A Periodic Review, Production Planning Model with Uncertain Capacity and Uncertain Demand—Optimality of Extended Myopic Policies

Abstract

Increasing product complexity, manufacturing environment complexity and an increased emphasis on product quality are all factors leading to uncertainties in production processes. These uncertainties are in the form of unplanned machine maintenance, varying production yields and rework, among others. In planning for production, an adequate model must incorporate these uncertainties into the representation of the production process. This paper treats the aggregate planning problem for a single product with random demand and random capacity. In the single-period problem, random capacity does not affect the optimal policy but results in a unimodal, nonconvex cost function. In the multiple-period and infinite-horizon settings order-up-to policies that are dependent on the distribution of capacity are shown to be optimal in spite of a nonconvex cost. In the infinite-horizon setting an intuitive description of the situation leads to the notion of a class of extended myopic policies, requiring the consideration of review periods of uncertain length.

Mitigating Supply Risk: Dual Sourcing or Process Improvement?

“…We note that such quantity hedging, i.e., "over" ordering, never occurs in a single-supplier random-capacity model (Ciarallo et al 1994). Quantity hedging protects the firm against capacity shortfall in the event that the other supplier experiences a capacity shortage and hence quantity hedging is valuable only when there are multiple suppliers.…”

“…This literature models reliability in three different but related ways: random capacity, e.g., Ciarallo et al (1994), Erdem (1999), random yield, e.g., Gerchak and Parlar (1990), Parlar and Wang (1993), Anupindi and Akella (1993), Agrawal and Nahmias (1997), Swaminathan andShanthikumar (1999), Federgruen andYang (2007a), and random disruption, e.g., Parlar and Perry (1996), Gürler and Parlar (1997), Tomlin (2006), Babich et al (2007). Financial default is another element of supply risk and has recently been explored by Babich et al (2007) and Swinney and Netessine (2008).…”

Capacitated Production Control with Virtual Lateral Transshipments

“…Other studies in this vein include Glasserman (1996), Glasserman andTayur (1994, 1997), Kapuscinski and Tayur (1998), and Tayur (1992). Ciarallo et al (1994) considered random capacity. They found the optimal policy to be still of the base-stock type.…”

A Production-Inventory System with Markovian Capacity and Outsourcing Option

“…Other studies in this vein include Tayur (1994, 1995), Kapuscinski andTayur (1998), andTayur (1992). Ciarallo et al (1994) considered a random, and yet still independent, capacity stream. They found the optimal policy to be still of the base-stock type.…”