection cost of each unit item are characterized as fuzzy variables, respectively. In order to maximize the expected long-run average profit, a random fuzzy EOQ model is constructed. Since it is almost impossible to find an analytic method to solve the proposed model, a particle swarm optimization (PSO) algorithm based on the random fuzzy simulation is designed. Finally, the effectiveness of the designed algorithm is illustrated by a numerical example.

Statistical dynamics in a chaotic Cournot model with complementary goods

This study sheds light on statistical properties of chaotic economic dynamics. To this end, it builds a simple Cournot dynamic model with two firms in which reactions functions are non-linear and goods are complements. When non-linearities get strong enough, the output adjustment process generates complex dynamics involving chaos. It is analytically as well as numerically demonstrated that for both firms, a long-run average profit taken along a chaotic trajectory can be higher than a profit taken at a stationary point. This result implies that chaotic dynamics can be beneficial from the long-run point of view.

RELIABILITY AND CHECK REPLACEMENT POLICY OF MECHANICAL EQUIPMENT UNDER PREDICTIVE MAINTENANCE

Most of mechanical equipments have 3 states: normal, abnormal and failure. When the equipments are checked and diagnosed in abnormal, they will accept predictive maintenance. And if the equipments fail, they will accept failure repair. It is assumed that the predictive maintenance makes equipments "as good as new", while the failure repair does not makes equipment "as good as new". Monotone process is introduced to describe the case that failure repair does not makes equipment "as good as new". Under above assumption and others, reliability and check replacement policy of mechanical equipments are studied by using probability analysis and vector markov process method. The explicit expression of the reliability index and average profit rate (i.e., the long-run average profit per unit time) are derived and the rule of feasibility for the optimal check replacement policy under the largest average profit rate is obtained. The corresponding optimal check replacement policy can be determined analytically or numerically. The research on the actual example shows that the result can provide some scientific basis for improving the reliability, safety and economic profit of mechanical equipments.

Statistical estimation algorithms for repairs-time limit replacement scheduling under earning rate criteria

In this paper, we formulate two repair-time limit replacement problems with imperfect repair under earning rate criteria with and without discounting. First, the optimal repair-time limits which maximize the long-run average profit rate and the expected total discounted profit over an infinite time horizon are analytically derived. Next, we develop the nonparametric algorithms for estimating the optimal repair-time limits, provided that the complete sample data of repair time are given. The basic idea is to apply the Lorenz statistics and to transform the underlying algebraic problems to the graphical ones. Finally, we present some numerical examples to show that the proposed algorithms can be useful to estimate the profit-based repair limit replacement schedule.

Profitable Chaos in a Duopoly Market with Asymmetric Production Externality

This study investigates an economic implication of chaotic fluctuations that are observed in a nonlinear economic dynamic model. To this end, it constructs a nonlinear discrete time Cournot duopoly model in which firms have U-shaped or inverted U-shaped reaction functions due to production externality and shows that chaotic output fluctuations can arise for strong nonlinearities. Two main results of this study are: (i) it is theoretically as well as numerically confirmed that one of the duopolists can benefit in the sense that the long-run average profit taken along a chaotic trajectory is higher than the profit taken at an equilibrium point while the other is disadvantaged if both duopolists are homogeneous; (ii) it is verified with numerical simulations that both duopolists can benefit from chaotic trajectories if they are heterogenous.

Can inventory chaos be welfare improving

This study demonstrates the possibility that chaotic fluctuations may be preferable to a steady state. For this purpose, it uses a simple macro disequilibrium model in which inventory can be chaotically fluctuated. In such a model, the profit of a firm as well as the utility of a consumer fluctuates. This raises the question of their average profitability and preferability in the long run. This study, with the aid of numerical examples, demonstrates that the long-run average profit can be greater than the profit obtained at the steady state while the long-run average utility is the same as the utility obtained at the steady state.

Preferable Disequilibrium Dynamics

This study demonstrates a possibility that chaotic fluetations may be preferable to a stationary state. For this purpose, it use a simple macro disequilibrium model in which inventory can be chaotically fluctuationed. Accordingly profit of a firm as well as utility of a consumer fluctutes. This raises the question of the average profitability and preferability in the long-run. This study, with an aid of numerical examples, demonstrates that the long-run average profit can be greater than Lhe profit obtained at the stationary state while the long-run average utility is idnetical with the utility obtained at the stationary state.

Optimal Expulsion Control—A Dual Approach to Admission Control of an Ordered-Entry System

In this paper we obtain the optimal admission control policy for a first-come, first-served (FCFS) M/M/m ordered-entry queueing system to maximize the expected discounted (and the long-run average) profit (reward minus cost). We introduce a new approach for determining the optimal admission control policy. The underlying idea of this approach is to construct a dual system: a preemptive last-come, first-served (LCFS-P) M/M/m ordered-entry queueing system that is subject to expulsion control. We show that an LCFS-P system with expulsion control is isomorphic to an FCFS system with admission control, and the two systems share the same optimal control policy. Eluding the conventional dynamic programming formulation, we approach the solution from behaviors of individual customers and their impact on the social outcome. This makes our analysis simple and intuitive and reveals a better insight into the structural properties of the optimal control policy. Besides providing formulas to compute the optimal threshold, we use the operational characteristics of the dual system to obtain an easily computable approximation for the optimal threshold. The applicability of the approach transcends well beyond the problem addressed in this paper.

Competitive Profits in the Long Run

Profit rates differ across industries. Explanations have often relied on static models of imperfect competition. This paper develops a dynamic model of perfect competition to demon- strate that long-run average profit rates differ even across competitive industries when the effects of sunk costs on entry and exit are considered. The hypothesis that firms maximize their present expected values has few empirical implications for long-run average profit rates, but it does have implications for the behaviour of variables over time; for example, industries with high variability in the number of firms should exhibit low variability in firm values. Recent work in industrial organization theory has resulted in several useful dynamic competitive models of industry evolution. These models are of three types. The first, due to Jovanovic (1982), is a model of passive learning where producers, uncertain about their productivity, acquire noisy information about how efficient they are.6 The second, due to Ericson and Pakes (1989), is a model of active learning where producers invest to increase the probability that they will become more efficient. The third, exposited in Lambson (1991), differs from the learning models of industry evolution by assuming that producers know how productive they are and that they all have access to the same technologies, but that they are uncertain about future market conditions. (The description of a market condition includes all relevant exogenous factors; for example, a market condition may consist of a vector of input prices and an output demand curve.) These three approaches are not mutually exclusive; rather they attempt to capture different aspects of reality. This paper applies the third approach to the question of why profit rates differ across industries, even in the long run. In so doing, it explicitly takes into account the effects of sunk costs, entry, exit, and random market conditions on the determination of long-run average profit rates. The existence of sunk costs generates hysteresis, that is, effects