A closed-form solution for the distribution free continuous review integrated inventory model

• Published in: Operational research Vol. 18; no. 1; pp. 159 - 186
• Main Authors: Gutgutia, Anuraag, Jha, J. K.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2018; Springer Nature B.V
• Subjects: Business and Management; Closed form solutions; Computational Intelligence; Customer services; Economic models; Exact solutions; Inventory management; Lead time; Management Science; Mathematical analysis; Mathematical models; Operations Research; Operations Research/Decision Theory; Order quantity; Original Paper; Production planning; Safety factors; Sensitivity analysis; Supply chains; Partial backorders; Defective items; Fill rate; Integrated inventory model; Distribution free demand; Controllable lead time
• ISSN: 1109-2858; 1866-1505
• DOI: 10.1007/s12351-016-0258-5

In this paper, we develop an integrated inventory model in a single-vendor single-buyer supply chain under an unknown demand distribution at the buyer. It is assumed that each lot delivered to the buyer contains a random fraction of defective items, and lead time can be reduced at an extra crashing cost. We also consider that the unmet demand at the buyer during the stockout period is partially backordered. A model is formulated to minimize the total expected relevant costs of the system considering an exact expression of the service level constraint to ensure that a certain percentage of customer orders are filled by the buyer. Closed-form expressions are derived for the optimal order quantity and safety factor for given lead time and shipment frequency, and then an algorithm is proposed to find the global optimal solution. Finally, a numerical example is presented to illustrate the solution procedure and sensitivity analysis is carried out to analyze the proposed model.