Abstract: This paper is concerned with the single-item
continuous review inventory system in which demand is stochastic
and discrete. The budget consumed for purchasing the ordered items
is not restricted but it incurs extra cost when exceeding specific
value. The unit purchasing price depends on the quantity ordered
under the all-units discounts cost structure. In many actual systems,
the budget as a resource which is occupied by the purchased items is
limited and the system is able to confront the resource shortage by
charging more costs. Thus, considering the resource shortage costs as
a part of system costs, especially when the amount of resource
occupied by the purchased item is influenced by quantity discounts,
is well motivated by practical concerns. In this paper, an optimization
problem is formulated for finding the optimal (r, Q) policy, when the
system is influenced by the budget limitation and a discount pricing
simultaneously. Properties of the cost function are investigated and
then an algorithm based on a one-dimensional search procedure is
proposed for finding an optimal (r, Q) policy which minimizes the
expected system costs.
Abstract: Most papers model Joint Replenishment Problem
(JRP) as a (kT,S) where kT is a multiple value for a common review
period T,and S is a predefined order up to level. In general the (T,S)
policy is characterized by a long out of control period which requires
a large amount of safety stock compared to the (R,Q) policy. In this
paper a probabilistic model is built where an item, call it item(i),
with the shortest order time between interval (T)is modeled under
(R,Q) policy and its inventory is continuously reviewed, while the
rest of items (j) are periodically reviewed at a definite time
corresponding to item