An integrated coordination model for a supply chain dealing with short life-cycle products operating under stock dependent demand

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An integrated coordination model for a supply chain dealing with short life-cycle products operating under stock dependent demand

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Abstract

The market demand of any product is generally influenced by quality, warranty, service, advertisement and sales promotion. Apart from these factors, the amount of stock displayed will also significantly influence the sales at retail level. Though, many inventory models have been developed based on stock dependency criterion, it has not received much attention from the researchers while designing supply chain contracts. This paper attempts to fill this gap. In this paper, an integrated coordination model is developed for a supply chain involving a manufacturer and a retailer dealing with short lifecycle products. The model combines both buyback contract and quantity discounts contract. Here, demand is modeled in additive fashion. Its formulation captures the three features: price-sensitivity, initial-stock dependency and uncertainty of demand. A numerical study is carried out to illustrate the model and sensitivity analysis is performed to analyze the impact of price-sensitivity, stock-dependency, and demand uncertainty on the supply chain performance The present study has shown that the integrated model is self-enforcing and
it is demonstrated that through the integrated coordination model, the system achieves Pareto-efficiency and a win-win situation.

Abstract
Introduction
Literature review
Development of the model
1. Assumptions
2. Notation
3. Non-coordinated setting
4. Determination of retailer's optimum order quantity under no returns case
5. Determination of retailer's optimum order quantity with returns
6. Coordinated setting (Centralized setting)
7. Determination of centralized optimum order quantity with returns
8. Determination of feasible wholesale price range to adopt centralized order quantity under returns
Numerical illustration
Conclusion and future work
References

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[...] Wang and Gerchak (2001) proposed a coordination model of a two-echelon supply chain with an initial stock level dependent demand. They pointed out through a price plus inventory-subsidy contract that the manufacturer could achieve not only channel coordination but also any desired allocation of the channel profit between himself and the retailer. Shi and Su (2004) have developed an integrated coordination model for a two stage supply chain that combines both returns policies and quantity discounts contract. However, they have not considered the effects of price-sensitivity and stock dependency in their model. [...]

[...] Vrat, “Inventory model for stock dependent consumption Opsearch, 23(1986), pp. 19-24. R.C. Baker and T.L. Urban, deterministic inventory system with an inventory-level-dependent demand The Journal of the Operational Research Society 39(1988), pp. 823-831. H. Soni and N.H. Shah, “Optimal ordering policy for stock-dependent demand under progressive payment scheme”, European Journal of Operational Research, 184(2008), pp. 91-100. T.A. Taylor, “Supply chain coordination under channel rebates with sales effort effects” , Management Science 48(2002), pp. 992-1007. Y. Wang and Y. Gerchak, “Supply chain coordination when demand is shelf-space dependent”, Manufacturing and Service Operations Management 3(2001), pp. [...]

[...] Goyal, “Supply chain coordination under inventory-level-dependent demand International Journal of Production Economics 113(2008), pp. 518-527. N.C. Petruzzi and M. Dada, “Pricing and newsvendor problem: A review with extensions”, Operations Research 47(1999), pp.183-194. TABLE I. Non-coordinated setting OPTIMUM VALUES Coordinated setting p * z * Q * pc* 18.6703 zc * 86.9294 Qc* 116.9723 Coordination benefit in rupees 700 b=5 TABLE II. PROFITS UNDER DIFFERENT SETTINGS 400 ΠR Non-coordinated- no returns scenario Non-coordinated- returns scenario (iii) Nash perfect equilibrium model Bargaining model * ΠM ΠT Stock dependency factor Figure Impact of stock dependency on coordination. [...]

[...] NUMERICAL ILLUSTRATION Π R ( Qc* , ) Π R ( , u = w0 ) 0 Which is equivalent to We have considered the following data for a supply chain dealing with short life-cycle products: Π R ( Qc* , ) Π R ( , ) w0 = 8 Rs, m = 6 Rs, s = 3 Rs, u = 3Rs Demand function is given by D = 100 5 p + 0.2 Q + ε Where, ε is a random variable which is uniformly Similarly, the manufacturer will opt for centralized ordering quantity when his profit due to centralized ordering quantity is greater than or equal to that under decentralized-no returns scenario. [...]

[...] Notation Following notation are used in the development of the model: Decision variables Q p w Retailer's order quantity Retail price per unit Wholesale price per unit Parameters w0 m s u Wholesale price per unit under no returns Manufacturing cost per unit Shortage cost per unit Buyback price per unit Market demand, Random variable Mean of the random variable Probability density function (pdf) of the market demand + Π R = pE min ( D ) w0Q sE D Q ) Defining, z = Q ( a bp + cQ ) , Q can be written as Substituting a bp + z c D ε µ f F Π xy D = a bp + cQ + ε and z = Q ( a bp + cQ ) , and after simplification, the retailer's profit function reduces to Cumulative distribution function (cdf) of the market demand Expected profit of entity x under scenario y a bp + z Π R = ( a bp p ) + ( pc w0 ) c s µ + ( p + s ) E min ( z , ε ) also, can be or T where M stands for manufacturer, R for retailer and T for total system; and y can be c or dc where c stands for centralized setting, and dc stands for decentralized setting) The cost parameters follow some straightforward assumptions to ensure internal consistency: p > w0 > m > 0 u w0 (iii) s 0 a bp + z Π R = ( a bp p ) + ( pc w0 ) c sµ + ( p + s ) ( µ Θ ( z ) ) where, Θ ( z ) is defined as Θ ( z ) = ( u z ) f ( u )du z B (see Appendix) C. [...]

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