Browsing by Subject "Renewal reward theorem"

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Open Access
An exact analysis on age-based control policies for perishable inventories
(Taylor and Francis, 2020-09-01) Poormoaied, S.; Gürler, Ülkü; Berk, E.
We investigate the impact of effective lifetime of items in an age-based control policy for perishable inventories, a so-called (Q, r, T) policy, with positive lead time and fixed lifetime. The exact analysis of this control policy in the presence of a service level constraint is available in the literature under the restriction that the aging process of a batch begins when it is unpacked for consumption, and that at most one order can be outstanding at any time. In this work, we generalize those results to allow for more than one outstanding order and assume that the aging process of a batch starts since the time that it is ordered. Under this aging process, we derive the effective lifetime distribution of batches at the beginning of embedded cycles in an embedded Markov process. We provide the operating characteristic expressions and construct the cost rate function by the renewal reward theorem approach. We develop an exact algorithm by investigating the cost rate and service level constraint structures. The proposed policy considerably dominates its special two-parameter policies, which are time-dependent (Q, T) and stock-dependent (Q, r) policies. Numerical studies demonstrate that the aging process of items significantly influences the inventory policy performance. Moreover, allowing more than one outstanding order in the system reaps considerable cost savings, especially when the lifetime of items is short and the service level is high.
Open Access
An inventory problem with two randomly available suppliers
(Institute for Operations Research and the Management Sciences, 1997) Gürler, Ü.; Parlar, M.
This paper considers a stochastic inventory model in which supply availability is subject to random fluctuations that may arise due to machine breakdowns, strikes, embargoes, etc. It is assumed that the inventory manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each supplier's availability is modeled as a semi-Markov (alternating renewal) process. We assume that the durations of the ON periods for the two suppliers are distributed as Erlang random variables. The OFF periods for each supplier have a general distribution. In analogy with queuing notation, we call this an Es1[Es2]/G1[G2] system. Since the resulting stochastic process is non-Markovian, we employ the "method of stages" to transform the process into a Markovian one, albeit at the cost of enlarging the state space. We identify the regenerative cycles of the inventory level process and use the renewal reward theorem to form the long-run average cost objective function. Finite time transition functions for the semi-Markov process are computed numerically using a direct method of solving a system of integral equations representing these functions. A detailed numerical example is presented for the E2[E2]/M[M] case. Analytic solutions are obtained for the particular case of "large" (asymptotic) order quantity, in which case the objective function assumes a very simple form that can be used to analyze the optimality conditions. The paper concludes with the discussion of an alternative inventory policy for modeling the random supply availability problem.