Technical Note—A Note on the Structure of Joint Inventory-Pricing Control with Leadtimes

In retailing operations, retailers face the challenge of incomplete demand information. We develop a new concept named K‐approximate convexity, which is shown to be a generalization of K‐convexity, to address this challenge. This idea is applied to obtain a base‐stock list‐price policy for the joint inventory and pricing control problem with incomplete demand information and even non‐concave revenue function. A worst‐case performance bound of the policy is established. In a numerical study where demand is driven from real sales data, we find that the average gap between the profits of our proposed policy and the optimal policy is 0.27%, and the maximum gap is 4.6%.

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“…Pang et al. () identified various properties of the optimal policy in the presence of positive leadtimes. Feng et al.…”

Section: Introductionmentioning

confidence: 99%

Joint Inventory and Pricing Coordination with Incomplete Demand Information

Song

Yang

2016

Production and Operations Management

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“…, Huh and Janakiraman , Pang et al. , Zipkin ).

L^{♮}

‐convexity is related to multimodularity through a unimodular coordinate transformation (Murota ).…”

Section: Literature Reviewmentioning

confidence: 99%

Joint Decisions for Blood Collection and Platelet Inventory Control

Chen

Zhou

2019

Production and Operations Management

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The present study investigates the benefit of joint decision making regarding whole blood collection and platelet production at a blood center. We consider a blood center that faces two types of platelet demands, differing in their freshness requirements and shortage penalty costs. We fully characterize the structure of the optimal policy regarding whole blood collection, platelet production, and inventory issuing, rationing and disposal. We find that the optimal platelet production quantity in each period is nonincreasing in the inventory levels of platelets and whole blood but that interestingly, the optimal blood collection effort may increase with the on‐hand platelet inventory level. We demonstrate with a real dataset that joint decision making leads to significant cost savings compared with separate decision making. The benefit is mainly derived from reduced blood collection and platelet production, better utilization of the collected whole blood, and reduced platelet shortage. For practical implementation, we develop a lookahead heuristic, which is shown to be very effective by numerical experiments.

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“…It is notable that in the periodic review model the base-stock policy is no longer optimal (Pang, Chen, and Feng [31]), which indicates that the continuous time model with Poisson demand does provide sharper results. Specifically, part (a) states that, for any given batch size Q, there exists a critical inventory level, the socalled optimal reorder point, r, above which no order should be issued.…”

Section: Discounted Profit Criterionmentioning

confidence: 99%

Coordinated Pricing and Inventory Control With Batch Production and Erlang Leadtimes

Pang¹,

Chen²

2014

Prob. Eng. Inf. Sci.

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This paper addresses a joint pricing and inventory control problem for a batch production system with random leadtimes. Assume that demand arrives according to a Poisson process with a price-dependent arrival rate. Each replenishment order contains a single batch of a fixed lot size. The replenishment leadtime follows an Erlang distribution, with the number of completed phases recording the delivery state of outstanding orders. The objective is to determine an optimal inventory-pricing policy that maximizes total expected discounted profit or long-run average profit. We first show that when there is at most one order outstanding at any point in time and that excess demand is lost, the optimal reorder policy can be characterized by a critical stock level and the optimal pricing decision is decreasing in the inventory level and delivery state. We then extend the analysis to mixed-Erlang leadtime distribution which can be used to approximate any random leadtime to any degree of accuracy. We further extend the analysis to allowing three outstanding orders where the optimal reorder point becomes state-dependent: the closer an outstanding order is to its arrival or the more orders are outstanding, the lower selling price is charged and the lower reorder point is chosen. Finally, we address the backlog case and show that the monotone pricing structure may not be true when the optimal reorder point is negative. 530Z. Pang and F.Y. Chen challenges intrinsic to problems with dynamically controllable prices (Federgruen and Heching [13]). In standard inventory models with fully backordering and exogenous prices (hence exogenous random demand), the impact of current inventory positions (= inventory levels + outstanding orders − backorders) is evaluated on the basis of the present value of expected inventory cost one order leadtime later. However, in the presence of positive leadtime, with dynamically controllable prices, these future costs depend on the pricing decisions of future periods during the leadtime, and they are therefore unspecified in the current period. An exact formulation requires a multi-dimensional state space to record the inventory levels on hand and on order, and is therefore very difficult to analyze. Pang, Chen, and Feng [31] represent the early effort to provide some partial characterization of the optimal policy structure for periodic-review systems. Our paper attempts to continue their effort to address the continuous-review systems.Furthermore, the literature on inventory-pricing control has also confined itself to models with arbitrary ordering sizes (i.e., lot-for-lot sizes), whereas in supply chains, materials often flow in fixed batch sizes. For example, consumer packaged goods typically arrive at stores in cartons or case packs, finished goods may be transported in full containers or truckloads, and work-in-process (WIP) is usually processed in some convenient lot sizes (Kapuscinski et al. [22]). In addition, a batch production system can serve as an approximation of a capacitated inventory s...

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Technical Note—A Note on the Structure of Joint Inventory-Pricing Control with Leadtimes

Cited by 77 publications

References 24 publications

Joint Inventory and Pricing Coordination with Incomplete Demand Information

Joint Inventory and Pricing Coordination with Incomplete Demand Information

Joint Decisions for Blood Collection and Platelet Inventory Control

Coordinated Pricing and Inventory Control With Batch Production and Erlang Leadtimes

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