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Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements

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  • Yonit Barron

    (Industrial Engineering and Management, Ariel University, Ariel 40700, Israel)

Abstract

We study an inventory control problem with two storage facilities: a primary warehouse (PW) of limited capacity M , and a subsidiary one (SW) of sufficiently large capacity. Two types of customers are considered: individual customers arriving at (positive and negative) linear rates governed by a Markov chain, and retailers arriving according to a Markov arrival process and bringing a (positive and negative) random number of items. The PW is managed according to a triple-parameter band policy ( M , S , s ) , 0 ≤ s < S ≤ M , under a lost sales assumption. Under this policy, as soon as the stock level at the PW falls below s , a refilling to S is performed by a distributor after a random lead-time. However, if the stock exceeds level S when the distributor arrives, no refilling is carried out, and only maintenance services are performed. Items that exceed level M are transferred to the SW at a negligible amount of time for those used in related products. Our cost structure includes a fixed order cost, a variable cost for each item supplied by the distributor, a cost for the additional maintenance, a salvage payment for each transferred item from the PW to the SW, and a loss cost for each unsatisfied item due to demands. We seek to determine the optimal thresholds that minimize the expected overall cost under the discounted criterion. Applying first-passage time results, we present a simple set of equations that provide managers with a useful and an efficient tool to derive the optimal thresholds. Sensitivity analysis and fruitful conclusions along with future scope of research directions are provided.

Suggested Citation

  • Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:864-:d:1061629
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    References listed on IDEAS

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    Cited by:

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    3. WonIl Lee & JaeWook Shin & BumYong Park, 2024. "The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates," Mathematics, MDPI, vol. 12(5), pages 1-14, February.

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