TY - JOUR
T1 - A dynamic ordering policy for a stochastic inventory problem with cash constraints
AU - Chen, Zhen
AU - Rossi, Roberto
PY - 2021/7
Y1 - 2021/7
N2 - This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product and sells it to customers while facing non-stationary demand. In each period, the retailer’s available cash restricts the maximum quantity that can be ordered. There is a fixed ordering cost incurred when an order is issued by the retailer. We introduce a heuristic (s;C(x); S )policy inspired by numerical findings and by a structural analysis. The policy operates as follows: when the initial inventory x is less than s and the initial cash is greater than the state-dependent value C(x),the retailer should order a quantity that brings inventory as close to S as possible; otherwise, the retailer should not order. We first determine the values of the controlling parameters s, C(x) and S via the results of stochastic dynamic programming and test their performance in an extensive computational study. The results show that the (s;C(x); S ) policy performs well, with a maximum optimality gap of less than 1%,and an average gap of approximately 0.03%. We then develop a simple and time-efficient heuristic method for computing policy (s;C(x); S ) by solving a mixed-integer linear programming problem: the average gap for this heuristic is less than 1% on our test bed.
AB - This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product and sells it to customers while facing non-stationary demand. In each period, the retailer’s available cash restricts the maximum quantity that can be ordered. There is a fixed ordering cost incurred when an order is issued by the retailer. We introduce a heuristic (s;C(x); S )policy inspired by numerical findings and by a structural analysis. The policy operates as follows: when the initial inventory x is less than s and the initial cash is greater than the state-dependent value C(x),the retailer should order a quantity that brings inventory as close to S as possible; otherwise, the retailer should not order. We first determine the values of the controlling parameters s, C(x) and S via the results of stochastic dynamic programming and test their performance in an extensive computational study. The results show that the (s;C(x); S ) policy performs well, with a maximum optimality gap of less than 1%,and an average gap of approximately 0.03%. We then develop a simple and time-efficient heuristic method for computing policy (s;C(x); S ) by solving a mixed-integer linear programming problem: the average gap for this heuristic is less than 1% on our test bed.
KW - stochastic inventory
KW - non-stationary demand
KW - cash-flow constraint
KW - (s;C(x); S ) policy
UR - https://www.sciencedirect.com/journal/omega
U2 - 10.1016/j.omega.2020.102378
DO - 10.1016/j.omega.2020.102378
M3 - Article
SN - 0305-0483
VL - 102
JO - Omega
JF - Omega
M1 - 102378
ER -