A two-echelon inventory model with lost sales

This paper considers a single-item, two-echelon, continuous-review inventory model. A number of retailers have their stock replenished from a central warehouse. The warehouse in turn replenishes stock from an external supplier. The demand processes on the retailers are independent Poisson. Demand not met at a retailer is lost. The order quantity from each retailer on the warehouse and from the warehouse on the supplier takes the same fixed value Q, an exogenous variable determined by packaging and handling constraints. Retailer i follows a (Q, R_i) control policy. The warehouse operates an (SQ, (S − 1)Q) policy, with non-negative integer S. If the warehouse is in stock then the lead time for retailer i is the fixed transportation time L_i from the warehouse to that retailer. Otherwise retailer orders are met, after a delay, on a first-come first-served basis. The lead time on a warehouse order is fixed. Two further assumptions are made: that each retailer may only have one order outstanding at any time and that the transportation time from the warehouse to a retailer is not less than the warehouse lead time. The performance measures of interest are the average total stock in the system and the fraction of demand met in the retailers. Procedures for determining these performance measures and optimising the behaviour of the system are developed.     

A decision model for berth allocation under uncertainty

This paper studies the berth allocation problem (BAP) under uncertain arrival time or operation time of vessels. It does not only concern the proactive strategy to develop an initial schedule that incorporates a degree of anticipation of uncertainty during the schedule’s execution, but also studies the reactive recovery strategy which adjusts the initial schedule to handle realistic scenarios with minimum penalty cost of deviating from the initial schedule. A two-stage decision model is developed for the BAP under uncertainties. Moreover, a meta-heuristic approach is proposed for solving the above problem in large-scale realistic environments. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed method.     

A model of interim information sharing under incomplete information

We propose a two-person game-theoretical model to study information sharing decisions at an interim stage when information is incomplete. The two agents have pieces of private information about the state of nature, and that information is improved by combining the pieces. Agents are both senders and receivers of information. There is an institutional arrangement that fixes a transfer of wealth from an agent who lies about her private information. In our model, we show that (1) there is a positive relation between information revelation and the amount of the transfers, and (2) information revelation has a collective action structure, in particular, the incentives of an agent to reveal decrease with respect to the amount of information disclosed by the other.     

A genetic-algorithm-based approach to the two-echelon capacitated vehicle routing problem with stochastic demands in logistics service

This paper addresses the two-echelon capacitated vehicle routing problem (2E-CVRP) with stochastic demands (2E-CVRPSD) in city logistics. A stochastic program with recourse is used to describe the problem. This program aims to minimize the sum of the travel cost and the expected cost of recourse actions resulting from potential route failures. In a two-echelon distribution system, split deliveries are allowed at the first level but not at the second level, thereby increasing the difficulty of calculating the expected failure cost. Three types of routes with or without split deliveries are identified. Different methods are devised or adapted from the literature to compute the failure cost. A genetic-algorithm-based (GA) approach is proposed to solve the 2E-CVRPSD. A simple encoding and decoding scheme, a modified route copy crossover operator, and a satellite-selection-based mutation operator are devised in this approach. The numerical results show that for all instances, the expected cost of the best 2E-CVRPSD solution found by the proposed approach is not greater than that of the best-known 2E-CVRP solution with an average relative gap of 2.57%. Therefore, the GA-based approach can find high-quality solutions for the 2E-CVRPSD.     

A mispricing model of stocks under asymmetric information

We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean-reverting Ornstein–Uhlenbeck process. Optimal portfolios and maximum expected log-linear utilities from terminal wealth for informed and uninformed investors are derived. We obtain analogous but more general results which nests those of Guasoni (2006) as a special case of the relative risk aversion approaching one.     

A two-echelon stochastic facility location model for humanitarian relief logistics

We develop a two-stage stochastic programming model for a humanitarian relief logistics problem where decisions are made for pre- and post-disaster rescue centers, the amount of relief items to be stocked at the pre-disaster rescue centers, the amount of relief item flows at each echelon, and the amount of relief item shortage. The objective is to minimize the total cost of facility location, inventory holding, transportation and shortage. The deterministic equivalent of the model is formulated as a mixed-integer linear programming model and solved by a heuristic method based on Lagrangean relaxation. Results on randomly generated test instances show that the proposed solution method exhibits good performance up to 25 scenarios. We also validate our model by calculating the value of the stochastic solution and the expected value of perfect information.     

An airline scheduling model and solution algorithms under stochastic demands

When setting a good flight schedule airlines not only have to consider their fleet supply and related operations, as well as market share, but also stochastic variations caused by daily passenger demands in actual operations. Most of the past research on short-term flight scheduling has used the average passenger demand as input to produce the final timetable and schedule, which means that daily passenger variations that occur in actual operations are neglected. To consider such stochastic disturbances we developed a stochastic-demand scheduling model. We employed arc-based and route-based strategies to develop two heuristic algorithms that can be used to solve the model. The test results, based on a major Taiwan airline’s operation, show the good performance of the model and the solution algorithms.     

Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands

We consider a two-level inventory system in which there are one supplier and multiple retailers. The retailers face stochastic, interdependent customer demands. Each location employs a periodic-review (R,nQ), or lot-size reorder point, inventory policy. We show that each location's inventory positions are stationary and the stationary distribution is uniform and independent of any other's.     

A cooperative inventory policy with deteriorating items for a two-echelon model

A cooperative inventory policy between supplier and buyer is proposed. Unlike other studies, we consider the case of deteriorating items and permit the completed back-order in the problem. We solve the problem without the condition of equal replenishments periods during a specified planning horizon and present a procedure to find the optimal solution. A case is presented to demonstrate the application of the proposed approach. The sensitivity analysis for a cooperation policy between supplier and buyer also are explored.     

A two-stage queueing network on form postponement supply chain with correlated demands

To ease the conflict between quick response and product variety, more and more business models are developed in supply chains. Among these, the form postponement (FP) strategy is an efficient tool and has been widely adopted. To the supply chain with FP strategy, the design mostly involves two problems: determination of customer order decoupling point (CODP) position and semi-finished product inventory control. In this paper, we develop a two-stage tandem queueing network with MAP arrival to address this issue. Particularly, we introduce a Markov arrival process (MAP) to characterize the correlation of the demand. By using of matrix geometric method, we derive several performance measure of the supply chain, such as inventory level and unfill rate. Our numerical examples show that both the variance and the correlation coefficient of the demand lead to more delayed CODP position and more total cost.     

A production-inventory model with probabilistic deterioration in two-echelon supply chain management

In this study, a production-inventory model is developed for a deteriorating item in a two-echelon supply chain management (SCM). An algebraical approach is applied to find the minimum cost related to this entire SCM. We consider three types of continuous probabilistic deterioration function to find the associated cost. The purpose of this study is to obtain the minimum cost with integer number of deliveries and optimum lotsize for the three different models. Some numerical examples, sensitivity analysis and graphical representation are given to illustrate the model. A numerical comparison between the three models is also given.     

Fair resource allocation for different scenarios of demands

This paper considers a resource allocation problem, which objective is to treat fairly all the system users. Usually the requests cannot be entirely predicted, but the manager can forecast the request evolution, this leading to a set of possible scenarios. Such a problem arises for instance in network bandwidth allocation as well as in storage space management. It also appears in the management of computer systems, such as computational grids or in cloud computing, when teams share a common pool of machines. Problems of fair resource sharing arise among users with equal access right but with different needs.Here the problem is tackled by a multi-criteria model, where one criterion is associated to one scenario. A solution is a policy, which provides an allocation for each scenario. An algorithm is proposed and analysed that lists all solutions which are Pareto optimal with regard to the different possible user request scenarios. The algorithm is used offline, but can be adapted, with some additional hypothesis, to be used online.     

Supply capacity acquisition and allocation with uncertain customer demands

We study a class of capacity acquisition and assignment problems with stochastic customer demands often found in operations planning contexts. In this setting, a supplier utilizes a set of distinct facilities to satisfy the demands of different customers or markets. Our model simultaneously assigns customers to each facility and determines the best capacity level to operate or install at each facility. We propose a branch-and-price solution approach for this new class of stochastic assignment and capacity planning problems. For problem instances in which capacity levels must fall between some pre-specified limits, we offer a tailored solution approach that reduces solution time by nearly 80% over an alternative approach using a combination of commercial nonlinear optimization solvers. We have also developed a heuristic solution approach that consistently provides optimal or near-optimal solutions, where solutions within 0.01% of optimality are found on average without requiring a nonlinear optimization solver.     

Integrated location and two-echelon inventory network design under uncertainty

In this paper, we propose a two-stage stochastic model to address the design of an integrated location and two-echelon inventory network under uncertainty. The central issue in this problem is to design and operate an effective and efficient multi-echelon supply chain distribution network and to minimize the expected system-wide cost of warehouse location, the allocation of warehouses to retailers, transportation, and two-echelon inventory over an infinite planning horizon. We structure this problem as a two-stage nonlinear discrete optimization problem. The first stage decides the warehouses to open and the second decides the warehouse-retailer assignments and two-echelon inventory replenishment strategies. Our modeling strategy incorporates various probable scenarios in the integrated multi-echelon supply chain distribution network design to identify solutions that minimize the first stage costs plus the expected second stage costs. The two-echelon inventory cost considerations result in a nonlinear objective which we linearize with an exponential number of variables. We solve the problem using column generation. Our computational study indicates that our approach can solve practical problems of moderate-size with up to twenty warehouse candidate locations, eighty retailers, and ten scenarios efficiently.     

Optimal allocation and backup of computer resources under asymmetric information and incentive incompatibility

This paper presents the optimal allocation and backup of computing resources in a multidivisional firm in the presence of asymmetric information and incentive incompatibility. A game-theoretic model is developed and transformed to a linear programming problem. The solution to this linear programming problem enables the corporate headquarters to design a resource allocation scheme such that the revelation principle prevails and all divisions tell the truth. To cope with the combinatorial explosion of complexity caused by the resource constraint, a greedy-type algorithm and an averaged version of the original linear programming problem are developed to provide the upper and lower bounds. The greedy-type algorithm generates exact solutions for a wide range of instances. The lower bounds coincide with the exact solutions for the cases where the computer resource is either scarce or abundant. The averaged-version resource allocation model with slight modifications solves the optimal computer backup capacity problem. It determines how much back up capacity the firm should purchase when the firm's computer breaks down.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

A simple model of corporate international investment under incomplete information and taxes

This paper extends the theory of corporate international investment in Choi (J. Int. Bus. Stud. 20: 145–155, 1989) in an environment where the segmentation of international capital markets for investors or the presence of agency costs provide some independence to corporate decisions. The model shows that the real exchange risk, the competition between firms in different markets and diversification gains affect corporate international investment. By accounting for the role of information as defined in the models of Merton (J. Finance 42: 483–510, 1987), Bellalah (Int. J. Finance Econ. 6: 59–67, 2001a) and Bellalah and Wu (Int. J. Theor. Appl. Finance 5(5): 479–495, 2002), the model embodies different existing explanations based on economic and behavioral variables. We show in a “two-country” firm model that real exchange risk, diversification motives and information costs are important elements in the determination of corporate international investment decisions. The dynamic portfolio model reflects the main results in several theories of foreign direct investment. Our model accounts for the role of information in explaining foreign investments. It provides simple explanations which are useful in explaining the home bias puzzle in international finance. Using the dynamical programming principle method, we provide the general solution for the proportion of firm’s total capital budget. We also use a new method to get explicit solutions in some special cases. This new method can be applied to solve other financial control problems. The simulating results are given to show our conclusion and the influence of some parameters to the optimal solution. The economic results can be seen as a generalization of the model in Solnik (J. Econ. Theory 8: 500–524, 1974).     

Tests for sphericity under correlated multivariate regression equations model

Summary In this paper, the authors investigated the asymptotic distribution theory connected with the likelihood ratio test (LRT)-like test statistic for sphericity under correlated multivariate regression equations (CMRE) model. An asymptotic expression is obtained for the null distribution of the above test statistic. Asymptotic nonnull distribution of the above test statistic under fixed alternatives is also derived. The above results are derived when the underlying distribution is multivariate normal. It was also shown that the above results are valid even when the joint distribution of the observations is elliptically symmetric. The authors also derived the asymptotic null distribution of the LRT-like test statistic when the observations on each variable are elliptically symmetric. This work was supported by the Air Force Office of Scientific Research under Contract F49620-82-K-0001. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

The impact of partial information sharing in a two-echelon supply chain

We consider a simple two-echelon supply chain composed of a manufacturer and a retailer in which the demand process of the retailer is an AR(1) where the random component is a function of both sides’ information. We focus on partial information sharing under which each side informs the other of an interval in which the exact value of its own component of demand lies. These various levels of information sharing can reduce the supply chain costs.     

A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.