RUUD TEUNTER [1] [*]
DIMITRIOS VALACHOS [2]
We analyze a discrete time inventory model with two
supply modes. Regular orders are placed periodically and arrive after a
deterministic lead time. Emergency orders, characterized by a shorter
deterministic lead time but higher purchase costs, can be placed in case of
imminent stock-outs. We propose and analyze flexible order-up-to policies with
emergency orders that arrive one, two, ..., up to some fixed number of time
units before a regular order arrives. Based on an approximate cost model, we
develop two sets of approximate
explicit
optimality conditions. The first set of conditions are rather complicated, but
simulation shows that they do lead to near-optimal policies in most cases. The
second set of conditions are very simple and seem more practical, but they only
lead to a near-optimal policy if there are enough emergency supply opportunities
in a review period to prevent most backorders.
1. Introduction
In this paper, we study a discrete time inventory system
with two supply modes, a regular mode and an emergency mode. Emergency orders
are characterized by a shorter deterministic lead time but a higher per item
purchase cost.
Regular orders are placed periodically following an
order-up-to policy on the inventory position (on hand + on order - backorders).
There are several reasons for companies to review their stocks periodically
rather than continuously. Chiang and Gutierrez (1996) mention the following:
* to avoid large reviewing costs;
* to save on ordering and transportation costs by
coordinating orders for different items;
* out of practical and organizational considerations;
* to comply with the suppliers Just-In-Time (JIT) system.
In this paper we will not discuss how to choose between
continuous and periodic review, or how to determine the right length of the
review period if the latter is chosen. We will simply assume that a periodic
review inventory system has been chosen, and that the length of the review
period is predetermined.
The main disadvantage of a periodic review system is
that, when moderate safety stock levels are used, stockouts are likely to occur
near the end of a supply cycle, that is, just before a regular order arrives.
For this reason, emergency ordering can be an attractive option, especially for
inventory systems with long review periods.
It is intuitively obvious that emergency orders should
arrive shortly before a regular order arrives, when the probability of a
stock-out is the highest. We therefore propose to only allow emergency orders
that arrive one, two, ..., up to some fixed number of time units before a
regular order arrives. The necessity and size of the emergency orders is
determined according to an order-up-to policy on the 'emergency inventory
position' (on hand + on emergency order - backorders). The emergency order-up-to
level may depend on the number of time units until the next regular order
arrives.
