Analysis of decentralized production-inventory system (original) (raw)

Analysis of a Decentralized Production-Inventory System

Manufacturing & Service Operations Management, 2003

We model an isolated portion of a competitive supply chain as a M/M/1 make-to-stock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., the capacity of his manufacturing facility, which behaves as a single-server queue with exponential service times. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate, and cost parameters are common knowledge to both agents. Under the continuous-state approximation where the M/M/1 queue has an exponential rather than geometric steady-state distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments replicates a cost-sharing agr...

M.: Analysis of a Decentralized Production-Inventory System

2003

We model an isolated portion of a competitive supply chain as a M/M/1 make-to-stock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., capacity, of his manufacturing facility, which behaves as a single-server queue with exponential service times. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate and cost parameters are common knowledge to both agents. Under the continuous state approximation that the M/M/1 queue has an exponential rather than geometric steady-state distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments based on backorder, inventory and ...

Inventory Control in a Decentralized Two-Stage Make-to-Stock Queueing System

International Journal of Systems Science

In an Enterprise network, several companies interact to produce families of goods. Each member company seeks to optimize his own production and inventory policy to maximize his profit. These objectives are generally antagonistic and can lead to contradictory choices in the context of a network with a high degree of local decisional autonomy. To avoid a global loss of economic efficiency, the network should be equipped with a coordination mechanism. The present paper describes a coordination contract negotiated between a manufacturer and a supplier. The purpose of the negotiation is to determine the price of the supplied intermediate goods and the delay penalty in case of a late delivery. For a manufacturer with a dominant contracting position, the outcome of the negotiation can be computed as a Stackelberg equilibrium point. Under the resulting contract, the two-stage supply chain reaches globally optimal running conditions with the maximal possible profit obtained by the manufacturer and the smallest acceptable profit obtained by the supplier.

A coordinated production and shipment model in a supply chain

International Journal of Production Economics, 2013

In this study, we consider the coordination of transportation and production policies between a single supplier and a single retailer in a deterministic inventory system. In this supply chain, the customers are willing to wait at the expense of a waiting cost. Accordingly, the retailer does not hold inventory but accumulates the customer orders and satisfies them at a later time. The supplier produces the items, holds the inventory and ships the products to the retailer to satisfy the external demand. We investigate both a coordinated production/transportation model and a decentralized model. In the decentralized model, the retailer manages his own system and sends orders to the supplier, while the supplier determines her own production process and the amount to produce in an inventory replenishment cycle according to the order quantity of the retailer. However, in the coordinated model, the supplier makes all the decisions, so that she determines the length of the replenishment and transportation cycles as well as the shipment quantities to the retailer. We determine the structure of the optimal replenishment and transportation cycles in both coordinated and decentralized models and the corresponding costs. Our computational results compare the optimal costs under the coordinated and decentralized models. We also numerically investigate the effects of several parameters on the optimal solutions.

COORDINATION ALTERNATIVES IN A MANUFACTURER/DEALER INVENTORY SYSTEM UNDER STOCHASTIC DEMAND

Production and Operations Management, 2009

This paper introduces a stochastic model of a distribution system where the stocking location is owned by a dealer (or retailer) and the product is supplied by a manufacturer. Inventory is managed by the dealer, and the manufacturer is responsible for delivery of the product through both regular replenishment and expedite shipment modes. The dealer and the manufacturer share the goal of providing a high level of customer service. Demand, moreover, is a function of the service level offered to the market by the dealer. We develop optimal stock control policies for the cases where each decision maker in turn is dominant and acts unilaterally while being constrained by the supply/demand linkages of the system. We also develop an optimum policy for the case where both levels are managed under centralized control (i.e., both levels cooperate). Results indicate that the expected profit for a dominant dealer (or dominant manufacturer) is higher under decentralized control than the optimal solution for either under centralized control. However, the centralized solution is a global-optimal solution and therefore will guarantee longterm stability. Differences between the various solutions are analyzed explicitly to estimate the cost of coordination.

A decentralized inventory control policy for supply chains

Eleventh IFAC Symposium on Large Scale Complex Systems Theory and Applications, 2007, 2007

The paper proposes a linear model with distributed delays to describe a multistage supply chain. The product structure determines the organisation of the network of enterprises that cooperate to manufacture end-products from raw materials. Autonomy of production units imposes structural constraints to the production and inventory policy. For the long-term time-horizon, an optimal global state feedback control policy is proposed to meet stationary stochastic demands for end-products. It is shown that this policy naturally satisfies the structural constraints of the decentralized problem and reduces to a sequence of local base-stock policies. This policy is then naturally extended to the short-term time-horizon with the objectives of reaching a target set while meeting the demand and respecting the constraints.

Analysis of Admission and Inventory Control Policies for Production Networks

IEEE Transactions on Automation Science and Engineering, 2000

Problems of inventory control and customer admission control are considered for a manufacturing system that produces one product to meet random demand. Four admission policies are investigated: lost sales, complete backordering, randomized admission, and partial backordering. These policies are combined with an integral inventory control policy, which releases raw items only when an incoming order is accepted and keeps the inventory position (total inventory minus outstanding orders) constant. The objective is to determine the inventory level and the maximum number of backorders, as well as the admission probability that maximize the mean profit rate of the system. The system is modeled as a closed queueing network and its performance is computed analytically. The optimal parameters for each policy are found using exhaustive search and convex analysis. Numerical results show that managing inventory levels and sales jointly through partial backordering achieves higher profit than other control policies.

Continuous review inventory policy for centralized and decentralized supply chain

INDIN '05. 2005 3rd IEEE International Conference on Industrial Informatics, 2005., 2000

We consider a two-echelon serial supply chain with stochastic demand and fixed lead-times. The inventories at both supplier and retailer stages are replenished based on (Q, R) policies with inventory holding costs and fixed ordering costs. We analyse centralized and decentralized behaviour of the supply chain, and propose the feasible algorithms for the centralized and decentralized solutions, respectively. We also obtain the solutions for Stackelberg games.

A multi-server queueing-inventory system with stock-dependent demand

IFAC-PapersOnLine

We consider a two-server service system in which idle servers produce and store preliminary services for reducing the sojourn time of incoming customers and increasing customers arrival rate. We model the system as a Markovian process and provide a method, based on matrix geometric (MG) analysis, to obtain closed-form solutions to the steady state probabilities and relevant performance measures. We show the relation of the elements in the rate matrix of the MG to Catalan numbers, and prove that the stability condition remains as is in the traditional M/M/2 queue, although the expected sojourn time of customers has been reduced. We provide an economic analysis for a system in which the PS capacity and the investment to increase customers' arrival rate are decision variables.

Inventory management in supply chain with stochastic inputs

2010

This thesis studies and proposes some new ways to manage inventory in supply chains with stochastic demand and lead time. In particular, it uses queuing principles to determine the parameters of supply chain stations with delayed differentiation (typical assemble-to-order systems) and went on to apply some previously known results of steady state of some queuing systems to the management of flow and work in process inventory in supply chain stations. Consideration was also given to the problem of joint replenishment in partially dependent demand conditions. The first chapter introduces the important concepts of supply chain, the role of inventory in a supply chain, and developing stochastic models for such system. It then went on to review the pertinent literature that has been contributed to the inventory management, especially using stochastic models. Chapter two presents a perishable inventory model with a multi-server system, where some services, having an exponentially distributed lead time, have to be done on the product before it is delivered to the customer. Customers whose demands are not met immediately are put in an orbit from where they send in random retrial requests for selection. The input stream follows a Markov Arrival Process, , and another flow of negative customers (typical of a competitive environment with customer poaching), also following an , takes customers away from the orbit. An (,) replenishment policy was used. The joint probability distribution of the number of busy servers, the inventory level and the number of customers in the orbit is obtained in the steady state. Various measures of ii stationary system performance are computed and the total expected cost per unit time is calculated. Numerical illustrations were made. Chapter three is also a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers are assumed to arrive following a quasi-random distribution. Items demanded are also made available after some service, exponentially distributed, has been done on the demanded item. Customers with unsatisfied orders join an orbit from where they can make retrials only if selected following a special rule. Replenishment follows an (,) policy and also has an exponentially distributed lead time. The intervals separating two successive repeated attempts are exponentially distributed with rate ߠ + ݅ߥ, when the orbit has ݅ customers ݅ ≥ 1. The joint probability distribution of the number of customers in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. Chapter four is a two-commodity continuous review inventory system, with three customer input flows, following the ; one for individual demand for product 1; another for bulk demand for product 2; and the third for a joint individual demand for product 1 and bulk demand for product 2. The ordering policy is to place orders for both commodities when the inventory levels are below prefixed levels for both commodities, using (,) replenishment. The replenishment lead time is assumed to have phase type distribution and the demands that occur during stock out period are assumed to be lost. The joint probability distribution for both commodities is obtained in the steady state case. Various measures of system performance and the total expected cost rate in the steady state are derived. Numerical illustrations were then done. Chapter five is a model that shows how the steady state parameters of a typical queuing system can be used in the dynamic management of flow and buffer in a Theory of Constraints () environment. This chapter is in two parts, and the typical ‫∞/1/ܯ/ܯ‬ production environment with 0 < ߩ < 1 was assumed. The optimal feed rate for maximum profit was obtained. In the first part, the model was considered without consideration for shortage cost. This model was then extended in the second part to a case where a fixed cost is charged for every unit shortage from the desired production level. Part A result was iii shown to be a special case of part B result; the unit shortage cost has been implicitly taken to be zero in part A. Chapter six is the concluding chapter, where the various possible applications of the models developed and opportunities for possible future expansions of models and areas of research were highlighted. The main contributions of this work are in the Supply Chain area of delayed differentiation of products and service lead time. Others include management of joint replenishment and optimisation of flow in a TOC environment. The key contributions to knowledge made in this thesis include: • A model of a multi-server retrial queue with arrival and negative arrival, and deteriorating inventory system in which inventory items are made available only after some work has been done on the inventory item before it is delivered to the customer. No previous model is known to have considered any queuing system with such multi-server system ahead of this chapter. • A model of a retrial queuing system with multi-server rule based in which the arrival pattern is quasi-random, the calling population is finite, and an exponentially distributed system service is done on the inventory item before being delivered to the customer. It has not been found in literatures that such models have been developed elsewhere. • A stochastic model of joint replenishment of stocks in which two products are being ordered together; one of such is ordered in bulk and the other in single units, but both could be ordered together and unfilled order during the replenishment leadtime is lost. No published work is known to have also addressed such systems. • The management of flow in a theory of constraint environment, which explicitly utilises the holding cost, shortage cost, product margin, the level of utilisation of the resource and the effect of such on the stocks (inventory) build up in the system. Such flows are then explicitly considered in the process of buffering the system. Most works have been known to focus on buffer and not the flow of the products in order to optimise the system profit goal. iv Some of the insights derived include • An understanding of how the system cost rate is affected by the choice of the replenishment policy in systems with arrival pattern so that controlling policies (reorder point and capacity) could be chosen to optimise system profit • The effect of correlated arrival in input system on the cost rate of the system • How the nature of input pattern and their level of correlation affect the fraction of the retrials in a retrial queue in a competitive environment that are successful and how many of such customers are likely to be poached away by the randomly arriving competitors. This has direct effect on the future market size. • The nature of utilisation, blocking and idleness of servers in typical retrial queues, such that there could be yet-to-be-served customers in the orbit while there are still idle serves in such systems • Management of utilisation of resources in stochastic input and processing environment with respect to the throughput rate of such systems. It was shown that it may not be profitable to strive to always seek to fully utilise the full capacity of a Capacity Constrained Resource, even in the face of unmet demands. Increase in utilisation should always be considered in the light of the effect of such on the throughput time of the products and the consequence on the system's profit goal. This decision is also important in determining the necessity and level of buffers allowable in the production system. v ACKNOWLEDGEMENTS My profound gratitude goes to so many people that have made this study possible. But particular mention needs to be made of some very special people. First and foremost, I would like to thank Professor VSS Yadavalli, who is my promoter. He is actually more than just a promoter, but a reliable mentor, guide, instructor, teacher, listener and guardian, both in official and personal capacities. I am indebted to you. I would also like to thank my family members, especially my loving and understanding wife, Ireti, and my kids who have been denied many valuable moments to share, so that we can rejoice at the realisation of this dream. I thank my parents and siblings for the foundations you all provided for me. It still helps my development. I thank the entire staff members of the department of Industrial and Systems Engineering of the University of Pretoria, for giving me the opportunity to work with this great team, and doing that without prejudice or let. I have been much better with you in my life. I would like to appreciate the efforts of Pastor and Dr (Mrs) Akindele, who encouraged and supported me to quit my comfort zone in the office to pursue this course of life, which actually has become my passion. And most importantly, my Lord and Master, Jesus Christ, who has made a person out of a mere birth that would have been without direction or hope in life. vi