Determining the retailer's replenishment policy considering multiple capacitated suppliers and price-sensitive demand

Hamza Adeinat, Jose Antonio Ventura

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

This article presents a mixed integer nonlinear programming model to find the optimal selling price and replenishment policy for a particular type of product in a supply chain defined by a single retailer and multiple potential suppliers. Each supplier offers all-unit quantity discounts as an incentive mechanism. Multiple orders are allowed to be submitted to the selected suppliers during a repeating order cycle. The demand rate is considered to be not constant but dependent upon the selling price. The model provides the optimal number of orders and corresponding order quantities for the selected suppliers, and the optimal demand rate and selling price that maximize the total profit per time unit under suppliers' capacity and quality constraints. In addition, we provide sufficient conditions under which there exists an optimal solution where the retailer only orders from one supplier. We also apply the Karush-Kuhn-Tucker conditions to investigate the impact of supplier's capacity on the optimal sourcing strategy. The results show that, there may exist a range of capacity values for the dominating supplier, where the retailer's optimal sourcing strategy is to consider multiple suppliers without fully utilizing the dominating supplier's capacity. A numerical example is presented to illustrate the proposed model.

Original languageEnglish (US)
Pages (from-to)83-92
Number of pages10
JournalEuropean Journal of Operational Research
Volume247
Issue number1
DOIs
StatePublished - Nov 16 2015

Fingerprint

Sales
Nonlinear programming
Supply chains
Quantity Discount
Incentive Mechanism
Profitability
Karush-Kuhn-Tucker Conditions
Mixed Integer Nonlinear Programming
Unit
Supply Chain
Programming Model
Nonlinear Model
Profit
Optimal Solution
Maximise
Demand
Policy
Replenishment policy
Suppliers
Retailers

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

Cite this

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abstract = "This article presents a mixed integer nonlinear programming model to find the optimal selling price and replenishment policy for a particular type of product in a supply chain defined by a single retailer and multiple potential suppliers. Each supplier offers all-unit quantity discounts as an incentive mechanism. Multiple orders are allowed to be submitted to the selected suppliers during a repeating order cycle. The demand rate is considered to be not constant but dependent upon the selling price. The model provides the optimal number of orders and corresponding order quantities for the selected suppliers, and the optimal demand rate and selling price that maximize the total profit per time unit under suppliers' capacity and quality constraints. In addition, we provide sufficient conditions under which there exists an optimal solution where the retailer only orders from one supplier. We also apply the Karush-Kuhn-Tucker conditions to investigate the impact of supplier's capacity on the optimal sourcing strategy. The results show that, there may exist a range of capacity values for the dominating supplier, where the retailer's optimal sourcing strategy is to consider multiple suppliers without fully utilizing the dominating supplier's capacity. A numerical example is presented to illustrate the proposed model.",
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N2 - This article presents a mixed integer nonlinear programming model to find the optimal selling price and replenishment policy for a particular type of product in a supply chain defined by a single retailer and multiple potential suppliers. Each supplier offers all-unit quantity discounts as an incentive mechanism. Multiple orders are allowed to be submitted to the selected suppliers during a repeating order cycle. The demand rate is considered to be not constant but dependent upon the selling price. The model provides the optimal number of orders and corresponding order quantities for the selected suppliers, and the optimal demand rate and selling price that maximize the total profit per time unit under suppliers' capacity and quality constraints. In addition, we provide sufficient conditions under which there exists an optimal solution where the retailer only orders from one supplier. We also apply the Karush-Kuhn-Tucker conditions to investigate the impact of supplier's capacity on the optimal sourcing strategy. The results show that, there may exist a range of capacity values for the dominating supplier, where the retailer's optimal sourcing strategy is to consider multiple suppliers without fully utilizing the dominating supplier's capacity. A numerical example is presented to illustrate the proposed model.

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