TY - JOUR

T1 - Cash-Flow Based Dynamic Inventory Management

AU - Katehakis, Michael N.

AU - Melamed, Benjamin

AU - Shi, Jim Junmin

N1 - Funding Information:
The authors are grateful to Dr. John Birge (the Departmental Editor), the Senior Editor, and the reviewers for valuable comments. The authors are also indebted to the valuable comments and useful suggestions provided by Dr. Matthew Sobel of Case Western Reserve University, and Dr. Xiuli Chao of the University of Michigan. The first author gratefully acknowledges support for this project from the National Science Foundation (CMMI-14-50743). The third author thanks NJIT for financial support for this research.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - Small-to-medium-sized enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this study, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. The firm's state at the beginning of each period is characterized by the inventory level and the capital level measured in units of the product, whose sum represents the “net worth” of the firm. Our study shows that the optimal ordering policy is characterized by a pair of threshold parameters as follows. (i) If the net worth is less than the lower threshold, then the firm employs a base stock order up to the lower threshold. (ii) If the net worth is between the two thresholds, then the firm orders exactly as many units as it can afford, without borrowing. (iii) If the net worth is above the upper threshold, then the firm employs a base stock order up to the upper threshold. Further, upper and lower bounds for the threshold values are developed using two simple-to-compute myopic ordering policies which yield lower bounds for the value function. We also derive an upper bound for the value function by considering a sell-back policy. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with extensive numerical studies.

AB - Small-to-medium-sized enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this study, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. The firm's state at the beginning of each period is characterized by the inventory level and the capital level measured in units of the product, whose sum represents the “net worth” of the firm. Our study shows that the optimal ordering policy is characterized by a pair of threshold parameters as follows. (i) If the net worth is less than the lower threshold, then the firm employs a base stock order up to the lower threshold. (ii) If the net worth is between the two thresholds, then the firm orders exactly as many units as it can afford, without borrowing. (iii) If the net worth is above the upper threshold, then the firm employs a base stock order up to the upper threshold. Further, upper and lower bounds for the threshold values are developed using two simple-to-compute myopic ordering policies which yield lower bounds for the value function. We also derive an upper bound for the value function by considering a sell-back policy. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with extensive numerical studies.

KW - inventory-finance decision

KW - myopic policy

KW - sell-back policy

KW - threshold values

UR - http://www.scopus.com/inward/record.url?scp=84976876660&partnerID=8YFLogxK

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U2 - 10.1111/poms.12571

DO - 10.1111/poms.12571

M3 - Article

AN - SCOPUS:84976876660

VL - 25

SP - 1558

EP - 1575

JO - Production and Operations Management

JF - Production and Operations Management

SN - 1059-1478

IS - 9

ER -