Fuzzy expert model for order cost efficiency in capacitated two-echelon distribution chains

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Fuzzy expert model for order cost efficiency in capacitated two-echelon distribution chains

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Abstract

The supply chain researchers are commonly trying to optimize one or more decision variables under stochastic conditions. This paper considers a capacitated two-echelon divergent distribution chain facing stochastic demand and order cost fluctuations. The limited storage facility of the upper echelon causes increase in number of orders to increase the service level of the system in terms of product fill rate. The increase in order frequency increases order related expenses curtailing inventory cost efficiency of the distribution system. Hence optimization of the total order cost of the distribution system is important in view of the overall customer satisfaction. In this paper an approximate total expected inventory cost model is developed for the divergent distribution chain with predetermined fill rate constraints on both the echelons. Apart from order cost the other cost elements considered are carrying cost, holding cost and backorder cost. Using the model a tradeoff study between higher fill rates (supply chain responsiveness) and lower inventory costs (supply chain efficiency) is conducted under varying demand conditions and order cost situations.

Keywords: capacitated supply chain, Fuzzy expert system, Order cost efficiency.

Abstract
Introduction
Mathematical model
1. Formulation of total holding cost at capacitated distributor stage
2. Formulation of product fill rate constraints at both echelons
Simulation study using fuzzy expert model and results
1. Formulation of fuzzy expert model
2. Fuzzy inference system used
3. Fuzzification process
4. Strategic fit of efficiency and responsiveness
Conclusions and extensions
References

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[...] developed a fuzzy based model for bullwhip effect in supply chains (2008). Phayung Meesad (2001) developed the quantitative measures for a Fuzzy Expert Systems. A fuzzy model for supplier selection in supply chain is developed by A. Amid et al. in 2006. This paper considers a two-echelon inventory system with several independent retailers and one sole capacitated distributor handling multi-product in monopolistic nature. The lead time for replenishing the orders placed by the retailers and capacitated distributor is assumed as constants. [...]

[...] Andersson J., Marklund J Decentralized inventory control in a two-echelon distribution system , European Journal of Operational Research, 127,483-506. Axsater S Approximate optimization of a two level distribution inventory system. International Journal of Production Economics, 81-82 (2003), 545-553. Axsater S Scaling down multi-echelon inventory problems. International Journal of Production Economics 255–261. Forsberg R Evaluation of policies for two-level inventory systems with generally distributed customer inter arrival times. European Journal of Operational Research 99, 401–411. [10]. Diks E.B., de Kok T., Lagodimos, A.G Multi-echelon systems: a service measure perspective. [...]

[...] Increase in number of replenishments will increase the order cost which in turn will hurt the supply chain efficiency directly. Hence a strategically fitted order cost value is essential to determine the efficiency of the chain for predetermined responsiveness. Here a continuous review policy is assumed, which means that when the inventory position declines to or below a batch size of Q is ordered such that the resulting inventory position after ordering is in the interval of R+Q). The following literature support is used to develop the model for the problem. [...]

[...] The fuzzy expert model developed above can be suitably used to fit the efficiency and responsiveness of the capacitated chain as per the strategic leverage and order cost variations Conclusions and Extensions In this paper, an approximate total cost function and a fuzzy expert model for a two-echelon distribution chain with one capacitated distributor and many independent retailers handling multi-product is developed with predetermined product fill rate constraints and order cost variation patterns. The major assumption made is the aggregated demand at both capacitated distributor and retailers follows Normal distribution and the unsatisfied demands are backordered at both the stages. [...]

[...] Qri Order Batch size of a retailer r for product i Q0i Order Batch size of the capacitated distributor for product i D0i Demand rate at the capacitated distributor for product i per unit time. Rri Reorder point of a retailer for product i. R0i Reorder point of the capacitated distributor for product i. Ari Ordering cost per order at retailers for product i. hri Holding cost per unit per unit time at a retailer for product i. h0i Holding cost per time at the capacitated distributor for product i. [...]

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