Vessel Arrival Process and Queueing in Marine Ports Handling Bulk Materials

We study the vessel arrival process in bulk ports handling either cargo containers or minerals. Then we introduce the SHIP/G/1 queue to be able to study the queueing behavior at the port. We present approximations for the asymptotic probabilities of delay and the number of vessels at the port. Numerical examples show the accuracy of the approximations. In appendices, we provide details of the analysis of the number of vessels at the port and the correlation properties of the vessel arrival process.     

Approximating Unreliable Queueing Networks Under the Assumption of Exponentiality

This paper deals with the approximate analysis and application of an unreliable closed queueing network to model the performance of a flexible manufacturing system. The service stations in the network are subject to breakdown and repair when active. An exact equivalent network is represented with two-stage Coxian service stations. We approximate the equivalent network by assuming exponentiality for the service completion time, which has a two-stage Coxian distribution. We validate the approximation for a wide range of model parameters and demonstrate the robustness of queueing network formulae to the assumption of exponentiality.     

Look-back policies for two-stage,pull-type production/inventory systems

We consider a two-stage, pull-type production/inventory system with a known service mechanism at the first stage. Set-ups and start-ups are involved in the operation of the second stage. We develop a production control policy for the second stage, within the class of (R, r) continuous-review policies, that minimizes the long run average total cost. We use a semi-Markov decision model to obtain an optimal policy for the operation of the second stage. The structure of the optimal policy suggests the use of a suboptimal look-back policy that delays the set-up at the second stage if the buffer lacks sufficient raw material. The performance of the system and the average total cost under the suboptimal policy can be obtained approximately using a decomposition algorithm. We show examples justifying the use of this suboptimal policy.This research is supported by the NSF Grant No. NSF-NCR-9110105, NSF Grant No. NSF-DDM-9014868 and by the North Atlantic Treaty Organization Grant No. NATO-CRG-900580.     

A multi-period inventory model with multi-dimensional procurement bidding

We consider a multi-period inventory model with raw material procurements carried out via a reverse auction. Bids are multi-dimensional, and they consist of supplier information of price, shortage quantity and lead time. This work is an extension of our earlier work that has focused on multi-dimensional procurement auctions in single-period inventory models, to multi-period settings. The new model is based on a hybrid approach combining stochastic dynamic programming and simulation.     

Approximate analysis of arbitrary configurations of open queueing networks with blocking

An algorithm for analyzing approximately open exponential queueing networks with blocking is presented. The algorithm decomposes a queueing network with blocking into individual queues with revised capacity, and revised arrival and service processes. These individual queues are then analyzed in isolation. Numerical experience with this algorithm is reported for three-node and four-node queueing networks. The approximate results obtained were compared against exact numerical data, and they seem to have an acceptable error level.Supported in part by a grant from CAIP Center, Rutgers University.Supported in part by the National Science Foundation under Grant DCR-85-02540.     

Approximate Analysis of Decentralized, Multi-Stage, Pull-Type Production/Inventory Systems

We consider a decentralized, pull-type manufacturing system with each stage having its own input and output stock keeping activities. Material handling between stages is carried out according to a fixed quantity, non-constant withdrawal cycle. We approximate the system behavior using a two-node decomposition approach, which decomposes the system into smaller subsystems. The analysis of two-node subsystems is achieved using a matrix-recursive approach due to phase-type modeling of certain random variables. Our solution algorithm resolved a major difficulty (due to batch transfers) in the analytical approach to study multi-stage manufacturing systems. We also discuss system behavior and suggest several rules-of-thumb to improve system performance.     

Approximate analysis and optimization of batch ordering policies in capacitated supply chains

Devising manufacturing/distribution strategies for supply chains and determining their parameter values have been challenging problems. Linking production management to stock keeping processes improves the planning of the supply chain activities, including material management, culminating in improved customer service levels. In this study, we investigate a multi-echelon supply chain consisting of a supplier, a plant, a distribution center and a retailer. Material flow between stages is driven by reorder point/order quantity inventory control policies. We develop a model to analyze supply chain behavior using some key performance metrics such as the time averages of inventory and backorder levels, as well as customer service levels at each echelon. The model is validated against simulation, yielding good agreement of robust performance metrics. The metrics are then used within an optimization framework to design the supply chain so as to minimize expected total system costs. The outcome of the optimization framework specifies how to move inventory throughout the supply chain and how to set inventory control parameters, i.e., reorder levels and replenishment batch sizes.     

Application of multi-dimensional procurement auction in single-period inventory models

Procurement is one of the major activities in the Manufacturing Resource Planning (MRP II), which is closely coupled with inventory management. Any improvement in this area will have a direct impact on the performance of the entire supply chain. Auction mechanism can be a successful procurement method when there are several potential suppliers available. In this paper, we consider a single-period inventory model when the selection of the supplier is done through a reverse auction with bids consisting of several attributes, namely price, shortage quantity, and lead time. The multi-dimensionality of the bid increases the complexity of the underlying problem creating a need for an approach to determine an approximate optimal target level. This is needed for the initiation of the auction and the procurement process. Monte-Carlo simulation method was used to investigate the performance of the approximation. Simulation results show that the analytical method provides an acceptable approximation for the optimal target inventory level.