Business Administration and Industrial Engineering

Cooperation can potentially improve competitiveness and profitability of firms with limited resources and production capacities. This article presents a continuous-time Markov chain model to study an assortment-based cooperation between two independent firms with limited capacity. An assortment-based cooperation is an agreement to combine the product assortments of two firms and offer the combined assortment to each firm's customers. Both centralized and decentralized cooperations are studied. In a centralized cooperation, firms jointly make replenishment decisions, whereas in the decentralized case, firms operate under independent base stock policies and manage product exchanges through a discount-based contract where each firm supplies its own product to the other firm at a discounted price and at an agreed-upon fill rate. Under this scheme, assortment-based cooperation also mandates each firm to effectively ration their inventories since they have to deal with two different demand streams. The discount-based contract yields the results of the centralized operation by using specific values of the contract parameters. It is shown that assortment-based cooperation is always beneficial for two symmetrical firms in both centralized and decentralized cooperation. Numerical experiments reveal that assortment-based cooperation is not always beneficial if the firms are not symmetrical.

We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, the customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's own production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system when it is managed according to this policy is evaluated. The subcontractors represent a set of capacity options, and we calculate the values of these options.

In this study, a Markovian fluid flow system with two stages separated by a finite buffer is considered. Fluid flow models have been analyzed extensively to evaluate the performance of production, computer, and telecommunication systems. Recently, we developed a methodology to analyze general Markovian continuous flow systems with a finite buffer. The flexibility of this methodology allows us to analyze a wide range of systems by specifying the transition rates and the flow rates associated with each state of each stage. In this study, in order to demonstrate the applicability of our methodology, we model and analyze a range of models studied in the literature. The examples we analyze as special cases of our general model include systems with phase-type failure and repair-time distributions, systems with machines that have multiple up and down states, and systems with multiple unreliable machines in series or parallel in each stage. For each case, the Markovian model is developed, the transition and flow rates are determined, and representative numerical results are obtained by using our methodology.

In this study, a Markovian fluid flow system with two stages separated by a finite buffer is considered. Fluid flow models have been analyzed extensively to evaluate the performance of production, computer, and telecommunication systems. Recently, we developed a methodology to analyze general Markovian continuous flow systems with a finite buffer. The flexibility of this methodology allows us to analyze a wide range of systems by specifying the transition rates and the flow rates associated with each state of each stage. In this study, in order to demonstrate the applicability of our methodology, we model and analyze a range of models studied in the literature. The examples we analyze as special cases of our general model include systems with phase-type failure and repair-time distributions, systems with machines that have multiple up and down states, and systems with multiple unreliable machines in series or parallel in each stage. For each case, the Markovian model is developed, the transition and flow rates are determined, and representative numerical results are obtained by using our methodology.

We consider Markovian models of discrete materials¯ow production systems. The transient behavior of a production line is investigated. Namely, mean and variance of the number of parts produced in a given time period conditioned on an arbitrary initial condition is determined by using a Markov reward model. Closed-form expression for the variance of the output from a single unreliable station is derived to illustrate the procedure. Then variance of the output from a general two-station production line with a ®nite buer is determined by using a set of recursive equations that exploits the special structure of the probability matrix. The relationship between the due-time performance and variability of the line is investigated by determining the probability of meeting a customer order on time and also the time to produce a given order approximately. Numerical experiments that investigate the relationships between the system parameters and production line dynamics are also included. Ó

In this study we present a planning methodology for a firm whose objective is to match the random supply of annual premium fruits and vegetables from a number of contracted farms and the random demand from the retailers during the planning period. The supply uncertainty is due to the uncertainty of the maturation time, harvest time, and yield. The demand uncertainty is the uncertainty of weekly demand from the retailers. We provide a planning methodology to determine the farm areas and the seeding times for annual plants that survive for only one growing season in such a way that the expected total profit is maximized. Both the single period and the multi period cases are analyzed depending on the type of the plant. The performance of the solution methodology is evaluated by using numerical experiments. These experiments show that the proposed methodology matches random supply and random demand in a very effective way and improves the expected profit substantially compared to the planning approaches where the uncertainties are not taken into consideration.

Abstract We consider a logistics spot market,where the transportation,orders from a number,of firms are matched,with two types of carriers through a reverse auction. In the spot market, local carriers compete with in-transit carriers that have lower costs. In order to analyze the effects of implementing a logistics spot market on these three parties: firms, local carriers, and in-transit carriers and also the effects of various system parameters, we develop a two-stage stochastic model. We first model,the auction in a static setting and determine,the expected auction price based on the number,of carriers engaging,in the auction and their cost distributions. We then develop a continuous-time,Markov,chain model,to evaluate the perfor- mance,of the system,in a dynamic,setting with random,arrivals and possible abandonment,of orders and carriers. By com- bining these two models, we evaluate the performance measures such as the expected auction price, price paid to the carriers, distribution of orders between local and in-transit carriers, and expected number of carriers and orders waiting at the logistics center in the long run. We present analytical and,computational,results related to the performance,of the system and,discuss operation,of such a logistics spot market,in Turkey. 2007 Elsevier B.V. All rights reserved. Keywords: Logistics; Markov,chain models; Performance,evaluation; Reverse auctions

We consider a continuous material-flow manufacturing system with an unreliable production system and a variable demand source which switches randomly between zero and a maximum level. The failure and repair times of the production system and the switching times of the demand source are assumed to be exponentially distributed random variables. The optimal production flow control policy that minimizes the expected average inventory carrying and backlog costs is characterized as a double-hedging policy. The optimal hedging levels are determined analytically by minimizing the closed-form expression of the cost function. We investigate two approximate single hedging policies. It is empirically shown that an approximate policy that uses a single hedging level which is the sum of a production uncertainty term and a demand uncertainty term gives accurate results for the expected average cost.

This study presents a mathematical programming representation of discrete-event systems with a continuous time and mixed continuous-discrete state space. In particular, continuous material flow production systems are considered. A mathematical programming representation is used to generate simulated sample realizations of the system and also to optimize control parameters. The mathematical programming approach has been used in the literature for performance evaluation and optimization of discrete material flow production systems. In order to show the applicability of the same approach to continuous material flow systems, this article focuses on optimal production flow rate control problems for a continuous material flow system with an unreliable station and deterministic demand. These problems exhibit most of the dynamics observed in various continuous flow productions systems: flow dynamics, machine failures and repairs, changing flow rates due to system status, and control. Moreover, these problems include decision variables related to the control policies and different objective functions. By analyzing the backlog, lost sales, and production and subcontracting rate control problems, it is shown that a mixed-integer linear programming formulation with a linear objective function and linear constraints can be developed to determine the simulated performance of the system. The optimal value of the control policy that optimizes an objective function that includes the estimated expected inventory carrying and backlog cost and also the revenue through sales can also be determined by solving a quadratic integer program with a quadratic objective function and linear constraints. As a result, it is shown that the mathematical programming representation is also a viable method for performance evaluation and optimization of continuous material production systems.

Empirical studies in retailing suggest that stock-out rates are considerably large in many product categories. Stock-outs result in demand spill-over, or substitution, among items within a product category. Product assortment and inventory management decisions can be improved when the substitution rates are known. In this paper, we present a method to estimate product substitution rates by using only Point-of-Sale (POS) data. Our practical approach clusters POS intervals into states where each state corresponds to a specific substitution scenario. We then consolidate available POS data for each state, and estimate the substitution rates using the consolidated information. We provide an extensive computational analysis of the proposed substitution rate estimation method. The computational analysis and comparisons with an estimation method from the literature show that the proposed estimation method performs satisfactorily with limited information.

We study a manufacturing firm that builds a product to stock to meet a random demand. Production time is deterministic, so that if there is a backlog, customers are quoted a lead time that is proportional to the backlog. In order to represent the customers' response to waiting, we introduce a defection function -the fraction of customers who choose not to order as a function of the quoted lead time. Unlike models with backorder costs, the defection function is related to customer behavior. Using a continuous flow control model with linear holding cost and Markov modulated demand, we show that the optimal production policy has a hedging point form. The performance of the system under this policy is evaluated, allowing the optimal hedging point to be found.

We consider the single period stochastic inventory (newsvendor) problem with downside risk constraints. The aim in the classical newsvendor problem is maximizing the expected profit. This formulation does not take into account the risk of earning less than a desired target profit or losing more than an acceptable level due to the randomness of demand. We utilize Value at Risk (VaR) as the risk measure in a newsvendor framework and investigate the multi-product newsvendor problem under a VaR constraint. To this end, we first derive the exact distribution function for the twoproduct newsvendor problem and develop an approximation method for the profit distribution of the N-product case (N42). A mathematical programming approach is used to determine the solution of the newsvendor problem with a VaR constraint. This approach allows us to handle a wide range of cases including the correlated demand case that yields new results and insights. The accuracy of the approximation method and the effects of the system parameters on the solution are investigated numerically.

Fluid flow models are used in the performance evaluation of production, computer, and telecommunication systems. In order to develop a methodology to analyze general Markovian continuous material flow production systems with two processing stages with an intermediate finite buffer, a general single-buffer fluid flow system is modelled as a continuous time, continuous-discrete state space stochastic process and the steadystate distribution is determined. Various performance measures such as the production rate and the expected buffer level are determined from the steady-state distributions. The flexibility of this methodology allows analysis of a wide range of models by specifying only the transition rates and the flow rates associated with the discrete states of each stage. Therefore, the method is proposed as a tool for performance evaluation of general Markovian continuous-flow systems with a finite buffer. The solution methodology is illustrated by analyzing a production system where each machine has multiple up and down states associated with their quality characteristics.

We consider an inventory management problem of a product category in a retail setting with Poisson arrival processes, stock-out based dynamic demand substitution, and lost sales. The retailer uses a fixed-review period, order-up-to level system to control the inventory levels. We present a computational method to determine the order-up-to levels that maximizes the expected profit with profit margins, inventory holding and substitution costs subject to service-level constraints. Determining expected sales, average inventory levels, and number of substitutions between all products for given demand rates, substitution probabilities, and order-up-to levels is not tractable when there are more than two products. Therefore we present efficient and accurate approximations to approximately compute the same performance measures. The approximate approaches are then used to solve the optimization problem by using a genetic algorithm. In a computational study, we discuss the impact of profit margins, inventory holding and substitution costs, and service level constraints on the order-upto levels and the expected profits. We show that a retailer can increase its expected profits by incorporating substitution among different products.

This study develops a station model for continuous¯ow production systems. The most prominent use of the model is as a building block for a general and¯exible decomposition method to analyse and design continuous materials¯ow production systems. Station breakdown and a ®nite capacity bu er are considered. Station inference caused by the blocking and starving phenomena is included in the station model. We assume that the time to station breakdown and station repair are exponentially distributed while the bu er is neither empty nor full. No restrictive assumptions are made about the distributions of the station breakdown and repair times when the station is blocked or starved, that is, while the bu er remains empty or remains full. The production rate and the expected level of the bu er are given in closed form. Numerical results that show the e ects of the input parameters on the production rate along with an overview of the decomposition methods are presented.