Initial Order Quantity Research Articles

Forewarned Is Forearmed? Contingent Sourcing, Shipment Information, and Supplier Competition

Problem definition: Dual sourcing and contingent sourcing are important risk-mitigation strategies to manage supply chain risks, including transportation-related losses of inbound orders. Contingent sourcing as a means of managing transportation risk is made possible by shipment information realized at in-transit inspection points or through shipment monitoring technologies. We examine the impact of contingent sourcing and shipment information in a setting where a buyer can source from two competing suppliers. One supplier (unreliable) has a long transportation lead time and is prone to in-transit yield loss; the other supplier (reliable) has a short, but nonzero, lead time with no yield loss. Methodology/results: We analyze a multistage game-theoretical model in which the two suppliers compete on wholesale prices and then, the buyer determines initial order quantities. Later, the buyer can place an emergency order with the reliable supplier based on shipment information, which reveals (possibly imperfectly) the status of the in-transit order from the unreliable supplier. We show that the buyer will adopt one of four possible sourcing strategies: (1) initially source only from the unreliable supplier but resort to the reliable supplier contingent on the updated shipment information, (2) diversify its initial order across the two suppliers but resort to the reliable supplier if needed, (3) diversify its initial order and not engage in contingent sourcing, or (4) sole source from the reliable supplier. Interestingly, contingent sourcing may or may not benefit the buyer because it may soften the competition between suppliers. Moreover, the buyer’s profit may not be monotonic in the accuracy of shipment information. Managerial implications: The buyer must design its supply base so that the unreliable supplier is particularly cost efficient if the buyer is to benefit from the possibility of contingent sourcing. The buyer may not always benefit from operational improvements that enhance shipment information accuracy because they may soften supplier competition. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0540 .

공급사슬 중단 및 수율 불확실성을 고려한 최적 공급업체 수와 주문량의 결정 및 보완주문 전략에 관한 연구

In this study, we developed an optimal sourcing strategy considering compensation orders to mitigate the supply chain disruption risks and yield uncertainty. Additionally, we proposed an approximation method that can perform quick calculations to ascertain the optimal number of suppliers and initial order quantity. Finally, by using a numerical example, we confirmed that if there is a disruption probability, it is desirable to distribute the risk by dividing the order into small portions from multiple suppliers. This study proposes an optimal procurement strategy under disruption risks and serves as a guide to establishing a procurement strategy that maximizes a firm's profit in the long term.

Option Contracts in Fresh Produce Supply Chain with Freshness-Keeping Effort

This study investigates a supply chain of fresh produce with consideration of option contracts and where stochastic market demand depends on freshness-keeping effort. Firstly, we investigate a benchmark scenario of an integrated supply chain with freshness effort and consideration of decreases in both the quality and quantity of produce while in the supply chain. Secondly, we introduce call, put, and bidirectional option contracts to mitigate risks of the retailer. A call option contract can reduce the underage risk, while a put option contract can reduce the overage risk, and a bidirectional option contract can reduce bilateral risks. We derive the optimal ordering decisions and freshness-keeping effort for a retailer in a supply chain of fresh produce with option contracts, and the conditions for achieving coordination of the supply chain. We find that the bidirectional option results in the highest option price and lowest option order quantity, while the call option results in the lowest initial order quantity and the put option results in the highest initial order quantity. Finally, numerical examples are given to demonstrate the impacts of various parameters on optimal decision-making. This paper provides managerial insights for reducing risk in fresh produce supply chains.

Coordination Mechanisms for the Two‐Echelon Newsvendor Model with Rapidly Responsive and Strategic Consumers

Aiming at the two-echelon newsvendor problem in which the market demand of commodities is random both in normal sales period and in liquidation period, this paper studies the pricing and ordering decision of retailers by using rational expectation equilibrium under the condition of considering consumersʼ strategic behavior and rapid response mechanism. Then, the decision-making problem under retailersʼ initial order quantity commitment is discussed, as well as the effect of commitment mechanism on supply chain performance. On this basis, both the two-part pricing contract and revenue-sharing contract are introduced to achieve supply chain coordination aiming at the profit maximization under the initial order quantity commitment mechanism. The results show that the rapid response mechanism can reduce the negative impact of consumers’ strategic behavior, and the initial order quantity commitment can further reduce the impact and improve the retailers’ profit. Both the two-part pricing contract and revenue-sharing contract can coordinate the whole supply chain in which the two-part pricing contract can distribute profit arbitrarily between manufacturers and retailers while the revenue-sharing contract can share risks among members of the supply chain.

Optimal pricing and ordering decisions with reference effect and quick replenishment policy

AbstractThis paper considers a revenue management problem in which a retailer determines joint pricing and ordering decisions for a single product over a two‐period selling horizon. The goal is to investigate the single and combined influences of reference effect (RE) and quick replenishment (QR) policy on the customers' purchasing behaviors, the retailer's optimal decisions, and the total profit of two periods. We first propose a discrete‐time joint pricing and ordering model with RE and QR policy in the presence of strategic customers. Then we extend to the other two models, in which the retailer does not implement the QR policy and the retailer ignores the customers' RE, to, respectively, explore the values of RE and QR policy to the retailer. Several significant results and managerial insights are derived through theoretical analysis and numerical experiments. Implementing the QR policy could help the retailer cut nearly half of the initial order quantity and improve the profit significantly, especially when the strength of RE is large and the storage cost is high. With the QR policy, if the retailer ignores the RE that factually exists in the customers' minds, she would set lower prices, place fewer initial order quantity, and lose much profit, especially when she sells luxury products or the customers' purchasing behaviors are strongly affected by RE.

Maximizing middlemen’s profit through a two-stage ordering strategy

In the era of e-commerce, middlemen serve as distributors that purchase wholesale products from suppliers and sell them to retailers. Middlemen have additional functions such as facilitating import and export, interacting with supply chain participants, playing a crucial role in connecting production to customer demand, and coordinating a supplier-middleman-retailer three-level supply chain. This study proposes a two-stage ordering strategy for the middleman to earn higher profits, compared to a single-stage ordering strategy, in a three-level supply chain. We introduce a heuristic solution methodology to find the optimal order quantity of multiple products for both the initial ordering and the follow-up ordering period that maximizes the middleman’s profit. Furthermore, we examine the influence of diverse costs including sourcing, stockout, and ordering costs, as well as minimum order quantity contract and demand variance on the middleman’s order quantity and profits. We found that these costs do not affect the total order quantity. However, they strongly affect the split between the initial and follow-up order quantities. In two-stage ordering system, a higher demand variance does not lead to significant profit reduction for middlemen. Our study provides an approach of using a two-stage ordering strategy for middlemen to increase their profits and mitigate the price and demand risks.

Contract coordination of emergency supply chain with government participation considering risk aversion of participants

For governments and nonprofit organizations such as the Red Cross, charity federation, through the contract form emergency relief materials reserve not for profit, but to cope with the future the possibility of natural disasters and public health events, the occurrence of natural disasters and public health events has great uncertainty, which makes the demand for emergency relief supplies have great randomness. On the basis of predecessors’ research, according to the use of options in the theory of supply chain coordination, to build the mathematical model based on option contract, research shows that option contracts can be achieved under the conditional value at risk of emergency relief supply chain coordination, in order to improve the effectiveness of emergency relief supply chain, with the increase of Co option purchase price, the government will increase by option order quantity q**, Q** way to reduce the initial order quantity q reduce material procurement cost; When the option purchase price Co is fixed, the supplier’s risk aversion increases with the decrease of the risk preference coefficient. In this case, the government, as the purchaser, needs to provide a higher option strike price Ce to encourage the supplier to produce according to the optimal output of the supply chain system.

Optimal order quantity in the presence of strategic customers

We consider a monopolistic retailer of a seasonal product who faces random demand of strategic customers. The selling season is segmented into two periods, a normal selling period and a sales or discounted price period. The retailer preannounces the total sales quantity and the prices offered in these periods. Customers have identical product valuation in the normal selling period. However, a customer’s valuation of the product in the sales period is his private information and is assumed to be randomly distributed. A strategic customer decides to either buy in the normal selling period or wait for the sales period by comparing his expected utility in the respective periods. In a market of such strategic customers, a retailer faces the problem of determining his optimal order quantity. Hence, in this research we consider a two-stage decision making process; in the first stage, the retailer decides the initial order quantity and in the second stage strategic customers decide to either buy during the normal selling period or wait for the sales period. The focus of this work is to determine the order quantity of the retailer which maximizes his expected profit in a monopoly market of such decision making strategic customers. We determine the optimal order quantity of the retailer given these optimal decisions of strategic customers by extending the work of Song et al. (Prod Oper Manag 28(5):1305–1319, 2019). Numerical illustrations and parametric analysis are performed to get insights about the developed model.

Modelling the procurement process and production disruption of a multilayer cruise supply chain

ABSTRACT The cruise service supply chain is integrated with cruise lines and cruise ship service suppliers to provide the seamless transition and to enhance the best possible customer experiences. Due to the short resupply window for the cruise ship and possible conflicts of self-interests with suppliers, it is crucial for cruise lines to establish the long-term reliable relationships with service providers. However, disruptions caused by weather issues or inaccurate estimations of onboard consumption are rather common. We study a cruise supply chain with customized contingent plans to investigate how effective incentive mechanisms work to create a win-win situation. Game theory is applied to model a cruise supply chain with the consideration of possible adverse selection and moral hazard. Customized incentive mechanisms are further developed for various suppliers with unique industry features. Results show that initial order quantity of onboard supplies only depends on the reliability of high-flexible suppliers and onboard consumption patterns. If the natural disasters affect the reliability of highly flexible suppliers, the cruise line could increase the wholesale price to create a competitive local market. Seasonal contracts are highly recommended to cruise lines with the consideration of various supply categories.

Order and exit decisions under non-increasing price curves for products with short life cycles

We consider a supplier selling a product with a relatively short life cycle and following a non-increasing price curve. Because of the short cycle, there is a single procurement opportunity at the beginning of the cycle. The objective of the supplier is to determine the initial order quantity and the time to remove the product from the market in order to maximize her profits. We study this problem in a continuous-time framework where the demand is modeled with a non-homogeneous Poisson process having a general intensity function and the pricing strategy is given by an arbitrary non-increasing function. We give a rigorous mathematical analysis for the problem and show how it can be solved in two stages. We also consider the special case with piecewise constant intensity and price functions. For this case, we show that the optimal exit time is included in the set of break points of these functions. This brings a fast method to obtain the optimal solution for this special case.

Multiperiod Production and Ordering Policies for a Retailer-Led Supply Chain through Option Contracts

This paper formulates two groups of multiperiod production and ordering models with call and bidirectional option contracts for a two-party supply chain consisting of one followed supplier and one dominant retailer, respectively. Based on dynamic programming theory, we characterize the optimal policy structures for two partners in each period. We also provide an approximation for the corresponding policy parameters evaluation in two cases. Then, we investigate the impacts of different option contracts and the demand risk on the decisions and performances of two members. Our results suggest that, whether concerning call or bidirectional option contracts, the optimal policies for two members always follow a base stock type. When the price parameters are the same for different option contracts, the service levels of both the system and the retailer are higher with call option contracts than with bidirectional ones, whereas the retailer’s inventory risk is lower with bidirectional option contracts than with call ones. Under the same conditions stated above, call option contracts can always benefit the supplier, but not the retailer. Owing to the retailer’s dominant position, call option contracts are better choice for the supply chain if the option (exercise) price is low (high), while bidirectional option contracts are more suitable choice for the supply chain if the option (exercise) price is high (low). In addition, an increase in the demand risk would prompt the supplier to increase his production quantity and the retailer to reduce the initial firm order quantity, either with call or bidirectional option contracts.

Pricing and order decisions with option contracts in the presence of customer returns

This paper develops a newsvendor model to examine the impact of customer returns on a firm's pricing and order decisions, in a case where the firm faces price-dependent stochastic demand and has the option of purchasing option contracts. The firm needs to decide the optimal initial order quantity, option order quantity, and retail price simultaneously. The firm's joint optimal decisions are derived for both single- and multi-periods. We examine the impact of two typical forms of customer returns: proportional to product sold, and increasing with selling price. We demonstrate that when customer returns increase with products sold, the firm will set a higher price and reduce both initial order quantity and option order quantity through the wholesale price contract and option contract, respectively, for the single-period problem. In the multi-period problem, when customer returns increase with products sold, the impact of customer returns depends strongly on the variation in product purchase costs (order costs and purchase costs of options) in each period. When customer returns increase with selling price, however, the firm will cut its price, and initially order more products with fewer options for both the single- and multi-period problems. Furthermore, numerical examples confirm that the presence of customer returns results in a significant decrease in the firm's profit. Option contract can be a tool to mitigate the negative impact of customer returns as with the option contract, the more the customer returns, the more the firm is motivated to provide a returns policy.

Call, put and bidirectional option contracts in agricultural supply chains with sales effort

This paper develops option contracts in a supplier-retailer agricultural supply chain where the market demand depends on sales effort. First, we examine a benchmark case of integrated supply chain with the loss rate. Second, we introduce three coordinating option contracts led by the supplier to reduce the retailer's risk, where the call option contract can reduce the shortage risk, the put option contract can reduce the inventory risk and the bidirectional option contract can reduce the bilateral risk. We find that both the optimal initial order quantity and the optimal option quantity increase with the sales effort and the option price will balance the influence of the loss rate on supply chain coordination. Furthermore, the bidirectional option price is the highest while its option quantity is the least, and the put option initial order quantity is the highest. Third, we also consider an option contract led by the retailer to reduce the supplier's wholesale risk. Among the above four option contracts, we find that the option quantity led by the retailer is the highest. Finally, the numerical examples present the impact of the parameters on the optimal decisions, and provide practical managerial insights to reduce the different risk in the agricultural supply chain.

Valuing quantity flexibility under supply chain disintermediation risk

We consider a supply chain with one supplier and one retailer in which the parties develop a quantity flexibility contract to specify the conditions of procurement activities. The contract allows the retailer to adjust the initial order quantity after the partial or full resolution of demand uncertainty, which helps the retailer reduce supply–demand mismatches. We use the multiplicative martingale model of forecast evolution to analyze the impact of lead-time reduction on the value of quantity flexibility for the retailer. We find that the shorter the lead time, the higher the value of quantity flexibility. Quantity flexibility may, however, also cause supply chain disintermediation problems for the retailer, such as the supplier bypassing the retailer and selling its products directly to end customers. We incorporate the “contracts as reference points” theory into our quantity flexibility contract model to capture the impact of supply chain disintermediation on the retailer's profit. This approach allows us to analyze the trade-off between decreasing supply–demand mismatches and increasing supply chain disintermediation problems. We show that the impact of lead-time reduction on decreasing the disintermediation risk highly depends on the critical fractile. We also find that the supplier's cost structure has a significant effect on the trade-off. When the supplier's initial investment cost is relatively low, the disintermediation problems become less important.

An EOQ model for deteriorating items with inventory dependent demand and initial order quantity dependent deterioration

This paper deals with an economic order quantity (EOQ) model for a deteriorating item with initial order quantity demand and inventory dependent deterioration under delay in payment scheme. Profit is obtained at different intervals of delay period and maximised. Numerical examples for different delay periods are given and percentage of profit is obtained. Sensitivity analysis of the example having maximum profit is carried out.

An EOQ model for deteriorating items with inventory dependent demand and initial order quantity dependent deterioration

This paper deals with an economic order quantity (EOQ) model for a deteriorating item with initial order quantity demand and inventory dependent deterioration under delay in payment scheme. Profit is obtained at different intervals of delay period and maximised. Numerical examples for different delay periods are given and percentage of profit is obtained. Sensitivity analysis of the example having maximum profit is carried out.

Inventory and Shipment Policies for the Online Movie DVD Rental Industry

The online movie rental industry in the United States has grown at a rapid pace during the past decade. Netflix and Blockbuster are two prime examples of companies that operate in this arena, each with a large subscriber base. These two companies employ two standard methods for movie delivery: streaming and DVD-by-mail services. Although the industry is clearly undergoing a transition into streaming service, a substantial fraction of subscribers continue to prefer the more traditional DVD-by-mail service. We will study the problem of how to efficiently manage DVD-by-mail service. An essential task in solving our problem is a proper modeling of subscriber demand. We will therefore first develop a demand formulation based on data from Blockbuster. This formulation is then used to construct a nonlinear mathematical program for making the following decisions: (i) the initial order quantity of a new movie (DVD) title and (ii) the shipment size of the title for every period (i.e., day) after its release. By exploiting the structure of this mathematical program, we develop a heuristic algorithm based on a simple shipment policy. Through extensive computational experiments, we demonstrate that our algorithm provides optimal or close to optimal solutions for practically relevant problem instances. The proposed policy and solution are simple, easy to understand, and easily implementable in practice.

Ordering and Pricing Strategies for Fresh Products with Multiple Quality Levels Considering Consumer Utility

In this paper, considering a scenario in which there are two quality levels of fresh products and introduction of consumer utility function, we studied the optimal ordering and pricing strategies under certain quantity. Our results showed that, facing the two quality levels of fresh products, retailers would not benefit from sales of lower quality of fresh products with the deterministic demand. In the pursuit of profit maximization, the initial order quantity is smaller than the potential demand for market.

Supply Chain Coordination in 2-Stage-Ordering-Production System with Update of Demand Information

It is necessary for a retailer to improve responsiveness to uncertain customer demand in product sales. In order to solve this problem, this paper discusses an optimal operation for a 2-stage-ordering-production system consisting of a retailer and a manufacturer. First, based on the demand information estimated at first order time <TEX>$t_1$</TEX>, the retailer determines the optimal initial order quantity <TEX>$Q^*_1$</TEX>, the optimal advertising cost <TEX>$a^*_1$</TEX> and the optimal retail price <TEX>$p^*_1$</TEX> of a single product at <TEX>$t_1$</TEX>, and then the manufacturer produces <TEX>$Q^*_1$</TEX>. Next, the retailer updates the demand information at second order time <TEX>$t_2$</TEX>. If the retailer finds that <TEX>$Q^*_1$</TEX> dissatisfies the demand indicated by the demand information updated at <TEX>$t_2$</TEX>, the retailer determines the optimal second order quantity <TEX>$Q^*_2$</TEX> under <TEX>$Q^*_1$</TEX> and adjusts optimally the advertising cost and the retail price to <TEX>$a^*_2$</TEX> and <TEX>$p^*_2$</TEX> at <TEX>$t_2$</TEX>. Here, decision-making approaches for two situations are made-a decentralized supply chain (DSC) whose objective is to maximize the retailer's profit and an integrated supply chain (ISC) whose objective is to maximize the whole system's profit. In the numerical analysis, the results of the optimal decisions under DSC are compared with those under ISC. In addition, supply chain coordination is discussed to adjust the unit wholesale price at each order time as Nash Bargaining solutions.

Dynamic bi-product bundle pricing problem

This paper addresses bundle pricing problem of two products in a stochastic environment so as to maximize net profit of a retailer. In the considered problem, it is assumed that customers are received upon a Poisson distribution and their demands follow a bi-variant distribution function. Also, it is assumed that products are sold individually or in the form of a bundle, which are offered from an initial stock of the products. To tackle the problem, a stochastic dynamic program is developed in which optimum values of the initial stock and order quantities of every planning period are determined. Moreover, prices of the individual products and their bundle are optimized. Also, the proposed dynamic program tackles bundling/ unbundling decisions taken in every planning period. A numerical example of a two planning period horizon is considered to validate the proposed model.