Modeling customer impatience in a newsboy problem with time-sensitive shortages

Customers across all stages of the supply chain often respond negatively to inventory shortages. One approach to modeling customer responses to shortages in the inventory control literature is time-dependent partial backlogging. Partial backlogging refers to the case in which a customer will backorder shortages with some probability, or will otherwise solicit the supplier's competitors to fulfill outstanding shortages. If the backorder rate (i.e., the probability that a customer elects to backorder shortages) is assumed to be dependent on the supplier's backorder replenishment lead-time, then shortages are said to be represented as time-dependent partial backlogging. This paper explores various backorder rate functions in a single period stochastic inventory problem in an effort to characterize a diversity of customer responses to shortages. We use concepts from utility theory to formally classify customers in terms of their willingness to wait for the supplier to replenish shortages. Under mild assumptions, we verify the existence of a unique optimal solution that corresponds to each customer type. Sensitivity analysis experiments are conducted in order to compare the optimal actions associated with each customer type under a variety of conditions. Additionally, we introduce the notion of expected value of customer patience information (EVCPI), and then conduct additional sensitivity analyses to determine the most and least opportune conditions for distinguishing between customer behaviors.Inventory control Customer responsiveness Time-dependent partial backlogging Demand uncertainty Utility theory

Inventory decisions for emergency supplies based on hurricane count predictions

This paper addresses a stochastic inventory control problem for manufacturing and retail firms who face challenging procurement and production decisions associated with hurricane seasons. Specifically, the paper presents a control policy in which stocking decisions are based on a hurricane forecast model that predicts the number of landfall hurricanes for an ensuing hurricane season. The multi-period inventory control problem is formulated as a stochastic programming model with recourse where demand during each pre-hurricane season period is represented as a convolution of the current period's demand and an updated estimate of demand for the ensuing hurricane season. Due to the computational challenges associated with solving stochastic programming problems, recent scenario reduction techniques are discussed and illustrated through an example problem. The proposed model specifies cost minimizing inventory strategies for simultaneously meeting stochastic demands that occur prior to the hurricane season while proactively preparing for potential demand surge during the season.Disaster relief planning Humanitarian logistics Supply chain management Stochastic programming Markov chain Bayesian regression

A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration

This paper addresses the integration of two emerging classes of scheduling problems which, for the most part, have evolved independently. These problem classes are (i) scheduling problems with time-dependent processing times and (ii) scheduling problems with rate-modifying activities (RMAs). The integration of these two concepts is motivated by human operators who experience fatigue while carrying out tasks and take rest breaks for recovery, but is also applicable to machines that experience performance degradation over time and require maintenance in order to sustain acceptable production rates. We explore a sequence-independent, single processor makespan problem with position-dependent processing times and prove that under certain conditions, the optimal policy is to schedule the RMA in the middle of the task sequence.Scheduling Rate-modifying activity Position-dependent processing times Makespan Human operator

Production planning for a deteriorating item with stochastic demand and consumer choice

This paper concerns inventory control of a deteriorating product with non-negligible procurement lead-time that perishes after a known number of periods. Demand for fresh products during each period is represented as a random variable with known probability distribution, but only a fraction of this demand is satisfied during any given period due to item deterioration. We derive the expected profit function for a two-period problem with one production opportunity before the selling season begins and a single product type with two-period shelf life. For the case in which demand during both periods is uniform, independent, and identically distributed, we identify sufficient conditions for the existence of an optimal solution and present a straightforward procedure for obtaining the solution.Inventory control Supply-chain Agriculture Consumer preferences