A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.

A Bayesian incentive compatible mechanism for decentralized supply chain formation

In this paper we consider a decentralized supply chain formation problem for linear multi-echelon supply chains when the managers of the individual echelons are autonomous, rational, and intelligent. At each echelon, there is a choice of service providers and the specific problem we solve is that of determining a cost-optimal mix of service providers so as to achieve a desired level of end-to-end delivery performance. The problem can be broken up into two sub-problems following a mechanism design approach: (1) Design of an incentive compatible mechanism to elicit the true cost functions from the echelon managers; (2) Formulation and solution of an appropriate optimization problem using the true cost information. In this paper we propose a novel Bayesian incentive compatible mechanism for eliciting the true cost functions. This improves upon existing solutions in the literature which are all based on the classical Vickrey-Clarke-Groves mechanisms, requiring significant incentives to be paid to the echelon managers for achieving dominant strategy incentive compatibility. The proposed solution, which we call SCF-BIC (Supply Chain Formation with Bayesian Incentive Compatibility), significantly reduces the cost of supply chain formation. We illustrate the efficacy of the proposed methodology using the example of a three echelon manufacturing supply chain.

Improving supply chain performance: Real-time demand information and flexible deliveries

In some supply chains, materials are ordered periodically according to local information. This paper investigates how to improve the performance of such a supply chain. Specifically, we consider a serial inventory system in which each stage implements a local reorder interval policy; i.e., each stage orders up to a local basestock level according to a fixed-interval schedule. A fixed cost is incurred for placing an order. Two improvement strategies are considered: (1) expanding the information flow by acquiring real-time demand information and (2) accelerating the material flow via flexible deliveries. The first strategy leads to a reorder interval policy with full information; the second strategy leads to a reorder point policy with local information. Both policies have been studied in the literature. Thus, to assess the benefit of these strategies, we analyze the local reorder interval policy. We develop a bottom-up recursion to evaluate the system cost and provide a method to obtain the optimal policy. A numerical study shows the following: Increasing the flexibility of deliveries lowers costs more than does expanding information flow; the fixed order costs and the system lead times are key drivers that determine the effectiveness of these improvement strategies. In addition, we find that using optimal batch sizes in the reorder point policy and demand rate to infer reorder intervals may lead to significant cost inefficiency. © 2010 INFORMS.

Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.

Experiences with an Object-Oriented, Multi-Stage Language

Metaphor is a multi-stage programming language extension to an imperative, object-oriented language in the style of C# or Java. This paper discusses some issues we faced when applying multi-stage language design concepts to an imperative base language and run-time environment. The issues range from dealing with pervasive references and open code to garbage collection and implementing cross-stage persistence.