Technical Note—Constant-Order Policies for Lost-Sales Inventory Models with Random Supply Functions: Asymptotics and Heuristic

The uncertainty in the supplier’s material flows has become a norm rather than an exception in supply chains. The supply uncertainty can result in unexpected inventory shortfall, amplifying lost sales. However, the design of inventory replenishment and product pricing policy to mitigate both supply uncertainty and demand loss remains unexplored. This is because the resulting dynamic planning problem is highly nonconcave and thus intractable. To address this challenge, we propose an approach that focuses on a class of intuitively appealing and practically plausible policies. Specifically, as the level of on-hand inventory increases, we expect an increased amount of demand fulfillment and a decreased product price. Applying the notion of stochastic functions, we show that, under general conditions of the stochastic supply and demand functions, the dynamic planning problem becomes a concave optimization problem over the restricted policy class. We further reduce the set of candidate policies to a refined class by excluding the dominated policies. A refined policy can be easily computed, and appropriately selected refined policies produce close-to-optimal profits. These developments allow us to evaluate the consequences of demand loss. In particular, demand retention through backordering can be beneficial when overstocking is costly in relation to understocking, but the benefit is insensitive to supply and demand uncertainties. Moreover, inventory-based dynamic pricing is more valuable in mitigating supply risk under lost sales than under backordering.

Section: Literature Reviewmentioning

confidence: 99%

The Effect of Supply Uncertainty on Dynamic Procurement and Pricing Strategies Under Lost Sales

Feng,

Li,

Shanthikumar

2024

“…An example is the recent study by Bu et al. (2020) who evaluate the constant‐order policy when facing a supply function that is stochastically linear in midpoint.…”

Section: Stochastic Functions To Describe Input–output Relationshipsmentioning

confidence: 99%

“…We shall remark that the notion of SL(mp) is useful to generalize the above analysis to incorporate supplier lead time (see, e.g., Erciyes et al 2016), a challenging problem in the inventory management literature. An example is the recent study by Bu et al (2020) who evaluate the constant-order policy when facing a supply function that is stochastically linear in midpoint.…”

mentioning

confidence: 99%

Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems

Feng¹,

Shanthikumar²

2022

U ncertainties involved in decision making often impose challenges to our ability of modeling and analyzing the reality. The purpose of this study is to demonstrate how one can go beyond the conventional optimization thinking, via taking a stochastic viewpoint, to push the boundaries of the analysis. We review the basic notions of stochastic orders and stochastic functions, with which the conventional (deterministic) way of modeling can be generalized. Based on the orders among distribution functions associated with random variables, we can treat the input-output relationship as stochastic functions in our models. This viewpoint, leads to extended functional properties in the stochastic sense. Taking the existing models involving inventory and pricing decisions, we show how the stochastic notions are powerful in simplifying and generalizing the analysis, as well as generating new insights.

“…We refer to Feng and Shanthikumar (2018) for detailed discussions on SL( mp ) and to Bu et al. (2020) for its recent application to lost‐sales inventory models with random supply functions.…”

Section: The Modelmentioning

confidence: 99%

“…This property plays a key role in establishing the concavity of the firm's optimal profit function and characterizing the firm's optimal policy. We refer to Feng and Shanthikumar (2018) for detailed discussions on SL(mp) and to Bu et al (2020) for its recent application to lost-sales inventory models with random supply functions.…”

Section: The Modelmentioning

confidence: 99%

Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts

Gong

Chen

Yuan

2022

Self Cite

A total minimum commitment contract is a supply contract under which a firm commits to buying a minimum quantity of a product from its supplier during the contract duration (e.g., 1 year). Such contracts are widely used in industries, because they provide the buyer with flexibility in terms of the timing and size of each order and the supplier with a guaranteed total order volume. Previous studies on such contracts have focused primarily on the firm's inventory decisions, and none of them has considered the coordination of inventory and pricing decisions. In this study, we fill this gap by studying dynamic inventory and pricing problems under a commitment contract. Under a general demand model with backlogging and zero lead time, we prove that the optimal policy is a committed-inventory-position-dependent basestock list-price policy and characterize its structural properties. We also conduct an extensive numerical study to derive further managerial insights. In particular, we find that dynamic pricing can substantially improve the firm's profitability and enables it to select contracts with large committed quantities and price discount rates, and that ignoring the commitment in joint pricing and ordering decisions can result in substantial profit loss. Finally, we partly extend our results to a lost-sales model and a backlogging model with lead times.