Advance Purchase Discount Research Articles

An extended weak aggregating algorithm for a two dimensional data-driven multi-stage newsvendor problem

We investigate a multi-stage newsvendor problem with advance purchase discount (APD) in this paper. At the beginning of a stage, the decision maker (DM) makes the advance ordering decision for all the periods in this stage; at the start of every period within the stage, the DM makes the regular ordering decision. In this problem, the only available information we can observe is the past demands. To solve this problem, we extend the weak aggregating algorithm (WAA) with one decision variable, an online learning approach based on the theory of prediction and learning with expert advice, to a two-dimensional problem that involves advance ordering decisions in stages and regular ordering decisions nested in each stage. The difficulty of the problem lies in transferring learned knowledge of demand information from stage to stage. We design a cross-stage knowledge transfer scheme and obtain online ordering solutions for both advance-order and regular-order. We show that our solutions converge to the optimal solutions asymptotically. In addition, we derive theoretical guarantees for total gains in one stage and cumulative gains for all stages in the planning horizon. Through numerical studies, we find that our solutions are competitive to those offered by the best experts in hindsight. Finally, we do the sensitivity analysis to illustrate the effectiveness of our algorithm under different parameter values.

Solving a Distribution-Free Multi-Period Newsvendor Problem With Advance Purchase Discount via an Online Ordering Solution

In this paper, we study a distribution-free multi-period newsvendor problem with advance purchase discount (APD). In addition to the regular-order placed at the beginning of each period, a decision-maker (DM) can also commit to an advance-order from the upstream supplier and receive discounts. The goal of the DM is to maximize total profits, and in this problem, the DM only has access to past demand data. To solve this problem, we apply an online method based on the theory of prediction and learning with expert advice to propose an explicit online ordering solution by using the fixed-stock policy as expert advice. With the properties of the gain function, we derive a theoretical result that guarantees, for any given advance-order quantity, the newsvendor’s cumulative gains achieved by the proposed online ordering solution converge to those from the best expert advice in hindsight for a sufficient large horizon. In addition, we extend the problem to the discrete case and obtain the corresponding explicit strategy and performance guarantee. Finally, numerical studies illustrate the effectiveness of the proposed solution, and the newsvendor’s total profits are comparable to the best expert advice. Sensitivity analysis also shows the robustness of the proposed solution.

Supply Chain Coordination under Carbon Emission Tax Regulation Considering Greening Technology Investment.

In this paper, we firstly derive the optimal strategies, including greening technology investment, production volume and order quantity decisions with stochastic demand, for the emissions-dependent supply chain composed of one manufacturer and one retailer. Then, an advance purchase discount (APD) contract and an option contract are applied to coordinate the supply chain. Moreover, an innovative prepayment-based option (PBO) contract is designed based on an APD contract and an option contract. We discuss the cash flow, the inventory risk allocation and the impacts of carbon emission tax under each contract. It is found that considering improving cash flow, preselling (or option selling) as a means of supporting the manufacturer with sufficient cash flow will help expand production and invest in greening technology. From the perspective of avoiding inventory risk, the APD contract benefits the manufacturer while the option contract benefits the retailer. However, the PBO contract generates intermediate allocations of inventory risk between manufacturer and retailer.

Advance Purchase Discounts for Supply Chain Finance System Coordination

The purpose of this paper is to study how advanced information about customer needs obtained through an Advance Purchase Discount (APD) contract can be exploited to coordinate the capital flow and enhance the efficiency of a two-stage supply chain (SC) under decentralized control in cases of stochastic customer demand. We developed an APD model in the form of an option contract, where the model and evaluation include the flexibility for the upstream firm to decide whether to provide a discount for an advance purchase at its own discretion. Applying the model to a Fortune 100 company, a leader in the Fast Mover Consumer Goods (FMCG) industry, showed that under certain conditions, and with suitably chosen contract parameters, management of decentralized control via APD contracts can lead to system-wide efficiency, and the individual decision makers pursue their own best interests, ensuring a win-win condition.

Simultaneous Optimization of Contingent and Advance Purchase Orders with Fixed Ordering Costs

We analyze a finite horizon periodic-review inventory model in the presence of advance purchase discount (APD). In addition to the opportunity to place a contingent order when required, the buyer can also commit to advance orders and receive discounts. Thus the buyer faces the following tradeoff: Contingent orders provide operational flexibility to respond to uncertain demands at a high purchase cost, whereas advance orders incur low purchase cost while sacrificing operational flexibility. We consider a simple and easy-to-implement APD scheme in which the buyer enjoys price discounts by committing at the outset to a fixed size of advanced order for each period along with contingent orders when required. We first show that for any given advance order size, an advance-order dependent (s, S) policy is optimal. We then find the advance order size together with the corresponding (s, S) policy that minimizes the buyer’s total cost.

Using Advance Purchase Discount Contracts under Uncertain Information Acquisition Cost

We study the use of advance purchase discount (APD) contracts to incentivize a retailer to share demand information with a dual‐sourcing wholesaler. We analyze such contracts in terms of two practical considerations that are relevant in this context but have been overlooked by previous work that has largely studied the direct offer of APD to customers: the retailer's information acquisition cost and the wholesaler's limited information about that cost. The wholesaler's limited knowledge of the retailer's cost leads to a departure—from the normal “full observability” APD design—that is asymmetric and depends on the extent of unobservability; if the uncertainty is small (resp., large) then the optimal discount is higher (resp., lower) than in the case of full observability. An APD contract that ignores the retailer's cost or the wholesaler's uncertainty about it will yield fewer benefits for the wholesaler and the supply chain. We offer a numerical illustration (calibrated on real industry data) establishing that for a representative product, an APD contract can improve the wholesaler's profit margin by as much as 3.5%.

Contracts and coordination: Supply chains with uncertain demand and supply

AbstractConsidering a supply chain with a supplier subject to yield uncertainty selling to a retailer facing stochastic demand, we find that commonly studied classical coordination contracts fail to coordinate both the supplier's production and the retailer's procurement decisions and achieve efficient performance. First, we study the vendor managed inventory (VMI) partnership. We find that a consignment VMI partnership coupled with a production cost subsidy achieves perfect coordination and a win‐win outcome; it is simple to implement and arbitrarily allocates total channel profit. The production cost subsidy optimally chosen through Nash bargaining analysis depends on the bargaining power of the supplier and the retailer. Further, motivated by the practice that sometimes the retailer and the supplier can arrange a “late order,” we also analyze the behavior of an advance‐purchase discount (APD) contract. We find that an APD with a revenue sharing contract can efficiently coordinate the supply chain as well as achieve flexible profit allocation. Finally, we explore which coordination contract works better for the supplier vs. the retailer. It is interesting to observe that Nash bargaining solutions for the two coordination contracts are equivalent. We further provide recommendations on the applications of these contracts. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 305–319, 2016

A model of advance selling with consumer heterogeneity and limited capacity

We study advance selling in a model with a capacity constraint for the seller and in the presence of both consumer heterogeneity and demand uncertainty. Buyers face different levels of uncertainty about their valuations in the advance selling period: one group of buyers (called informed buyers) know their individual valuations while the other group (called uninformed buyers) only know the distribution of their valuations. We find that the seller’s optimal pricing strategy depends on his capacity size as well as the size of informed buyers. For a small capacity size, the Constant Price strategy with the highest possible price is adopted. For sufficiently large capacity sizes, both Advance Purchase Discount and Advance Purchase Premium strategies may be optimal. In general, the larger the size of informed buyers the more likely an Advance Purchase Premium strategy is adopted.

Using Advance Purchase Discount Contracts: Operational Cost, Cost Opacity, and Timing

Advance purchase discount (APD) contracts can incentivize a retailer to share demand information with a dual-sourcing wholesaler. We analyze such contracts in terms of three practical considerations that have previously been overlooked: the retailer’s operational cost of adopting an APD scheme, the wholesaler’s limited information about it, and the contract’s timing. The wholesaler’s limited knowledge of the retailer’s cost leads to a departure — from the normal “full observability” APD design — that is asymmetric and depends on the extent of unobservability; thus, if the uncertainty is small (resp., large) then the optimal discount is higher (resp., lower) than in the case of full observability. Finally, a wholesaler can adjust the contract’s timing to synchronize the supply chain to his benefit. An APD contract that ignores the retailer’s cost or the wholesaler’s uncertainty about it, or is implemented in a suboptimal sequence, will yield fewer benefits for the wholesaler and the supply chain. We offer a numerical illustration (calibrated on real industry data) establishing that, for a representative product, an APD contract can improve the wholesaler’s profit margin by as much as 3.5%.

Push, Pull, or Both? A Behavioral Study of How the Allocation of Inventory Risk Affects Channel Efficiency

In this paper we experimentally investigate how the allocation of inventory risk in a two-stage supply chain affects channel efficiency and profit distribution. We first evaluate two common wholesale price contracts that differ in which party incurs the risk associated with unsold inventory: a push contract in which the retailer incurs the risk and a pull contract in which the supplier incurs the risk. Our experimental results show that a pull contract achieves higher channel efficiency than that of a push contract, and that behavior systematically deviates from the standard theory in three ways: (1) stocking quantities are set too low, (2) wholesale prices are more favorable to the party stocking the inventory, and (3) some contracts are erroneously accepted or rejected. To account for these systematic regularities, we extend the existing theory and structurally estimate a number of behavioral models. The estimates suggest that a combination of loss aversion with errors organizes our data remarkably well. We apply our behavioral model to the advance purchase discount (APD) contract, which combines features of push and pull by allowing both parties to share the inventory risk, in a separate experiment as an out-of-sample test, and we find that it accurately predicts channel efficiency and qualitatively matches decisions. Two practical implications of our work are that (1) the push contract performs close to standard theoretical benchmarks, which implies that it is robust to behavioral biases, and (2) the APD contract weakly Pareto dominates the push contract; retailers are better off and suppliers are no worse off under the APD contract. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.1940 . This paper was accepted by Serguei Netessine, operations management.

The Effect of Inventory Risk on Supply Chain Performance

In this analysis we experimentally investigate how altering the inventory risk in a two-tier supply chain affects both the total supply chain profits and the distribution of profits between the two parties. We evaluate three wholesale-price contracts, each differing in which party incurs the risk associated with unsold inventory; a Push contract where the retailer incurs the risk, a Pull contract where the supplier incurs the risk, and an Advance-Purchase Discount (APD) contract where both parties share the risk. Our primary results are that total supply chain profits increase when switching from the Push contract to the Pull contract, as theory suggests, but that there is no improvement in supply chain profits when moving from the Pull contract to the APD contract. We also find that, contrary to standard theory, the APD contract is superior to the Push contract in terms of both retailer and supplier profits, suggesting that a Push contract should never be considered when an APD contract is a possibility.

Pareto analysis of supply chain contracts under satisficing objectives

Supply chain coordination has become critical to firms as increased pressure is placed on them to improve performance. We evaluate the performance of Push, Pull, and Advance-purchase discount (APD) contracts in a manufacturer–retailer supply chain where one or both firms have a satisficing objective of maximizing the probability of achieving a target profit. We identify the resulting operational modes of the supply chain and potential conflicts over the preferred contracts under the Push, Pull, and APD contracts. When both firms are satisficing, conflict over the preferred contract arises when the manufacturer has an ambitious profit target or the retailer has a low profit target. We show that the Push contract can result in a large decrease in the expected profit of a risk-neutral manufacturer when the retailer maximizes the probability of achieving her maximum expected profit. We find that a modified buy-back and profit guarantee contracts can provide significant Pareto improvement over Push or APD contracts when the manufacturer is risk-neutral and the retailer is satisficing, while revenue-sharing contracts cannot. In contrast, revenue sharing and modified buy-back contracts are Pareto dominant under certain conditions when the manufacturer is satisficing and the retailer is risk-neutral.

Advance-purchase discounts as a price discrimination device

In an intertemporal setting in which individual uncertainty is resolved over time, advance-purchase discounts can serve to price discriminate between consumers with different expected valuations for the product. Consumers with a high expected valuation purchase the product before learning their actual valuation at the offered advance-purchase discount; consumers with a low expected valuation will wait and purchase the good at the regular price only in the event where their realized valuation is high. We characterize the profitmaximizing pricing strategy of the monopolist. Furthermore, adopting a mechanism design perspective, we provide a necessary and sufficient condition under which advance-purchase discounts implement the monopolist’s optimal mechanism.

Synchronizing Global Supply Chains: Advance Purchase Discounts

We study the economics of sharing demand information between a dual sourcing firm and its network of retailers. Our analysis demonstrates that employing Advance Purchase Discount (APD) contracts in these supply chains removes significant impediments to information sharing. Essentially, these contracts synchronize the timeline of the dual sourcing firm's decisions with the actions of its network of retailers. This enables accurate, timely, and self-enforcing information sharing, which reduces the demand - supply mismatches, and improves the profitability of each of the agents in the supply chain. We provide prescriptions on the appropriate design of contracts that enable this Pareto-improving information sharing. Next, we extend this analysis to incorporate realistic constraints on the dual sourcing firm's limited knowledge of its retailers' operational costs and information quality. We characterize “certainty-equivalent” values of the unknown retailer parameters, which facilitate analogous prescriptions for the design of APD contracts in these realistic settings. It is interesting that the unobservability of retailer parameters leads to an asymmetric and “degree-of-unobservability dependent” departure from the full-observability design of the APD contract. If the uncertainty in the unobserved parameter is small, then the optimal discount is higher compared to the case of full observability; conversely, when the uncertainty is large, the optimal discount is lower. It is significant that, despite the departure in the design of the APD contract, this analysis reiterates that the benefits of APDs persist even under this practical constraint. Finally, we report on the application of our prescription to a U.S.-based apparel wholesaler. Using data derived from the operations of this firm, we estimate that APD-enabled improved information sharing can increase net profits by about 17%.

Two-Wholesale-Price Contracts: Push, Pull, and Advance-Purchase Discount Contracts

The allocation of inventory ownership affects the inventory availability in a supply chain, which in turn determines the supply chain performance. In this paper, we consider a supplier-retailer supply chain in which the supplier starts production well in advance of the selling season, and the retailer is offered two ordering opportunities at different points in time. An early order is allowed before the supplier’s production decision, and a late order is allowed after the completion of production and after observing the demand. When the two wholesale prices change, we illustrate how the inventory decision rights and ownership are shifted and/or shared between the two firms, resulting in push, pull, or advance-purchase discount contracts. We then characterize the complete set of Pareto-dominant contracts for any given two-wholesale-price contract. We find that Pareto improvement can be achieved when inventory ownership is shifted from individual to shared and sometimes vice versa. In the latter case, push contracts not only are more likely to offer Pareto improvement, but also can achieve higher supply chain efficiency than pull contracts. We also identify conditions that enable Pareto improvement by introducing a new ordering opportunity to firms that had been bound by a single ordering opportunity without renegotiating the existing wholesale price, and we demonstrate through a numerical study that the adoption of the new ordering opportunity can significantly improve supply chain efficiency. We show that such Pareto improvement is more likely to happen when demand is more volatile.

A Deterministic Model for a Manufacture System with an Advance Purchase Discount

Most production planning models assume that the backorder or advance purchase price is the same as the regular purchase price. In practice, since most advance purchase customers may expect to purchase items at discount prices, the purchasing behavior of these customers may differ from the regular purchase customers. In the present paper, we developed a production planning model for dealing with a manufacturing system with an advance purchase discount. The objective of the paper is to maximize the unit time profit by jointly determining the advance purchase discount rate and the size of a production run.

The Allocation of Inventory Risk in a Supply Chain: Push, Pull, and Advance-Purchase Discount Contracts

While every firm in a supply chain bears supply risk (the cost of insufficient supply), some firms may, even with wholesale price contracts, completely avoid inventory risk (the cost of unsold inventory). With a push contract there is a single wholesale price and the retailer, by ordering his entire supply before the selling season, bears all of the supply chain's inventory risk. A pull contract also has a single wholesale price, but the supplier bears the supply chain's inventory risk because only the supplier holds inventory while the retailer replenishes as needed during the season. (Examples include Vendor Managed Inventory with consignment and drop shipping.) An advance-purchase discount has two wholesale prices: a discounted price for inventory purchased before the season, and a regular price for replenishments during the selling season. Advance-purchase discounts allow for intermediate allocations of inventory risk: The retailer bears the risk on inventory ordered before the season while the supplier bears the risk on any production in excess of that amount. This research studies how the allocation of inventory risk (via these three types of wholesale price contracts) impacts supply chain efficiency (the ratio of the supply chain's profit to its maximum profit). It is found that the efficiency of a single wholesale price contract is considerably higher than previously thought as long as firms consider both push and pull contracts. In other words, the literature has exaggerated the value of implementing coordinating contracts (i.e., contracts that achieve 100% efficiency, such as buy-backs or revenue sharing) because coordinating contracts are compared against an inappropriate benchmark (often just a push contract). Furthermore, if firms also consider advance-purchase discounts, which are also simple to administer, then the coordination of the supply chain and the arbitrary allocation of its profit is possible. Several limitations of advance-purchase discounts are discussed.