## Abstract

Supply chains with either perishables or non-perishables have been well-studied as evidenced through extant published literature. Among these studies, very few consider supply chains with both perishable and non-perishable products. Since the early 2000s, RFID (Radio-Frequency IDentification) tags have been increasingly used in supply chains that deal with perishables as well as non-perishables. While there is a reasonably large amount of published literature on RFID use in supply chains, we are unaware of any that considers the dynamics of RFID-generated information in supply chains that simultaneously involve perishables substitutable by non-perishables in retail environments. We attempt to address this void. We consider the relative benefits of sensor-enabled RFID tag use in supply chains that simultaneously contain perishables substitutable by non-perishables. We also derive expressions for conditions on their dynamics through specific consideration of their pre-determined and actual expiry dates. We operationalize our analysis from the perspective of retailers and customers.

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## References

Akkerman, R., Farahani, P., & Grunow, M. (2010). Quality, safety and sustainability in food distribution: A review of quantitative operations management approaches and challenges.

*OR Spectrum,**32*(4), 863–904.Bassok, Y., Anupindi, R., & Akella, R. (1999). Single-period multiproduct inventory models with substitution.

*Operations Research,**47*(4), 632–642.Hoffmann, W., Kiesner, C., Clawin-Rädecker, I., Martin, D., Einhoff, K., Lorenzen, P. C., Meisel, H., Hammer, P., Suhren, G., & Teufel, P. (2006). Processing of extended shelf life milk using microfiltration.

*International Journal of Dairy Technology,**59*(4), 229–235.Hu, Y., Qu, S., Li, G., & Sethi, S. P. (2021). Power structure and channel integration strategy for online retailers.

*European Journal of Operational Research*. https://doi.org/10.1016/j.ejor.2019.10.050.Inderfurth, K. (2004). Analytical solution for a single-period production-inventory problem with uniformly distributed yield and demand.

*Central European Journal of Operations Research,**12*, 117–127.Jing, F., & Mu, Y. (2020). Dynamic lot-sizing model under perishability, substitution, and limited storage capacity.

*Computers & Operations Research, 122*.Li, G., Zhang, X., Chiu, S.-M., Liu, M., & Sethi, S. S. (2019). Online market entry and channel sharing strategy with direct selling diseconomies in the sharing economy era.

*International Journal of Production Economics,**218*, 135–147.Lorenzen, P. C., Clawin-Rädecker, I., Einhoff, K., Hammer, P., Hartmann, R., Hoffmann, W., Martin, D., Molkentin, J., Walte, H. G., & Devrese, M. (2011). A survey of the quality of extended shelf life (esl) milk in relation to HTST and UHT milk.

*International Journal of Dairy Technology,**64*(2), 166–178.Lu, J., Zhang, J., & Zhang, Q. (2018). Dynamic pricing for perishable items with costly price adjustments.

*Optimization Letters,**12*, 347–365.Mallidis, I., Vlachos, D., Yakavenka, V., & Eleni. Z. (2018). Development of a single period inventory planning model for perishable product redistribution.

*Annals of Operations Research*.Mou, S., Robb, D. J., & DeHoratius, N. (2018). Retail store operations: Literature review and research directions.

*European Journal of Operational Research,**265*(2), 399–422.Nahmias, S. (2010). Mathematical Models for Perishable Inventory Control. In J. J. Cochran (Ed.)

*Wiley encyclopedia of operations research and management science*(pp. 1–17).Nahmias, S., & Pierskalla, W. P. (1976). A two-product perishable/nonperishable inventory problem.

*SIAM Journal on Applied Mathematics,**30*(3), 483–500.O’Connor, M. C. (2006). Cold-chain project reveals temperature inconsistencies.

*RFID Journal*(1 December).Pardo, G., & Zufia, J. (2012). Life cycle assessment of food preservation techniques.

*Journal of Cleaner Production,**28*, 198–207.Piramuthu, S., Wochner, S., & Grunow, M. (2014). Should retail stores also RFID-tag ‘cheap’ items?

*European Journal of Operational Research,**233*(1), 281–291.Reefke, H., & Sundaram, D. (2018). Sustainable supply chain management: Decision models for transformation and maturity.

*Decision Support Systems,**113*, 56–72.Rong, A., Akkerman, R., & Grunow, M. (2011). An optimization approach for managing fresh food quality throughout the supply chain.

*International Journal of Production Economics,**131*(1), 421–429.Schmidt, V. S., Kaufmann, V., Kulozik, U., Scherer, S., & Wenning, M. (2012). Microbial biodiversity, quality and shelf life of microfiltered and pasteurized extended shelf life (ESL) milk from Germany, Austria and Switzerland.

*International Journal of Food Microbiology,**154*(1–2), 1–9.Shin, H., Park, S., Lee, E., & Benton, W. C. (2015). A classification of the literature on the planning of substitutable products.

*European Journal of Operational Research,**246*(3), 686–699.Tromp, S. O., Rijgersberg, H., Pereira da Silva, F. I. D. G., & Bartels, P. V. (2012). Retail benefits of dynamic expiry dates—Simulating opportunity losses due to product loss, discount policy and out of stock.

*International Journal of Production Economics,**139*, 14–21.Tu, Y.-J., Zhou, W., & Piramuthu, S. (2018). A novel means to address RFID tag/item separation in supply chains.

*Decision Support Systems,**115*, 13–23.Urien, P., & Piramuthu, S. (2014). Elliptic curve-based RFID/NFC authentication with temperature sensor input for relay attacks.

*Decision Support Systems,**59*, 28–36.Van der Goot, A. J., Pelgrom, P. J., Berghout, J. A., Geerts, M. E., Jankowiak, L., Hardt, N. A., Keijer, J., Schutyser, M. A., Nikiforidis, C. V., & Boom, R. M. (2016). Concepts for Further sustainable production of foods.

*Journal of Food Engineering,**168*, 42–51.Zahiri, B., Jula, P., & Tavakkoli-Moghaddam, R. (2018). Design of a pharmaceutical supply chain network under uncertainty considering perishability and substitutability of products.

*Information Sciences,**423*, 257–283.Zhang, X., Li, G., Liu, M., & Sethi, S. S. (2021). Online platform service investment: A bane or a boon for supplier encroachment.

*International Journal of Production Economics, 235*, 108079.Zhang, J., Xie, W., & Sarin, S. C. (2020). Multiproduct newsvendor problem with customer-driven demand substitution: A stochastic integer program perspective.

*INFORMS Journal on Computing*.Zhang, J., Xie, W., & Sarin, S. C. (2021). Robust multi-product newsvendor model with uncertain demand and substitution.

*European Journal of Operational Research,**293*(1), 190–202.Zhang, L., Zhang, G., & Yao, Z. (2020). Analysis of two substitute products newsvendor problem with a budget constraint.

*Computers & Industrial Engineering,**140*, 106235.Zhao, Y., Smith, J. R., & Sample, A. (2015). NFC-WISP: An open source software defined near field RFID sensing platform.

*Proceedings of UBICOMP/ISWC*(pp. 369–372).Zhou, W. (2009). RFID and item-level information visibility.

*European Journal of Operational Research,**198*(1), 252–258.Zhu, Z., Chu, F., Dolgui, A., Chu, C., Zhou, W., & Piramuthu, S. (2018). Recent advances and opportunities in sustainable food supply chain: A model-oriented review.

*International Journal of Production Research,**56*(17), 5700–5722.

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## Appendix

### Appendix

### Proof for negative second derivative of (3)

This is seen from the six terms in this expression in which the first, fourth, fifth and sixth are effectively always negative and the third is positive. The second term is positive or negative depending on the value of *n*.

We show that the second derivative is negative in two steps. First we show that the magnitude of the third term is less than that of the last term. We then show that the magnitude of the second term is less than the fifth term.

which is the same as \(s^p(1 - e^{-\lambda t_e}) \lessgtr P^p_r(1 - e^{-\lambda t_e})\) substituting \(P_r^{{\underline{p}}}\) for \(P_r^p\) as this is more restrictive which reduces to \(s^p < P^p_r\).

Since the second term could be positive sometimes, we consider the magnitude of the second term and the fifth term for a fixed *s* to show that the latter dominates the former thereby rendering the entire second derivative negative.

which is the same as \(s^n(1.5n-1) \lessgtr {P^n_r}\).

The highest value of LHS occurs when \(n=1\). When \(n=1\), we have \(0.5s^n < P^n_r\). Similarly, the lowest value of LHS occurs when \(n=0\). When \(n=0\), we have \(-s^n < P^n_r\). \(\square \)

### Proof for negative second derivative of (5)

The second derivative of (5), which is the denominator of (6), is negative as all except for the second term are always effectively negative.

Since the second term could be positive sometimes, we consider the magnitude of the second term and the last term for a fixed *s* to show that the latter dominates the former thereby rendering the entire second derivative negative.

which is the same as \(2s^n(1.5n-1)\lessgtr {P^n_rn}\).

The highest value of LHS occurs when \(n=1\). When \(n=1\), we have \(s^n < P^n_r\). Similarly, the lowest value of LHS occurs when \(n=0\). When \(n=0\), we have \(-2s^n < 0\). \(\square \)

### Proof for negative second derivative of (7)

The second term could be positive sometimes depending on the value of *n*.

Since the second term could be positive sometimes, we consider the magnitude of the second term and the third term for a fixed *s* to show that the latter dominates the former thereby rendering the entire second derivative negative.

which is the same as \(\frac{s^n}{2}(1.5n -1) \lessgtr {nP^n_r}\).

The highest value of LHS occurs when \(n=1\). When \(n=1\), we have \(s^n < 4P^n_r\). Similarly, the lowest value of LHS occurs when \(n=0\). When \(n=0\), we have \(-0.5s^n < 0\). \(\square \)

### Proof for negative second derivative of (9)

Since the last term could be positive sometimes, we consider the magnitude of the last term and the third term for a fixed *s* to show that the latter dominates the former thereby rendering the entire second derivative negative.

which is the same as \({2s^n}(1.5n-1) \lessgtr P^n_rn\).

The highest value of RHS occurs when \(n=1\). When \(n=1\), we have \({2s^n}(1.5-1) \lessgtr P^n_r \Rightarrow s^n < P^n_r\). Similarly, the lowest value of RHS occurs when \(n=0\). When \(n=0\), we have \(-2s^n < 0\). \(\square \)

### Proof of Lemma 3.3

We show that \(Q_r^{*} > Q_r^{[RFID]*}\) based on (4) and (6) for the \(t_e > t_{q^*}\) case. We then show (8) > (10) for the \(t_{q^*} \ge t_e\) case.

We first consider expressions (4) and (6). To operationalize this, we first compare the numerator of these expressions. We then compare their denominators.

The numerators:

which reduces to

Now, the numerator from (4) on the left hand side of the above-expression is larger than the numerator from (6) on the right hand side since the expression in the square-brackets is negative and \( P^p_rt_{q^{*}} > R_r\).

We now compare the denominators.

which reduces to

Here, the denominator from (4) on the left hand side of the above-expression is less than the denominator from (6) on the right hand side.

Based on the comparisons above, the numerator and denominator of (4) are more than and less than respectively vs. the numerator and denominator of (6). The result follows.

We next show \(Q_r^{*} > Q_r^{[RFID]*}\) based on (8) and (10) for the \(t_{q^*} \ge t_e\) case. Again, to operationalize this, we first compare the numerator of these expressions. We then compare their denominators.

The numerators:

which reduces to

As all the terms on the right hand side are positive, the above inequality holds. I.e, the numerator of \(Q_r^{*}\) is much less than that of \(Q_r^{[RFID]*}\).

The denominators:

which reduces to

In the above, there are three terms on both sides. The first and third terms on the left hand side are more in magnitude than the first and third terms on the left hand side. The second term on the right hand side is four times that of the second term on the left hand side. However all the terms on both sides are effectively negative and the last term on the left hand side dominates all the individual terms. Therefore, the left hand side is less than the right hand side with a magnitude that dwarfs the numerator comparison. Therefore the result follows.

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Stefánsdóttir, B., Grunow, M. & Piramuthu, S. Dynamics of sensor-based information in supply chains with perishables substitutable by non-perishables.
*Ann Oper Res* **329**, 1357–1380 (2023). https://doi.org/10.1007/s10479-022-04763-8

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DOI: https://doi.org/10.1007/s10479-022-04763-8