How Many Pieces of Ice Cream Cake to Order?


The EOQ (economic order quantity) model celebrated its 100 birthday last year, being first published in February 1913 by Harris.  The EOQ model has held the test of time as it is still commonly used in practice and even has its own app (I guess it ages gracefully!).  To celebrate, the International Journal of Production Economics launched a special issue and I am happy to report that we are part of the party – our paper “A New Inventory Model for Cold Items that Considers Costs and Emissions” has been accepted.  Our model (an extension of the EOQ model) considers unit freezer capacities and analyzes inventory decisions based on both a financial and an environmental objective function.  This research was led by Ph.D. Student Ali Bozorgi, who is co-advised by Dima Nazzal (at Georgia Tech) and myself.  Using our model, we should be able to determine how many pieces of ice cream cake to order for the birthday party!  🙂

The paper specifics: 

A new inventory model for cold items that considers costs and emissions

Ali Bozorgi *, Jennifer A. Pazour* & Dima Nazzal**

*Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL, 32816, USA

**H. Milton Stewart School of Industrial and Systems Engineering
Georgia Institute of Technology, Atlanta, GA USA 30332


to appear in the Special Issue Celebration of the 100th Anniversary of the EOQ Model for the International Journal of Production Economics (IJPE).

ABSTRACT: A new inventory model that considers both cost and emission functions is proposed for environments where temperature-controlled items need to be stored at a certain, non-ambient temperature and to do so modular temperature-control units are used.  Transportation unit capacity and storage unit capacity are considered, which results in non-linear, non-continuous cost and emissions functions. A set of exact algorithms are developed to find the optimal order quantity based on cost and emission function minimization, and the mathematical proof of the optimality of the solutions are presented.  Using a variety of parameter ratios, a set of experiments are run to show the effectiveness of the proposed model compared to the current models in the literature and to provide managerial insights into the cold item inventory problem. Optimum order quantity for cost function optimization and emission function optimization are compared against each other and the tradeoff between the functions is analyzed to provide insights.


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