Perishable material sourcing and final product pricing decisions for two-echelon supply chain under price-sensitive demand

Highlights

• We consider deterioration rate, processing capacity, and price-sensitive demand.

• The supply chain is built as a Stackelberg competition to obtain the best response.

• A strategy of less profit but quicker turnover does not increase their profits.

• Improving storage conditions or processing capacity can raise the overall profits.

• The retailer has an optimal replenishment cycle to maximize profitability.

Abstract

This paper considers a single product supply chain involving a producer/processor and a retailer. The producer/processor procures and processes perishable materials such as fruits and milk whose demand are often price-sensitive. We model the dyadic relationship as a Stackelberg game to understand how product perishability and the price-sensitive demand of such products can influence the procurement, production, and sale. The producer/processor is the leader and decides on the processing time of the materials and the wholesale price of the product to maximize profit. The retailer as the follower decides on the sale price of the product and order quantity to maximize profit under a price-sensitive demand setting. Propositions and lemmas for optimality are posed, and the model is validated numerically. Our results suggest that the retailer’s profit cannot be worse than the producer/processor under a price elastic demand. With a high deterioration rate or shrinkage, the producer/processor should improve the storage conditions or processing capacity within certain constraints for better overall supply chain profitability. Finally, both the producer/processor and the retailer need to consider the price sensitivity of consumers when making pricing decisions.

Introduction

Fresh food such as fruits, milk, and meat are highly perishable. Many food processors rely on chemical processes, such as sterilization, pasteurization, or by adding preservatives to such products to increase the shelf life, sometimes turning these products into other forms of food related products such as fruit cheese. These kinds of products account for over 40% of retail sales (Buck and Minvielle, 2013).

Our paper targets such perishable products. This class of products has some unique characteristics, including short lifetime, rapid deterioration, stringent food safety and quality requirements, and relatively high shrinkage. Further, due to these characteristics, some degree of economic loss occurs during the harvesting, processing, storage, delivery, and retail. In the US, spoilage amounted to $500 million in 2003 according to the Grocery Manufacturers of America (Karaesmen, Scheller-Wolf, and Deniz, 2011). In 2019, the World Journal reported that the US is the world’s worst food waste country, with about 60 million tons of agricultural products discarded each year, worth about 160 billion dollars (World Journal, 2019). Globally, of all the food produced in the supply chain, around 24% is wasted in terms of kcals (Kummu et al., 2012).

With greater consumer awareness of the environmental consequences of food waste, more measures are taken to reduce unnecessary food shrinkage. Hence, the processor/producer not only needs to satisfy the orders from the retailer, but also needs to reduce waste and operational costs, and manage the profit margin. The aim of this paper is to optimize the strategies of both parties to achieve a win–win situation and stem the unnecessary waste and shrinkage costs.

Due to the highly substitutable nature of food products, the price elasticity of the demand for these products is high. In short, the sale price of these products affects consumer demand. In the retail market, the sale price of a product is critical in attracting retail consumers to buy. Sana (2011) developed an Economic Order Quantity model using two demand functions: a quadratic decreasing function of price, and a negative power function of price. As the negative power function of price is more commonplace (Wu et al., 2009, Lau et al., 2007, Urban and Baker, 1997), our paper applies the negative power function of price for the product under study.

Our study treats a two-player, two-echelon supply chain, in which the processor/producer processes the food materials into products, for distribution to the retailer, who then sells to the consumers. The relationship between the upstream and downstream actors can be cooperative or non-cooperative. Focusing on non-cooperative relationships, we apply a Stackelberg game, whereby both parties seek to increase their profits. Further, we assume a large-scale producer (i.e. Nestle, PepsiCo) and the general retailer (i.e. grocer or small supermarkets). The producer usually has stronger bargaining power over its retailers. Hence, the producer/ processor dominates the supply chain, with the retailer as a follower (Saberi et al., 2019, Huang et al., 2018, Liu et al., 2007, Sudhir, 2001, Kadiyali et al., 2000). At the heart of this research, we seek answers to the following questions:

• What are the optimal processing time and the order quantity of the materials, and the optimal wholesale price of the product considering the deterioration rate of the materials, and the processor’s profit?

• What are the retailer’s optimal order quantity and the optimal unit sale price of the products, to maximize the retailer’s profit?

• What are the cost ranges that the processor/producer would like to improve the material storage conditions or raise the maximum processing capacity?

To the best of our knowledge, the extant literature suffers from a lack of studies that jointly focus on material perishability (i.e. deterioration rate), processing capacity, and price-dependent demand of products in a two-echelon supply chain. Thus, we seek to understand the influence of a material’s shrinkage rate, and price-dependent demand on the decisions and profit of the processor/producer and retailer. Our contribution can enrich the existing literature on the two-echelon supply chain model of perishable products under price-dependent demand.

Our results inform that the processor/producer and the retailer should set their sale price based on profit. Moreover, the strategy of seeking small profits but quicker turnover by one player does not necessarily increase the profit for both parties. Within a certain cost range, the processor/producer can reduce the deterioration rate (or extend the lifetime) to effectively raise the overall supply chain profitability. This paper posits that the retailer has an optimal replenishment cycle to manage the shrink reduction (Buck and Minvielle, 2013), and thus maximum profitability.

The rest of the paper is organized as follows. In Section 2, the related literature is reviewed. Section 3 describes our research problem and the decision model. Section 4 conducts a numerical analysis and a sensitivity analysis. Finally, Section 5 concludes the paper.