Inventory control in production–inventory systems with random yield and rework: The unit‐tracking approach

Abstract

This paper considers a single-stage make-to-stock production-inventory system under random demand and random yield, where defective units are reworked. We examine how to set cost-minimizing production/order quantities in such imperfect systems, which is challenging because a random yield implies an uncertain arrival time of outstanding units and the possibility of them crossing each other in the pipeline. To determine the order/production quantity in each period, we extend the unittracking/decomposition approach, taking into account the possibility of order-crossing, which is new to the literature and relevant to other planning problems. The extended unit-tracking/decomposition approach allows us to determine the optimal base-stock level and to formulate the exact and an approximate expression of the per-period cost of a base-stock policy. The same approach is also used to develop a state-dependent ordering policy. The numerical study reveals that our state-dependent policy can reduce inventory-related costs compared to the base-stock policy by up to 6% and compared to an existing approach from the literature by up to 4.5%. From a managerial perspective, the most interesting finding is that a high mean production yield does not necessarily lead to lower expected inventory-related costs. This counterintuitive finding, which can be observed for the most commonly used yield model, is driven by an increased probability that all the units in a batch are either of good or unacceptable quality. K E Y W O R D Sbase-stock policy, inventory control, random yield, rework, unit-tracking approach INTRODUCTIONWe consider a single-stage make-to-stock productioninventory system under random demand and random yield, where defective units are reworked. Random yield refers to the number of items meeting the desired quality requirements, set either by a company itself or externally, for example, by the US Food and Drug Administration (FDA) for pharmaceutical products or the Federal Communications Commission (FCC) for electronic products. Our goal is to determine the ordering policy that minimizes the total average inventory-related cost per period, comprised of holding costs for all units on stock and backorder costs for all units that cannot be satisfied immediately from stock on hand.

Inventory control strategy: based on demand forecast error

“…Previous works, such as Wang and Gerchak (1996), have shown that the order-up-to policy is optimal when only considering variable capacity; while the reorder point policy is optimal when both variable capacity and random yield are taken into account. Berling and Sonntag (2022) analyzed inventory systems with random yields and introduced the concept of rework, where products that do not meet standards are delivered at a later time. The authors used decomposition algorithms to determine the optimal base inventory level; however, their study is limited to a single stage and does not consider updates from the production stage.…”

Cost minimizing planning of container inspection and repair in multiple facilities

“…In particular, the problem falls into the categories of inventory management in reverse logistics, planning work and rework processes and lifetime inspection and maintenance planning for deteriorating engineering systems. Reverse logistics deals with the reuse processes in supply chains, see (Fleischmann et al 1997 ), (de Brito and Dekker 2004 ), (Kim and Glock 2014 ), (Cobb 2016 ), (Berling and Sonntag 2022 ). In a closed-loop supply chain, demands are satisfied by new and repaired products, which leads to a complex problem of planning the original production and the repair.…”

Control de inventarios y gestión rentable en mypes comerciales de calzados

“…El control de las existencias, también conocido como gestión de inventario, es una parte crucial de la gestión rentable de una empresa en la práctica contable empresarial (Berling & Sonntag, 2022). El objetivo principal es optimizar el equilibrio entre tener suficiente inventario para satisfacer la demanda de los clientes y minimizar los costos asociados con el almacenamiento y la gestión del inventario (Córdova et al, 2022).…”