A Vendor-Buyer Inventory Model for Food Products Based On Shelf-Life Pricing


Gusti Fauza
School of Engineering, University of South Australia, Dept. of Food Science and Technology, Sebelas Maret University, Surakarta, Indonesia

Yousef Amer
School of Engineering, University of South Australia

Sang-Heon Lee
School of Engineering, University of South Australia

Hari Prasetyo
Pusat Studi Logistik dan Optimisasi Industri (PUSLOGIN), Industrial Engineering, Universitas Muhammadiyah Surakarta, Indonesia


Research on coordinated inventory policy for perishable items between a manufacturer and a retailer has been extensively done. The majority studies however assumed that the stored item starts to deteriorate instantaneously once its production process completed. This may be suitable for representing the characteristic of certain perishable items such as alcohol or radioactive materials. In many cases, particularly for food products such as fruits, vegetables, meat and bakeries, over the shelf-life the quantity remains constant while the value does degrade once the product is approaching its expiration date. Despite this phenomenon, less research addresses this issue, particularly in a multi-echelon supply chain system. Therefore, this research deals with inventory policy for a manufacturer-retailer system considering value degradation for food products. A mathematical model representing the system is proposed. A shelf-life based pricing function is applied to represent the value degradation of the product. The objective function is to maximise the joint profit per unit time which is achieved by optimising the length of manufacturer’s production cycle (T) and the ordering frequency of finished goods (n) over the production cycle. The numerical test for the established model demonstrates that the model outperforms the existing model in terms of its potential capability of returning a significant profit improvement.

Keywords: deteriorating items, inventory model, value degradation, shelf-life based function

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Recently, the growth of research in the supply chain management area has created a new way in managing inventories of a multi-echelon system (Ben-Daya et al., 2008). A conventional inventory management approach where a company only focuses on its own inventory, disregarding their partner’s situation, may lead to suboptimal improvement. Due to fiercer competition in the market nowadays, each company is advised to work collaboratively with their partners in managing the inventory across the supply chain (Msimangira and Venkatraman, 2014) to achieve the optimal performance of the whole system.

A collaborative approach in managing the production and inventory between two parties i.e. manufacturer and retailer, can be achieved by determining the economic production and ordering lot sizes jointly between these two parties. This concept was initially introduced by Goyal (1977). In this scenario, the production and order quantities are decided by considering the joint variable cost between the manufacturer and the retailer. The model assumed an infinite production rate and a lot-for-lot shipment policy. Later, Hill (1997) relaxed this assumption to a general shipment policy and a finite production rate. Many other studies in this field (Avijit and Seung-Lae, 1995; Ha and Kim, 1997; Kim and Ha, 2003) eradicated the limitation of the requirement to have the production lot being completed before delivering the ordering batches to the retailer. More recently, other factors such as investment to reduce some related costs, stochastic demand and three layer systems are investigated by many scholars in this area (Ben-Daya et al., 2008). All of the studies mentioned above, however, assume that the items can be stored infinitely.

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This section presents the procedure for formulating a new inventory model considering food shelf-life and customers’ WTP.

It is a common phenomenon in a retailer that customers prefer to buy a product with a longer remaining lifetime i.e. the customers’ WTPs decrease once the product approaches its expiration date (Tsiros and Heilman, 2005). Consequently, to maintain the demand and avoid outdated items, the retailer offers a discount to those outdating products. It is also mentioned that the customers’ WTPs over time can decrease linearly such as in pre-cut lettuce, pre-cut carrots, milk and yoghurt or exponentially such as in beef and chicken. In this research, a linear WTP decrease is assumed before establishing the model (Figure 1).

A numerical test is conducted in this research to examine the behaviour of the proposed model. The parameter used in the numerical test is adopted from Kim and Ha (2003) with a slight modification to suit the proposed model as shown by Table 1.

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A production-inventory model considering a shelf-life based price function which incorporates the value loss because of customers’ perception on product quality has been established. The numerical test reveals that the proposed model may lead to a reduction in the number of outdated items and increase in the total profit of the manufacturer-retailer system in comparison to the existing model. The sensitivity analysis indicates that the optimal profit is relatively steady as the majority input parameters fluctuate. From the error analysis it is further shown that this deviation insignificantly affects to the total expected profit. These results demonstrate that the proposed model not only outperforms the benchmark model but also it is robust to any parameter change.

The vendor-buyer inventory model proposed in this research has not incorporated the procurement of raw material. Thus, it is expected that the total profit could be further extended by accommodating the raw material procurement planning. In addition, noting that deterioration characteristics of raw materials may behave differently from finished goods, proposing different approaches to dealing with quality loss in raw materials can be a challenging subject for investigation. Therefore, extending this model to an integrated production-inventory system which covers a raw material procurement strategy and accommodating efforts to preserve the quality or value loss to lengthen the product shelf-life could be potential for further research avenues.

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About Authors

Gusti Fauza received the Bachelor degree from Andalas University and master degree from Institute Technology of Bandung Indonesia. Currently, she is a Ph.D. student in the School of Engineering University of South Australia and a lecturer in food science and technology in Sebelas Maret University. Research in supply chain management, specifically inventory models, is her main interest. Now, she is working in inventory models for perishable items from supply chain management perspective.

Yousef Amer holds a Ph.D in Mechanical and Manufacturing Engineering from the School of Engineering, University of South Australia. Currently he is a Program Director in the School of Engineering University of South Australia. He has 18 years’ experience in automation, manufacturing, operations, logistics and supply chain management in various firms in Adelaide, both global and local. His research interests include simulation-based Lean Six-Sigma and Design for Six-Sigma, Artificial Intelligence, Manufacturing Strategy and Technology, Sustainability in Product and Service development, Lean and Green Supply Chain Modelling, Optimisation and Simulation and Sustainable Nano-manufacturing. He aims to develop links and collaboration with industry to foster relevant and innovate research. He has published books and many papers in academic journals, including International Journal of Production Economic and International Journal of Production Research, Journal Tribology International, and International Journal of Robotics and Computer Integrated Manufacturing.

Sang Heon Lee received a B.ESc degree in aeronautical engineering from Inha University Korea, and M.ESc in mechatronics from the University of New south Wales, and a Ph.D. degree in System Engineering from Australian National University. He is currently a program director and a senior lecturer in the School of Engineering, the University of South Australia. His current research focus is on development of efficient algorithm for green supply chain and digital image processing in agricultural and medical applications. His main research interests are in the area of discrete-event systems, fuzzy logic control and neural networks. He has published over 100 papers in academic journals and conference publications, including International Journal of Production Economic, International Journal of Production Research, Journal Tribology International, and International Journal of Robotics and Computer Integrated Manufacturing.

Hari Prasetyo received his Bachelor and Master degrees from Institute Technology of Bandung, Indonesia and completed his Ph.D in the School of Engineering, University of South Australia. He is currently a senior lecturer and a member of centre for logistics and industrial optimisation (PUSLOGIN) in Industrial Engineering department, Universitas Muhammadyah Surakarta. His research interest is in the area of inventory, logistics and supply chain modelling and optimisation.