Coordinating Inventory Control and Pricing Strategies Under Batch Ordering
Bibliographic record
Abstract
In this paper we investigate joint pricing and inventory control problems in a finite-horizon, single-product, periodic-review setting with certain/uncertain supply capacities. The demands in different periods are random variables whose distributions depend on the posted price exhibiting the additive form. The order quantity in each period is required to be of integral multiples of a given specific batch size (denoted by Q). Inventory replenishment incurs a linear ordering cost. Referred to as the cost-rate function, the sum of holding and backorder costs can either be convex or quasi-convex. The objective is to determine a joint ordering and pricing decision that can maximize the total expected profit over the planning horizon. We first consider the case in which the cost-rate function is convex and show that the modified (r, Q) list-price policy is optimal for the system with certain and limited capacities, a special case of which is the (r, Q) list-price policy when capacities become unlimited. As supply capacities become random, the optimal policy follows a new structure wherein the optimal order-up-to level and posted price must be coordinated to make the optimal safety stock level follow the (r, Q) policy. We further consider the case of a quasi-convex cost-rate function, which may arise when a service level constraint is used as a surrogate for the shortage cost. We demonstrate that the (r, Q) list-price policy is optimal for the system without supply capacity constraints. In addition, extensions to several other models are discussed. The enabling technique is based on the notion of Q-jump convexity and its variants.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".