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Journal ArticleDOI

Performance evaluation and optimization of a two-stage production-distribution system with batch orders and finite transportation time

TL;DR: In this paper, the authors proposed an analytical method for performance evaluation and optimization of a production-distribution system composed of a warehouse supplied from an upstream manufacturing plant, where customer orders arrive randomly with random order size and the production capacity is finite.
About: This article is published in IFAC Proceedings Volumes.The article was published on 2005-01-01 and is currently open access. It has received 3 citations till now.

Summary (2 min read)

1. INTRODUCTION

  • A production-distribution system can be viewed as a network of manufacturing plants, warehouses and customers through which orders and products flow.
  • Numerous performance evaluation and optimization approaches have been developed in order to evaluate and help decision making about inventory levels and service targets.
  • Transportation from plant to warehouse is performed on the basis of replenishment orders and the transportation time is constant.
  • More specifically, the analytical approach needs only the first two moments of random variables of the system to evaluate the order-to-delivery lead time of the warehouse, the total inventory on order and the inventory holding and backlogging cost.
  • In Section 4, numerical results are given to compare the analytical approach and the simulation.

2 THE PRODUCTION-DISTRIBUTION SYSTEM

  • This paper considers a two-stage productiondistribution system with an upstream production plant supplying a downstream warehouse .
  • The plant processes orders from the warehouse according to its available capacity and on a FIFO basis.
  • The quantity of each order is a random positive integer variable X and the quantities of different orders are iid random variables.
  • The inventory of the warehouse is managed following a base-stock control policy.
  • The total time elapsed between the arrival of a replenishment order at the plant and the moment when the order is ready from delivery to the warehouse is the plant lead time, denoted as Ls.

3. PERFORMANCE EVALUATION

  • This section addresses the performance and cost evaluation of the production-distribution system.
  • The authors first evaluate the first and/or second moments of the following performance variables: Ls: lead-time at the plant for a typical order unit (not batch) issued by the warehouse .
  • The replenishment orders issued by the warehouse are not split till delivery at the warehouse.
  • Given the service time distribution of the M/G/1 queue, generating function of the queue length of M/G/1 can be used to compute the second moment of NB by using the third moment of service time (Cooper, et al., 1981;Buzacott, et al., 1993).
  • As the purpose of this paper is to propose a performance evaluation by using only the first two moments of any random variable, the approach presented in (Cooper, et al., 1981;Buzacott, et al., 1993) can not be used directly.

3.2 The transport system model

  • Notice that the arrival process at the transportation system is the departure process of replenishment orders from the plant and it is in general not a Poisson process.
  • Let us approximate the arrival process of batches at the transportation system as a Poisson process.

3.5 Fill rate estimation

  • For the warehouse which directly supplies external customer demand, the fill rate is an important indicator of the required customer service level, and strongly depends on the base stock level.
  • The authors define it as the percentage of order units filled from stock without delay.

4. NUMERICAL RESULTS

  • The aim of this section is to validate by simulation the analytical results presented in the previous section.
  • In order to obtain faithful simulation results, a very long simulation time of 10,000,000 time units is used.
  • Even though a number of approximations are made in the analytical approach, the second moment estimation of the inventory on order N is very good with error no more than 3.5%.
  • Another interesting phenomenon is that the quality of the result seems to be rather insensitive to the traffic intensity ρ.
  • To minimize the objective function C(R), the authors use the conjugate gradient method [Press, et al.,1994], which is a standard technique for nonlinear optimization.

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Citations
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Proceedings ArticleDOI
02 Jul 2007
TL;DR: Numerical experiments show that this new method, based on random search in a neighborhood structure called the most promising area, can efficiently solve the discrete optimization problem proposed in this paper.
Abstract: This paper deals with inventory cost optimization of a multi-stage production-distribution system subject to non analytical constraints. These kind of constraints need to be evaluated by simulation. Therefore, the method that we propose addresses problems where both the performance evaluation and the constraints are evaluated via a stochastic, discrete-event simulation. It is based on random search in a neighborhood structure called the most promising area. A special attention is given to optimizing the allocation of the simulation budget. We show that under some assumptions, the algorithm converges to a set of local optimal solutions with probability 1. This approach is applied to cost optimization of a production-distribution system subject to fill rate specifications. Numerical experiments show that this new method can efficiently solve the discrete optimization problem proposed in this paper.

1 citations

Journal ArticleDOI
TL;DR: To minimize the average total inventory holding and demand backlogging cost, a simulation based optimization method is developed that can efficiently solve the discrete optimization problem proposed in this paper.
Book ChapterDOI
14 Dec 2020
TL;DR: In this article, the authors address the integration of two-level supply chain with multiple items, production facility and retailers' demand over a considered discrete time horizon, and aim at implementing a solution to minimize the sum of the costs at the manufacturing facility and the retailers.
Abstract: In this paper we address the integration of two-level supply chain with multiple items, production facility and retailers’ demand over a considered discrete time horizon. This two-level production distribution system features capacitated production facility supplying several retailers located in the same region. If production does take place, this process incurs a fixed setup cost as well as unit production costs. In addition, deliveries are made from the plant to the retailers by a limited number of capacitated vehicles and routing costs are incurred. This work aims at implementing a solution to minimize the sum of the costs at the production facility and the retailers. The methodology adopted to tackle this issue is based on a hybrid heuristic, greedy and genetic algorithms that uses strong formulation to provide a good solution of a guaranteed quality that are as good or better than those provided by the MIP optimizer with a considerably larger run time. The results demonstrate that the proposed heuristics are effective and performs impressively in terms of computational efficiency and solution quality.
References
More filters
01 Jan 1994
TL;DR: The Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.
Abstract: Note: Includes bibliographical references, 3 appendixes and 2 indexes.- Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08

19,881 citations


"Performance evaluation and optimiza..." refers methods in this paper

  • ...In this paper, we propose to approximate fN(x) by a log-normal distribution (Saporta,1990) with mean mN and variance σ2N: 2 2(ln ) /(2 )1( ) 2 x M S Nf x eSx π − −≈ (27) With 2 2 2ln( 1) N N S m σ = + and ....

    [...]

  • ...Instead we propose to approximate the distribution of service time for one unit by a log-normal distribution (Saporta,1990) with mean mτ and variance 2 τσ ....

    [...]

Book
24 Jan 2000
TL;DR: In this article, one item with a constant demand rate and time-varying demands is described. But, the model is based on a single item with constant lead times.
Abstract: 1 General Introduction2 Systems and Models3 One Item with a Constant Demand Rate4 Time-Varying Demands5 Several Products and Locations6 Stochastic Demand: One Item with Constant Leadtimes7 Stochastic Leadtimes: The Structure of the Supply System8 Several Items with Stochastic Demands9 Time-Varying, Stochastic Demand: Policy Optimization Bibliography Appendix A: Optimization and Convexity Appendix B: Dynamical Systems Appendix C: Probability and Stochastic Processes Appendix D: Notational Conventions

1,709 citations


"Performance evaluation and optimiza..." refers background in this paper

  • ...A detailed presentation of the main inventory control policies can be found in (Zipkin,2000)....

    [...]

Book
01 Jan 1993
TL;DR: In this article, the evolution of manufacturing system models: an example of a single stage "produce-to-order" system and a single-stage "buy-and-buy" system is presented.
Abstract: 1 Discrete Part Manufacturing Systems 2 Evolution of Manufacturing System Models: An Example 3 Single Stage 'Produce-to-Order' Systems 4 Single Stage 'Produce-to-Stock' Systems 5 Flow Lines 6 Transfer Lines 7 Dynamic Job Shops 8 Flexible Machining Systems 9 Flexible Assembly Systems 10 Multiple Cell Manufacturing Systems 11 Unresolved Issues: Directions for Future Research Appendix A: Standard Probability Distributions Appendix B: Some Notions of Stochastic Ordering Appendix C: Nonparametric Families of Distributions

1,565 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a survey of the main areas of research in probabilistic analysis of variables in the context of regression and regression logistique, including relation between variables and their correspondances.
Abstract: Table des matieres : I. Outils probabilistes. 1. Modele probabiliste. 2. Variables aleatoires. 3. Couples de variables aleatoires, conditionnement. 4. Vecteurs aleatoires. Formes quadratiques et lois associees. II. Statistique exploratoire. 5. Description unidimensionnelle de donnees numeriques. 6. Description bidimensionnelle et mesures de liaison entre variables. 7. L'analyse en composantes principales. 8. L'analyse canonique et la comparaison de groupes de variables. 9. L'analyse des correspondances. 10. L'analyse des correspondances multiples. 11. Methodes de classification. III. Statistique inferentielle. 12. Distributions des caracteristiques d'un echantillon. 13. L'estimation. 14. Les tests statistiques. 15. Methodes de Monte-Carlo et de reechantillonnage (Jack-knife, bootstrap). IV. Modeles predictifs. 16. La regression simple. 17. La regression multiple et le modele lineaire general. 18. Analyse discriminante et regression logistique. 19. Methodes algorithmiques, choix de modeles et principes d'apprentissage. V. Recueil des donnees. 20. Sondages. 21. Plans d'experiences. Annexes. Bibliographie. Index des noms. Index.

875 citations


"Performance evaluation and optimiza..." refers methods in this paper

  • ...In this paper, we propose to approximate fN(x) by a log-normal distribution (Saporta,1990) with mean mN and variance σ2N: 2 2(ln ) /(2 )1( ) 2 x M S Nf x eSx π − −≈ (27) With 2 2 2ln( 1) N N S m σ = + and ....

    [...]

  • ...Instead we propose to approximate the distribution of service time for one unit by a log-normal distribution (Saporta,1990) with mean mτ and variance 2 τσ ....

    [...]

BookDOI
01 Jan 1989

459 citations

Frequently Asked Questions (2)
Q1. What have the authors contributed in "Performance evaluation and optimization of a two-stage production- distribution system with batch orders and finite transportation time" ?

This paper proposes an analytical method for performance evaluation and optimization of a production-distribution system composed of a warehouse supplied from an upstream manufacturing plant. 

Their future research work consists in extending the approach to a network of production-distribution systems with random transportation time.