In practice, suppliers
(e.g., manufacturers and distributors) often require their customers (e.g.,
retailers) to order either none or at least a certain amount of units –
Minimum Order Quantity (MOQ). While MOQ provides a way for the
suppliers to achieve economies of scale in production/transportation, it
presents a substantial challenge for the customers to manage inventories
efficiently. Unlike fixed ordering costs and fixed batch sizes, MOQ
received much less attention in the literature.
My research in this area
focuses on identifying and computing efficient inventory replenishment
policies for firms to handle MOQ.
Zhao, Y., M.N. Katehakis (2006). On the Structure of Optimal Ordering Policy of
Stochastic Inventory Systems with Minimum Order Quantity. Probability
in the Engineering and Informational Sciences 20: 257-270.
Abstract: This paper analyzes a
single-product inventory system over a finite time horizon, and models this
type of problem as a stochastic dynamic program. A new concept,
dubbed M-increasing functions, is introduced, which
allows us to characterize the optimal
inventory policies everywhere in the state-space outside of a given region
for each time period, and obtains simple bounds for these regions. The
complex structure of the optimal policies is exemplified for a number of
Zhou, B., Y. Zhao,
M.N. Katehakis (2007). Effective Control Policies for Stochastic
Inventory Systems with a Minimum Order Quantity and Linear Costs. International
Journal of Production Economics 106: 523-531.
Abstract: This paper proposes
and analyzes a new heuristic policy, called (s, t) policy,
for single-product inventory systems with MOQ constraints. The paper
demonstrates via a numerical study that the best (s, t)policy
has a performance close to that of the optimal policy, and it always
outperforms the best feasible (s, S)policies which are commonly
used in practice. On average, the performance improvements are significant.
M.N. Katehakis & Y. Zhao
(2009). Managing stochastic
inventory systems with free shipping option. European Journal
of Operational Research 196: 186-197.