A Mathematical Approach to Ordering Policy Selection for Cold Items in a Warehouse with Different Operational Constraints

Document Type: Research Paper

Authors

Department of Indusrtial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Abstract

According to the importance of keeping temperature-dependent products, the present study investigated the inventory control of cold products. In this study, a warehouse with limited space and ambient temperature is assumed. Based on the assumptions of the problem, the best ordering system for cold products should be selected from the two fixed order size and periodic review systems by formulating a mixed integer nonlinear programming model. The objective of the model is to minimize the sum of costs, including adjusting the temperature of the products and the cost of producing fluoride gas produced by keeping them in the refrigerator and for both types of ordering systems, taking into account different constraints consisting of warehouse space, available budget, the storage temperature of the products in the warehouse and the maximum number of cold products that can follow any ordering system. Finally, by solving the model, the type of ordering system for each product, the ordering system characteristics and their storage temperature are obtained. After solving the model, sensitivity analysis is performed on different parameters including available space for holding the products at the warehouse, available budget, the minimum number of the products that can follow a specific ordering system and shortage cost and the results are discussed.

Keywords


Barman, H., Pervin, M., Roy, S.K., and Weber, G. W., (2020). Back-ordered inventory model with inflation in a Cloudy-Fuzzy environment, Journal of Industrial and Management, Vol.13 (5), pp. 1-22.

Blackburn, J., and Scudder, G., (2009). Supply Chain Strategies for Perishable Products: The Case of Fresh Produce, Production and Operations Management, Vol.18 (2), pp.129-137.

Das, S. C., Zidan, A. M., Manna, A. K., Shaikh, A. A., and Bhunia, A. K., (2020). An application of preservation technology in inventory control system with price dependent demand and partial backlogging, Alexandria Engineering Journal, Vol. 59, pp. 1359-1369.

Fattahi, P., Hajipour, V., and Nobari, A., (2015). A bi-objective continuous review inventory control model: Pareto-based meta-heuristic algorithms, Applied Soft Computing, Vol. 32, pp. 211-223.

Ferguson, M., Jayaraman, V, and Souza, G.C., (2007). An application of the EOQ model with nonlinear holding cost to inventory management of perishables, European Journal of Operational Research, Vol. 180, pp. 485-490.

Gharaei, A., Pasandideh, S.H.R., and Arshadi Khamseh, A., (2017). Inventory model in a four-echelon integrated Supply chain: Modeling and optimization, Journal of Modelling in Management, Vol. 12 (4), pp. 739-762.   

Hsiao, Y.H., Chen, M.C., and Chin, C.L., (2017). Distribution planning for perishable foods in cold chains with quality concerns: Formulation and solution procedure, Trends in Food Science & Technology, Vol. 61, pp. 80-93.

James, S.J., James, C., and Evans, J.A., (2006). Modelling of food transportation systems a review, International Journal of Refrigeration, Vol.29, pp. 947-957.

Khan, M. A. A., Shaikh, A. A., Panda, G. C., Konstantaras, I., and Cárdenas‐Barrón, L. E., (2020). The effect of advance payment with discount facility on supply decisions of deteriorating products whose demand is both price and stock dependent, International Transactions in Operational Research, Vol.27(3), pp. 1343-1367.

Khan, M. A. A., Shaikh, A. A., Panda, G. C., Bhunia, A. K., and Konstantaras, I., (2020). Non-instantaneous deterioration effect in ordering decisions for a two-warehouse inventory system under advance payment and backlogging, Annals of Operations Research, Vol. 289(2), pp.1-33.

Khan, M. A. A., Shaikh, A. A., Panda, G. C., and Konstantaras, I., (2019). Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme, RAIRO-Operations Research, Vol. 53(5), pp. 1691-1708.

Khan, M. A. A., Shaikh, A. A., Panda, G. C., Konstantaras, I., and Taleizadeh, A. A., (2019). Inventory system with expiration date: Pricing and replenishment decisions, Computers & Industrial Engineering, Vo.132, pp. 232-247.

Mokhtari. H., Salmasnia, A., and Asadkhani, J., (2020). A New Production-Inventory Planning Model for Joint Growing and Deteriorating Items, International Journal of Supply and Operations Management, Vol. 7, pp.1-16.

Pervin, M., Mahata G.C. and Roy S.K., (2015). An inventory model with demand declining market for deteriorating items under trade credit policy, International Journal of Management Science and Engineering Management, Vol. 11, pp. 243-251.

Pervin. M., Roy, S.K. and Weber, G., (2018). Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Ann Oper Res, Vol. 260, pp. 437-460.

Pervin, M. and Roy S.K., (2017). A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items. Numerical Algebra Control and Optimization, Vol.7 (1), pp. 21-50.

Pervin, M. and Roy S.K., (2018). An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numerical Algebra, Control and Optimization, Vol. 8(2), pp. 169-191.

Pervin, M., (2019). Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy, Journal of Industrial and Management Optimization, Vol.15 (3), pp. 1345-1373.

Rafie-Majd, Z., Pasandideh, S.H.R, and Naderi, B., (2018). Modelling and Solving the Integrated Inventory-Location-Routing Problem in a multi-period and multi-perishable Product Supply Chain with Uncertainty: Lagrangian Relaxation Algorithm, Computers and Chemical Engineering, Vol. 109, pp.9-22.

Redmond, G.A., Gormley, T.R., and Butler, F., (2004). The effect of short- and long-term freeze-chilling on the quality of cooked green beans and carrots, Innovative Food Science and Emerging Technologies, Vol. 5, pp. 65-72.

Rong, A., Akkerman. R., and Grunow, M., (2011). An optimization approach for managing fresh food quality throughout the supply chain, International Journal of Production Economics, Vol. 131, pp. 421-429.

Saha, S., and Chakrabarti, T., (2018). Two-Echelon Supply Chain Model for Deteriorating Items in an Imperfect Production System with Advertisement and Stock Dependent Demand under Trade Credit, International Journal of Supply and Operations Management, Vol. 5, pp. 207-217.

Saif, A., and Elhedhli, S., (2016). Cold supply chain design with environmental considerations: A simulation-optimization approach, European Journal of Operational Research, Vol. 251, pp. 274-287.

Shaikh, A. A., Das, S. C., Bhunia, A. K., Panda, G. C., and Khan, M. A. A., (2019). A two-warehouse EOQ model with interval-valued inventory cost and advance payment for deteriorating item under particle swarm optimization, Soft Computing, Vol.23(24), pp.13531-13546.

Shaikh, A. A., Khan, M. A. A., Panda, G. C., and Konstantaras, I., (2019). Price discount facility in an EOQ model for deteriorating items with stock‐dependent demand and partial backlogging, International Transactions in Operational Research, Vol.26 (4), pp. 1365-1395.

Sundara Rajan, R., and Uthayakumar, R., (2015). A two-warehouse inventory model for deteriorating items with permissible delay under exponentially increasing demand, International Journal of Supply and Operations Management, Vol. 2, pp. 662-682.  

Tao, Y., Lee, L.H., Chew, E.P., Sun, G., and Charles, V., (2017). Inventory control policy for a periodic review system with expediting, Applied Mathematical Modelling, Vol. 49, pp. 375-393.

Tripathi, R.P., (2014). Inventory Model for deteriorating Items with Four level System and Shortages, International Journal of Supply and Operations Management, Vol. 1, pp. 216-227.

Zanoni, S., and Zavanella, L., (2007). Single-vendor single-buyer with integrated transport-inventory system: Models and heuristics in the case of perishable goods, Computers & Industrial Engineering, Vol. 52, pp. 107-123.

Zanoni, S., and Zavanella, L., (2012). Chilled or frozen? Decision strategies for sustainable food supply chains, Int. J. Production Economics, Vol.140, pp. 731-736.

Zhang, G., Habenicht, W., and Ernst Ludwig Spieß, W., (2003). Improving the structure of deep frozen and chilled food chain with tabu search procedure, Journal of food engineering, Vol. 60, pp. 67-79.

Zhao, X., Qiu, M., Xie, J., and He, Q., (2012). Computing (r, Q) policy for an inventory system with limited sharable resource, Computers and operations research, Vol. 39, pp. 2368-2379.