(195f) Incorporating Cross-Perishability Effects in Optimization of Supply Chains of Multiple Perishable Products: Modeling and Solution Strategies

Effectively managing the supply chain of perishable products (such as fresh fruit, dairy and meat products, as well as, pharmaceuticals) is critical for mitigating losses and ensuring adequate product quality to the end consumer. The quality of perishable products typically degrades at a rate commensurate with their movement through the supply chain. Multiple environmental factors such as storage and transportation temperature, humidity, and light exposure, demonstrably influence product quality, as measured by objective and subjective metrics (firmness, color, moisture content). These factors additionally exert a significant impact on operational costs of the supply chain^1-4.

A common practice in retail supply chains involves the co-storage of perishable goods of different categories (e.g., different types of fruits and vegetable being stored together). Interaction effects among co-stored perishables due to chemical or biological reactions may either prolong or shorten their shelf lives⁵. This mutual influence is referred to as “cross-perishability.” There are two primary mechanisms of cross-perishability: ethylene gas emission and microbial contamination^6-7. Ethylene gas, produced by ripening fruits and used commercially for ripening, accelerates chlorophyll degradation in nearby produce. Microbial spoilage, influenced by storage temperature and packaging, is a separate but significant contributor especially in the storage and transport of meat.

Despite its economic impact and significance, to our knowledge, cross-perishability has not yet been incorporated in perishable inventory management problems. In fact, the rigorous modeling of perishability (even without accounting cross-perishability) has only been initiated relatively recently¹. Incorporating the dynamic nature of product quality degradation within supply chain models presents a significant challenge. The resulting large-scale optimization problems become computationally intractable, even for moderately sized systems with a single product type³.

Motivated by the above, this work introduces – for the first time, to our knowledge – a framework for modeling cross-perishability effects in supply chain optimization problems. Our focus is on short-term production and distribution planning. The model considers the quality degradation rate of each product type to be dependent on the co-stored quantities (or mass fractions) of other items. The model is formulated as a Mixed Integer Nonlinear Program (MINLP) but, structurally, it involves summations over decision variables, which hamper its implementation as a mathematical program. To this end, we propose two different approaches. First, a decomposition that alternates between estimating quality degradation rates and solving a problem whereby these degradation rates are fixed; the resulting problem is a relatively easier to solve Mixed Integer Linear Program (MILP). The second approach is proposed as a baseline, and involves the reformulation of the original MINLP by means of auxiliary binary variables to an equivalent formulation whereby the indices are no longer decision variables. We prove that this problem is equivalent to the original representation.

In a few illustrative case studies of different sizes, we observe that the sequential decomposition approach arrives at the optimal solution at much higher rates than the reformulation technique, which serves as our benchmark.

References:

1. Rong A, Akkerman R, Grunow M. An optimization approach for managing fresh food quality throughout the supply chain. International Journal of Production Economics. 2011;131(1):421-429. doi:https://doi.org/10.1016/j.ijpe.2009.11.026
2. Lejarza F, Baldea M. Closed-loop optimal operational planning of supply chains with Fast Product Quality Dynamics. Computers &; Chemical Engineering. 2020;132:106594. doi:10.1016/j.compchemeng.2019.106594
3. Lejarza F, Baldea M. An efficient optimization framework for tracking multiple quality attributes in supply chains of perishable products. European Journal of Operational Research. Published online May 2021. doi:https://doi.org/10.1016/j.ejor.2021.04.057
4. Lejarza F, Pistikopoulos I, Baldea M. A scalable real-time solution strategy for supply chain management of fresh produce: A Mexico-to-United States cross border study. International Journal of Production Economics. 2021;240:108212. doi:https://doi.org/10.1016/j.ijpe.2021.108212
5. Yang Y, Chi H, Tang O, Zhou W, Fan T. Cross perishable effect on optimal inventory preservation control. European Journal of Operational Research. 2019;276(3):998-1012. doi:https://doi.org/10.1016/j.ejor.2019.01.069
6. Bhattacharjee D, Dhua RS. Influence of Ethylene Absorbents on Shelf Life of Bitter Gourd (Momordica charantia L.) Fruits during Storage. International Journal of Current Microbiology and Applied Sciences. 2017;6(5):1553-1563. doi:https://doi.org/10.20546/ijcmas.2017.605.169
7. Al Ubeed HMS, Wills RBH, Bowyer MC, Vuong QV, Golding JB. Interaction of exogenous hydrogen sulphide and ethylene on senescence of green leafy vegetables. Postharvest Biology and Technology. 2017;133:81-87. doi:https://doi.org/10.1016/j.postharvbio.2017.07.010