Quality and Operations Management in Food Supply Chains

Inventory Planning with Preservation Investments

A lot of researches deal with inventory management of perishable products, where their production or distribution planning is based upon an exogenous perishable rate. For example, fruits in supermarkets will perish in the selling period until they are not safe to eat. However, with the development of preservation technologies, the products' perishability can be reduced by making investment in equipment, production processes, and so on. In other words, the perishable rate highly depends on not only the natural perishable rate largely determined by environmental factors (such as temperature, humidity, light, oxygen content, and microbial content) but also the preservation technology used in the warehouse and transportation vehicles.

Although the perishing process for food products is natural and cannot be stopped, it can be slowed down by specialized equipment, such as refrigerators and humidifiers, to make temperature low and humidity suitable for certain fruits. Hence, it is practical and important to consider inventory decisions with preservation technology investment decision. Enterprises' preservation investment is often combined with other decisions, like pricing or replenishment decisions. The goal is to maximize the total profit or minimize the total cost by finding an optimal set of preservation investment level, price, or ordering quantity.

Single Level Supply Chain Inventory Models

Some studies focus on a single firm's preservation and inventory decisions. Hsu et al. first developed an analytical Economic Ordering Quantity (EOQ) model considering both ordering policies and preservation investment for perishable products. Under the assumption that the deterioration rate is exponentially linked to the investment level, they proposed a method to determine the optimal replenishment cycle, shortage period, order quantity, and preservation technology cost so as to maximize the total profit per unit time. Numerical examples were presented to obtain further results. Lee and Dye extended the model of Hsu et al. by assuming that market demand is linked to inventory level and shortages are allowed and partially backlogged. An algorithm was also proposed to solve the optimization model and determine the optimal replenishment and preservation technology investment.

Dye and Hsieh assumed that the deterioration cost is associated with both the preservation investment and the time instance. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time over the infinite planning horizon. Dye assumed that the deterioration rate is non-instantaneous and controllable. The generalized productivity of invested capital, deterioration, and time-dependent partial backlogging rates were used to model the inventory system. The uniqueness of the global maximization was proved using fractional programming.

Chen and Dye proposed a finite time horizon inventory and preservation investment model, in which the preservation investment can be different in each replenishment cycle. They utilized particle swarm optimization to solve the nonlinear programming problem. He and Huang studied the optimal preservation, pricing, and ordering decisions for a kind of seasonal products. Hsieh et al. formulated an Economic Production Quantity (EPQ) model for deteriorating items with time-varying demand and controllable deterioration rate in a limited time horizon. A particle swarm optimization approach was also employed to solve the nonlinear programming problem.

Singh and Sharma studied an inventory model with ramp-type demand rate, controllable deterioration rate, and two-level trade credit, in which shortages were allowed and partially backlogged. Bardhan et al. also studied an inventory problem with preservation investment for non-instantaneous deteriorating products. They studied two models depending on the on-hand stock finish time: before and after the deterioration starts. Yang et al. introduced the credit period theory into inventory models with preservation investment decisions. They studied a retailer selling perishable products to customers and offering a credit period to its customers to buy the products. They established a model to determine the optimal trade credit periods, preservation technology investment, and ordering strategies that maximize the total profit over a finite planning horizon.

Unlike previous studies, Dye and Yang treated the selling price as a decisions variable. They considered customers' reference price behaviors and proposed a joint dynamic pricing and preservation technology investment model for a perishable inventory system with time- and price- sensitive demand. Theoretical results were obtained to demonstrate the existence of an optimal solution for the inventory problem. A simple iterative algorithm was utilized to solve the proposed model by employing the theoretical results. Features of the proposed model were illustrated with sensitivity analysis.

Kouki et al. extended the known (r,Q) inventory models by assuming products are perishable. They studied the impacts of the application of Time Temperature Integrator (TTI) technology on the inventory management decisions. The TTI technology enables firms to accurately monitor products' freshness and gives information on products' remaining shelf lives. Zhang et al. studied dynamic service investment problem simultaneously with preservation investment for perishable products. The analytical solution for dynamic service investment was obtained under the given sales price, preservation technology, and replenishment cycle by solving an optimal control problem. The impact of common resource constraint on the optimal investment policy was investigated. They found that for a relatively low common resource capacity, the firm prefers to invest in service improvement rather than preservation technology. Mishra studied an EPQ problem considering uncertain and controllable deterioration rate. Following Day and Yang, Mishra et al. studied an inventory model that considers demand rate as a function of stock and selling price. They established an EOQ model considering preservation investment, product deterioration, and two types of backordering scenarios. Li et al. studied an inventory control problem considering the optimal packaging decisions to extend the product shelf life. High quality packaging helps to better preserve the products but leads to higher costs for sellers. The goal is to minimize the total costs by choosing an appropriate packaging strategy.

Two Level Supply Chain Inventory Models

The preservation investment problem has also been studied in two-level supply chains. Tayal et al. developed a two-level supply chain model, in which the products are perishable and the deterioration rate is controllable. Also, customers' demand is sensitive to the products' expiration rate. Zhang et al. studied a two-level inventory model for deteriorating items with controllable deterioration rate and price-dependent demand. They derived the optimal decisions for both the decentralized and the centralized models. They found that the two-level supply chain can be coordinated with a revenue sharing and cooperative investment contract. The results show that only when the revenue sharing rate lies roughly between 1/2 and 3/4 can the contract perfectly coordinate supply chains in most cases, which has an important implication in supplying chain coordination of deteriorating items with preservation investment. Shah et al. studied an inventory model in a two-level supply chain consisting of a manufacturer and a retailer. The manufacturer offers a trade credit to the retailer and the retailer's deterioration rate is time dependent and linked with preservation investment. The retailer also offers partial trade credit to the buyers. Giri et al. studied a two-level supply chain model with product deterioration, controllable deterioration rate, and unreliable production.

Multiple Facility Inventory Models

Researchers also considered the preservation investments for a multifacility supply chain. Cai et al. studied the optimal ordering policy and fresh product keeping efforts in a multilevel supply chain with long transportation distance and high deterioration rate for intransit products. Yu and Nagurney developed a network-based food supply chain production model under oligopolistic competition and perishability, with a focus on fresh produce. The product differentiation is characterized by the different product freshness and food safety concerns, as well as the evaluation of alternative technologies associated with various supply chain activities.

Tsao studied a joint model considering location, inventory, and preservation decision-making problem for non-instantaneous deteriorating items under delay in payments. In the author's model, an outside supplier provides a credit period to the wholesaler that has a distribution system with distribution centers. The goal is to determine the locations, the number, the replenishment time of the distribution centers, and the preservation investments. Tsao studied the network design problems in a supply chain including distribution centers and retailers considering trade credit arrangements, preservation investment, and product deterioration. The goal is to determine the optimal locations of distribution centers, assignment of retailers to distribution centers, replenishment time, and preservation investment to maximize the total profit.

Summary

In this subsection, the inventory problems combined with food preservation investment is presented. We classify the existing papers into three categories for different supply chain structures, that is, single level supply chain, two-level supply chain, and multilevel supply chain. The research contributions are presented in each part.