Dynamic lateral transshipment policy of perishable foods with replenishment and recycling
Introduction
The operation costs and environmental problems caused by food waste require constant attention, considering that sustained population and consumption growth mean that global demand for food is likely to grow for at least another 40 years (Godfray et al., 2010). In the food supply chain, the retail system is directly exposed to highly uncertain customer demands, thus the overstock and shortage figure can be very high (Haijema, 2013). As a result, the retail system generates huge amounts of food waste in both developed and developing countries (Godfray et al., 2010). Therefore, some studies point out that the government should strengthen regulation of waste in the food retail system (Garske et al., 2020, Szulecka and Strom-Andersen, 2022), and the food retail system needs to be systematically improved (Notarnicola, Tassielli, Renzulli, Castellani, & Sala, 2017). In other words, as the subject and object of regulation, both the government and the food retail system are facing challenges from food waste.
From a regulator's perspective, in order to reduce the economic losses and greenhouse gas emissions caused by food waste, many countries have passed laws to limit food waste and encourage retailers to donate their food that is about to expire. For example, France has banned the destruction (landfill and incineration) of unsold food products and toughened its legal penalties for food waste with high fines, and Italy has enacted an anti-food waste law (so-called “Gadda law”) to encourage enterprises or farms to donate food products that are still edible and meet hygiene standards through tax reduction and other means (Garske et al., 2020). The United States also has recognized the importance of food waste issues, and a variety of laws associated with food waste management are set to allow and incentivize individuals, organizations and businesses to reduce their food waste. In addition, in some developing countries where food waste is also very serious (Chen et al., 2021, Gao et al., 2021, Rahmi et al., 2020), anti-food waste legislation is also gaining traction. For example, in order to achieve sustainable development, China has established relevant laws to limit food waste and encourage food recycling through donation. The Indonesian government has also legislated to encourage the conversion of expired food into renewable energy (Yana et al., 2022). However, it is worth noting that compared with developed countries, anti-food waste legislation in developing countries still needs to be improved. For example, China's anti-food waste law does not have detailed provisions for rewards for food donation and punishment for food waste. Therefore, it is necessary to conduct quantitative research on the effects of regulatory policies to support a more detailed food regulatory framework from a theoretical perspective.
The retail system also faces two huge challenges. Firstly, excessive inventory may lead to huge amounts of food waste, holding cost and possible disposal cost of expired foods. Secondly, the shortage of inventory will lead to loss of sales. For dealing with these adverse effects that are caused by unbalanced inventory and improving the performances of retail system, for retailers, in addition to recycling (donating) some inventories, they can also rebalance their inventory by reducing orders or applying lateral transshipment (LT), which are important tools in perishables inventory management that concentrate on different stages in the supply chain and play different roles. Here, the LT problem usually focuses on the inventory rebalancing between retailers (Meissner & Senicheva, 2018). According to the applying times (Paterson, Kiesmüller, Teunter, & Glazebrook, 2010), LT can be divided into proactive LT (Allen, 1958), reactive LT (Krishnan and Rao, 1965), and hybrid LT (Burton & Banerjee, 2005). Replenishment problem mainly concentrate on the ordering problem between retailers and supplier (Haijema, 2014, Haijema and Minner, 2016). Recycling problems focus on the control of recovery of overstock or returns (Feng et al., 2013, He and Zhao, 2012, Koh et al., 2002, Zhang et al., 2019). Recently, the LT problem combined with replenishment has been extensively researched in the field of commercial inventory system (Glazebrook, Paterson, Rauscher, & Archibald, 2015). Meanwhile, recycling of perishables has received considerable attention in recent years (Fu et al., 2019; Prescott et al., 2020, Zhang et al., 2019). It is of great importance to understand how the retail system combines the three inventory balancing methods to reduce food waste in order to maximize profits. However, rare studies have taken recycling at the retailer level into account in the LT problem.
Based on the above considerations, this work aims to study the dynamic LT policy with replenishment and recycling (e.g., donating to feed hungry people) to reduce food waste and improve the performance of the food retail system. In addition, this study will also explore how different regulatory frameworks adopted by the government will affect food waste in the retail system. This study selects festival food as a special case, considering that the adverse effects of unbalanced inventory are especially evident in festival foods. Different from traditional perishables with fixed or dynamic shelf life (Buisman, Haijema, & Bloemhof-Ruwaard, 2019), festival foods have a fixed expiration date. For example, the moon cake, a traditional Chinese cake stuffed with lotus seed paste and egg yolk, is consumed by the Chinese when celebrating the mid-Autumn festival. The demand for moon cakes is high a few weeks before the Mid-Autumn Festival, so the shortage of moon cakes will cause a lot of sales losses. However, after the Mid-Autumn Festival, demand will fall to almost zero, and the remaining inventory will have a negative impact on the environment and the economy. Therefore, for the central decision makers of a festival food retail system (FFRS), it is necessary to take some appropriate measures to rebalance the inventory of the system.
The main works of this study are as follows. The object we consider in this study is an FFRS composed of multiple retailers and managed by a central decision maker. The central decision maker need to rebalance the inventory of the system for multiple periods prior to the festival. Therefore, the inventory control process with LT, replenishment and recycling can be expressed as follows. Between each pair of periods, the central decision maker reviews the residual inventory state of each retailer, then makes decisions on LT, replenishment and recycling to balance the inventories. The review period is set as 1 week, the objective periods is set as four weeks before the festival, and the replenishment lead time and LT time is assumed to be negligible (Ching et al., 2003, Meissner and Senicheva, 2018). Then, in each sales period, retailers meet the stochastic demands by consuming their on-hand inventory, and understock will directly lead to loss of sale. Therefore, considering that understock usually leads to loss of sales, proactive LT is considered as more suitable for this work. We assume that the revenue of retail system includes sales revenue and recycling revenue, the operating cost include holding costs, replenishment cost and cost of LT. In addition, to encourage retailers to reduce waste, i.e., improve the environmental performance, we set punish costs for the remaining inventory after the festival. The goal of the retail system is to maximize the total profit in the target periods. In order to optimize the total profit of FFRS, we formulate the inventory problem as a dynamic programming (DP) in this work. In principal, this DP can be solved by applying Bellman’s equation. However, as pointed in Godfrey and Powell, 2002, Meissner and Senicheva, 2018, when the size of the state and decision spaces of DP are huge, it is impossible to find the optimal policy for real-world sized problem by taking the appropriate time, e.g., multiple location and multiple periods problem. Therefore, we apply two kinds of approximate dynamic programming (ADP) to obtain near optimal inventory policy, respectively. The result shows that, compared with the inventory policy without recycling, both proposed near optimal inventory policies can improve the profitability and reduce food waste.
The main contributions of this study are as follows. First, this work studies the dynamic LT policy with replenishment and recycling simultaneously. Here, although some studies of LT policy have considered recycling at the customer level (Ghomi-Avili et al., 2017, Jabbarzadeh et al., 2018), rare studies have taken recycling at the retailer level into account in LT problem. To the best of our knowledge, only Yavari and Zaker (2020) consider recycling at the retailer level in LT problem of perishable goods inventory management simultaneously. However, the uncertainties in their work are modeled using a finite number of scenarios, each of which happens with a known probability, and it is difficult to select the scenarios and calculate the probabilities for each scenario (Ni, Shu, & Song, 2018). This study models the uncertainties by using the distribution of the demand for each time period and location, which can be estimated by the actual demand during the previous time periods (Meissner & Senicheva, 2018). Second, this study explores how different regulatory frameworks adopted by the government will affect food waste in the retail system, by examining the effects of incentives for food donation and penalties for food waste on retailer inventory strategies. The conclusion of this study can provide decision-making support for anti-food waste legislation in developing countries.
In overview the paper is organized as follows. In Section 2, we discuss the relevant literature. Section 3 presents the inventory problem formulation and introduces the approximate dynamic programming. In Section 4, we introduce two proposed inventory policies that are based on quasi-myopic approximation and look forward approximation. Then, in Section 5, we design a numerical study and discuss the results that report the performance of our proposed inventory policies. Finally, Section 6 concludes the paper.
Section snippets
Literature review
Our work is related to two distinct areas of LT research, i.e., proactive LT problem and LT problem of perishables. In this section, we review relevant studies in these areas.
Problem formulation
We consider a centralized FFRS which is formed by multiple retailers. The festival foods we considered are discrete items and are measured in pieces or boxes. In each sale period, demand in each retailer will be fulfilled as long as the retailer has enough stocks on hand. Otherwise, backorder is not allowed and the sales will be lost. Considering that no matter when it is produced, festival food will be regarded as expired after the specific festival, all its inventories are viewed as
Approximations and policies
In this section, two extensively used and researched approximate methods are applied to obtain the simulation of. The first one is Quasi-Myopic policy, which compares the benefit of making a transshipment (or recycling) now and never again with performing a no-transshipment (or recycling) (Paterson et al., 2010), and then straightforward simulates expected value function. The second one is look forward policy, which assumes that transshipment (or recycling) may occur in each period, and
Transshipment policies
In this section, we analyze the performance of the policies proposed in the paper, i.e., LFP and QMP policy. In addition, we prove the efficiency of the proposed policy by comparing results of simulation experiments conducted with previous policies proposed by Meissner and Senicheva (2018) as follows.
1) No recycling policy.
No recycling policy (NRP) allows retailers to balance their inventories through replenishment and lateral transshipment. However, no recycling is allowed under this policy.
Conclusion
In response to increasingly unsustainable food consumption, some countries have put in place regulatory frameworks to reduce food waste in the retail system through measures to encourage recycling and penalize waste. However, few researches focus on the LT problem combined with recycling. To full in this gap in existing researches and reduce the economic losses and environmental problems caused by food waste and thus improve the performance of the festival food retail system, the dynamic
CRediT authorship contribution statement
Yuqi Wei: Conceptualization, Methodology, Software. Min Yang: Data curation, Writing – original draft. Jingxian Chen: Visualization, Investigation. Liang Liang: Supervision. Tao Ding: Software, Validation, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This research is supported by the National Natural Science Foundation of China under Grants (No. 71971074, 72201130, 72171122, 72271080, 71801068, 72171073, 72188101, 72102112); Fundamental Research Funds for the Central Universities (No. PA2021KCPY0032).
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