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The present article investigates the issue of channel coordination of a manufacturer and a retailer facing stochastic demand that is sensitive to promotional effort. In newsvendor setting, the return policy, sharing contract on promotional effort, and discount on whole sales price provided by the manufacturer have been shown to be able to align incentives of the members of the chain. An analytical method has been provided to determine the optimal contract parameters of the channel. Numerical examples are also illustrated to justify the model.

Coordination among the members of a supply chain is an essential strategic issue. In supply chain coordination, i.e., in contract system, the upstream member offers a set of appropriate contract (with negotiation) parameters to the downstream member such that they enrich nearer to their expected target profits. In decentralized supply chain, there exist many profit margins in which each member does not bother the margin of the entire supply chain when making a decision. A proper coordination contract overcomes the problem of decentralized supply chain. Among other strategies, return/buyback policy, sharing of promotional effort and cash discount on sales prices are well-explored factors of a contract to achieve the target of the members of the chain. Return/buyback policy is widely used in industries such as fashion, apparel, books, computers, toys, etc. Quite often, the demand of the end customers is uncertain in nature. Consequently, the retailer has to face the overstocking or under stocking of the inventory. Return policy mitigates the risk of overstocking faced by the retailer. Promotional effort is another important strategy to enhance the demand of the goods in a market. A retailer can increase the demand of the goods by applying promotional effort such as advertising, sales team, gift, discount on sales price, attractive shelf space, etc. All of these efforts are costly. In centralized supply chain, the costs related to the promotional effort are shared by the members of the chain. Incorporating the above factors, a single period with one manufacturer and one retailer production–inventory model is investigated. The manufacturer is responsible for contract parameters before the production season. The manufacturer produces goods and delivers to the retailer before the selling season. The expected profits of both the members are formulated by trading off sales revenues, cost for promotional effort and discount on sales price. Then, it is analyzed in the light of centralized and decentralized systems. The rest of the paper is organised as follows: Section 2 provides literature review of the works in this direction, Section 3 contains the notations of the parameters and variables, Section 4 formulated the model, Section 5 illustrates numerical examples, and Section 6 concludes the proposed work.

This paper makes several theoretical and practical contributions applied in industries. It generalizes the framework for order quantity while sales price and advertising/promotional costs shared by the manufacturer and the retailer for uncertain demand of the end customers are considered altogether. It also demonstrates how the coordinating contract of incentives controls the overall performance of the chain. The generalized model is tested by usual distribution function applied in industries. These results are very useful for the manufacturer and the retailer to decide how to coordinate the supply chain. The managerial insights of the findings of the proposed model are highlighted as follows: i) The return/buyback policy can stimulate the retailer's incentive to order more because he/she can invest more in advertising/promotional effort that attracts the end customers to buy more. ii) In coordinating contract, the ranges of discount on whole sale prices can motivate both the parties to achieve their target profits. iii) The ranges of sharing of promotional costs (e.g., advertising, gift, sales team, etc.) suggest both the parties to achieve their target profits. iv) Overstock or under stock may occur due to uncertainty in demand of the end customers. Buyback contract helps the retailer and the manufacturer to share the risk embedded. In a buyback contract, the whole sale price and the price of buyback for each unsold unit are determined by the manufacturer and the retailer in the SC. The contribution of the present article is quite new in inventory literature. In the previous literature, the effect of promotional effort (γ(ρ)) is considered as unbounded increasing function of ρ. It is the fact that γ(ρ) is not unbounded in nature. As a result, the author considers an appropriate realistic function γ(ρ) which is an increasing function of ρ such that γ(ρ)ϵ[0, τ] ∀ τ ϵ[0, ∞). Moreover, the model is developed by considering random factor (x) of the demand as well as the promotional effort simultaneously. The propositions are also established for setting the optimal strategies for sharing the factors (e.g., promotional cost, cash discount) of the agreement of the parties of the SC. The present model can be extended many ways in future. It may be extended for multi-item products, allowing shortages of the products at each stage of the chain. Deterministic values of the parameters are another limitation of this article. The values of parameters may vary with dynamic behaviour of the market. This limitation may be relaxed by considering the fuzzy parameters in future.