Optimal process control policies under a time-varying cost structure

Quality experts have recognized two types of quality costs resulting from failure of control; namely, internal and external failure costs of control. Explicitly considering the difference between internal and external failure costs in designing statistical process control procedures is especially important in today’s business environment because (1) inventory holding time is strategically kept very short because of the just-in-time philosophy, and (2) product values decrease at a very fast rate over time because of advances in technology and keen competition. In this paper, we develop a process control model under a time-varying cost structure, based on internal and external failure costs. Using the model, we also study the process control policies when the value of the product may decrease over time. We consider two forms of product perishability. The first is an exponential product value drop, and the second is a fixed life product life.     

Cost Comparisons for Out-of-Phase Inventory Models

Inventory costs for a fixed time period have traditionally been determined by allocating total costs per cycle uniformly throughout that cycle as well as any partial cycles. This procedure for cost allocation has led to the solution of numerous inventory problems, most notable of which is the anticipated price-increase model. When comparing two out-of-phase inventory models, if costs are accounted for when they occur over a fixed planning horizon, inventory policies should be changed to reflect the impact of this different cost-allocation procedure. For the anticipated price-increase model, the ‘optimal’ order quantity as well as the implied savings in inventory costs will be different when cost models are developed based on these different cost-allocation methods. If the objective is to maximize over a fixed planning horizon the actual savings in inventory costs as they occur, the cost models presented here should be used.     

Myopic control of stochastic inventories with intermittent updates: continuous <Emphasis Type="Italic">versus</Emphasis> periodic replenishment

A manufacturer who is responsible for supplying a retailer with a single product is considered. The retailer sells the product in response to stochastic demand and provides the manufacturer with periodic updates about his inventories. Replenishing the retailer's inventory under two myopic base-stock policies is addressed. These policies, referred to as vendor managed inventory, represent a relatively new approach to allocating responsibility in the replenishment process. Specifically, the manufacturer, who is responsible for the retailer's inventories, can replenish them either continuously at any point in time or periodically, at one point in time for each period. The myopic replenishment policies that are considered are of a base-stock type. It is shown that the selected policies become optimal as the number of review periods tends to infinity. Furthermore, the two replenishment alternatives are compared in terms of both base-stock levels and expected costs, including those for inventory holding/shortage and transportation costs. Although continuous rather than periodic replenishment is evidently more expensive in terms of transportation costs, it is shown that even when the transportation cost constitutes more than 55% of the total average cost, it may still be preferable to replenish continuously rather than periodically.     

The impact of product recall on advertising decisions and firm profit while envisioning crisis or being hazard myopic

The occurrence of a product recall can have a disastrous effect on the firm responsible for the recall. Any major recall by a firm can negatively affect the goodwill of the firm. Consequently, the firm incurs a substantial indirect cost due to decline in sales and loss in profit. Moreover, a competitor’s opportunistic reaction can intensify the recalling firm’s damages. Strategic use of advertising recovers lost goodwill and mitigates the damages made by a product recall. In this paper, using a goodwill based model under a differential game framework, we analyze the equilibrium strategies of two competing manufacturers when either one firm or both can issue a product recall at a random time, and investigate (i) the firms’ equilibrium advertising strategies (ii) analyze the impact of the recall on a firm’s profit (iii) introduce and investigate the effect of “hazard myopia” (a firm’s inability to foresee the crisis likelihood) on a firm’s advertising decisions and profit. Our study finds that the equilibrium advertising strategies of competing firms depend on the impact and likelihood of the recall. Notably, we find that when both the firms are focal firms without the prior knowledge of who will recall first in a planning horizon, adjusting optimal advertising at an appropriate time is essential. Surprisingly, a product-recall with a minor impact can increase the focal firm’s long-term expected profit. On the other hand, hazard myopia can be profitable if the long-term effect of the recall is small. Our findings suggest that advertising levels of firms should differ in pre-recall and post-recall regimes depending on the impact and likelihood of the recall.     

Full-line or specialization strategy? The negative effect of product variety on product line strategy

This paper studies the product line decisions of firms under two consumer segments differing in their quality-sensitivity. We focus on a negative impact of the product variety on the consumers’ motivation to purchase, while each product is horizontally differentiated. In the presence of this impact and high fixed costs relative to variable costs, it is shown that when a highly quality-sensitive segment exists, it is always advantageous for the monopoly to specialize in only one product serving this segment. However, the appearance of a competitor can drastically change the product line in the market. Under the duopolistic setting where two firms sequentially determine their product lines, we show that the leader gains a better financial result by offering its product to the low segment for many cases, including the case where no product is offered to the high segment by either of the firms who are in equilibrium. Furthermore, we obtain another interesting result that indicates that the follower’s profit can exceed the leader’s profit when the quality-sensitivities between the two consumer segments are sufficiently different, even though the two firms are symmetric except for the order of their product offerings.     

Analysis of a dual-sourcing service provision game with symmetric and asymmetric vendors

This paper models a service provision game between two vendors under symmetric and asymmetric cost structures, who compete in first-period service quality levels with each other, with the aim of winning the larger share of the buyer’s fixed reward in the second period. This game differs from the previous studies in that the buyer maintains dual sourcing over two periods and thus has different characteristics. We show that this service provision game has distinct mixed-strategy equilibria with the vendors under symmetric and asymmetric cost structures. We find that the larger the winner’s share in the second period, the higher the vendors’ first-period service quality levels. However, increasing the winner’s share in the second period does not necessarily benefit the vendor with the lower marginal cost, but surely hurts the equilibrium profit of the vendor with the higher marginal cost.     

Autonomous and induced production learning under price and quality competition

Recent empirical studies indicate that improvements in product conformance quality exhibit learning-by-doing patterns. We address quality improvement in a competitive duopoly market for partially substitutable products characterized by levels of quality that are not necessarily identical. The products’ quality is described with a hazard rate that can be improved both by accumulating production experience (autonomous learning) and quality improvement efforts (induced learning). Given that defective items are fully reimbursable and the demands exhibit increasing returns to scale, we derive Nash equilibrium pricing and induced learning effort dynamic policies. We show that when the effectiveness of autonomous learning prevails over the effectiveness of efforts in induced learning, equilibrium prices gradually grow over time; the trend is quite the opposite when autonomous learning is less effective than induced learning.     

Optimal pricing and donation policy for fresh goods

This paper studies a socially responsible food-retailer’s operational planning problem for a continuously deteriorating inventory over two periods with the consideration of donation and quality-sensitive customers. Each year, millions of tonnes of food are wasted causing economic, environmental, and social misfortunes, while at the same time millions are undernourished. Besides expired items, edible foods are often deliberately disposed of to attract quality-sensitive consumers. We address this issue by presenting an optimization model that incorporates a retailer’s corporate social responsibility act, in the form of charitable donations, and makes use of the internet of things (IoT)-enabled condition tracking technologies to accurately estimate the effective (true) quality of the goods and its impacts on consumer demand. We formulate a quality-dependent newsvendor problem (QDNP) to determine the stocking quantity and the regular price of the goods at the beginning of the selling season, and the second-period price and donation policy at the end of the first period. The optimal donation policy at the end of the first period depends on the quality (time to expiration), on-hand inventory, and donation reward. Moreover, for a given inventory level, expected food waste is always greater in the absence of donations. QDNP outperforms the no-donation model, particularly when the uncertainty is high and/or the length of the second period is short. Interestingly, the two models react to an increase in uncertainty oppositely: QDNP orders more to alleviate future shortages, whereas, no-donation policy orders less to avoid future disposal costs at the end of the selling season.     

Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.     

Impacts of inventory shortage policies on transportation requirements in two-stage distribution systems

This paper investigates the impacts inventory shortage policies have on transportation costs in base-stock distribution systems under uncertain demand. The model proposed demonstrates how backlogging arrangements can serve to decrease the variability of transportation capacity requirements, and hence the magnitude of transportation costs, when compared with policies that expedite demand shortages. The model shows how inventory policy decisions directly impact expected transportation costs and provides a new method for setting stock levels that jointly minimizes inventory and transportation costs. The model and solution method provide insights into the relationship between inventory decisions and transportation costs and can serve to support delivery policy negotiations between a supplier and customer that must choose between expediting and backlogging demand shortages.     

Credit Policy and Inventory Control

Credit policies are shown to be important in the basic economic order quantity inventory model. An economic order quantity model is derived which explicitly considers possible credit periods allowed by suppliers. This model is shown to be very sensitive to the length of the credit period, and to the relationship between the credit period and inventory level. It is also shown to be more sensitive to estimates of demand for inventory items and less sensitive to order costs than the basic economic order quantity model. A practical example illustrates this sensitivity, shows how inventory costs may be considerably reduced by taking the existence of a credit period into account, and demonstrates the implications for inventory and credit policies.     

Supply chain coordination for newsvendor-type products with two ordering opportunities and demand information update

This paper studies a coordination issue with two ordering opportunities in a two-echelon supply chain, where one manufacturer sells a single newsvendor-type product through one buyer. The manufacturer does not hold inventory and activates production or order with an infinite capacity and a fixed setup cost in response to the buyer’s order. The buyer places two orderings during the selling period of the product: one happens at the beginning of the period and the other at some specified time within the selling period. The whole selling period is divided into two stages or sub-periods by the buyer’s second order. The stochastic demands in the two sub-periods are assumed to be auto-correlated. The excess demand before the second order is partially backordered, whereas the excess demand at the end of the selling season is utterly lost. Under both the centralized and decentralized settings, we develop the models of how the buyer determines his two-ordering policies. We analyse the existence and uniqueness of the optimal solutions to the models and present the corresponding analytical solutions. Furthermore, we propose an improved revenue-sharing contract that can realize the perfect coordination of the supply chain and study how the revenue-sharing policies affect the supply chain members’ decisions. Finally, we show the superiority of the presented two-ordering strategy through numerical examples.     

不完全信息动态二维价格博弈模型及其分析

单位生产成本为不完全信息条件下,本文首先讨论了两个企业关于具有一定替代性的两种产品价格的动态二维博弈模型,并求得其精练Bayes均衡.然后分析了当两种产品不存在替代关系时,企业对这两种产品价格进行动态博弈的精练Bayes均衡相当于对这两种产品单独进行博弈的精练Bayes均衡的简单组合.     

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.     

Bullwhip effect in a supply chain model with multiple delivery delays

We develop a model of differential equations for a supply chain with delivery time delays between every adjacent firms. Based on the supply chain model, we provide a new perspective of the bullwhip effect and show that the bullwhip effect is intrinsic in supply chains in the sense that the equilibrium state of each firm in the supply chain is a cumulative forward product of the ratios of order fulfillment and placement between adjacent firms toward the end customer demand. We also show that it is the multiple time delays instead of the constant end consumer demand that determine the stability of the equilibrium states. However, the consumer demand has impacts on the stability of the equilibrium states of the supply chain when the end retailer’s inventory decisions are linearly related to the end consumer demand.     

Coordinating pricing and inventory control in a fluctuating environment

This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts： the deterministic component, which is influenced by the price, and the stochastic component （perturbation）. The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog （or surplus） costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of （s,S,p）-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost （these costs are all state-dependent） is convex.     

Competitive Multi-period Pricing for Perishable Products: A Robust Optimization Approach

We study a multi-period oligopolistic market for a single perishable product with fixed inventory. Our goal is to address the competitive aspect of the problem together with demand uncertainty using ideas from robust optimization and variational inequalities. The demand function for each seller has some associated uncertainty and we assume that the sellers would like to adopt a policy that is robust to adverse uncertain circumstances. We believe this is the first paper that uses robust optimization for dynamic pricing under competition. In particular, starting with a given fixed inventory, each seller competes over a multi-period time horizon in the market by setting prices and protection levels for each period at the beginning of the time horizon. Any unsold inventory at the end of the horizon is worthless. The sellers do not have the option of periodically reviewing and replenishing their inventory. We study non-cooperative Nash equilibrium policies for sellers under such a model. This kind of a setup can be used to model pricing of air fares, hotel reservations, bandwidth in communication networks, etc. In this paper we demonstrate our results through some numerical examples.     

Signaling advertising by multiproduct firms

We consider the use of advertising expenses as quality signals in multiproduct firms, extending previous results on single product firms. In our model, a firm introduces sequentially two products whose qualities are positively correlated. We investigate whether there exist information spillovers from the first to the second market. We show that, when correlation is high, the equilibrium in market 2 depends on the quality reputation the firm has gained in market 1. Moreover, if a firm with a high-quality product 1 wants to separate from its low-quality counterpart, it needs to advertise more in this market than if the qualities of the two products are unrelated. This advertising level signals not only high quality in the first market, but also the likely quality of the second product. Thus, advertising in the first market has information spillovers in the second market.     

Technology acquisition with technological progress: effects of expectations,rivalry and uncertainty

We study the effect of expectations regarding technological progress on a firm's technology adoption decision in a duopoly. New generation technologies become available, one in each period, with successive generations representing better and better performance. A game theoretic framework is used involving two identical firms competing in the same market over two periods. It is shown that expectations retard adoption of the first period technology. It is also shown that an asymmetric equilibrium results in higher social welfare, and that more investment does not necessarily mean higher levels of welfare. Uncertainty is shown to have either no effect or a negative effect on the adoption of the current technology when Nash equilibrium holds. However, when subgame perfect equilibrium holds, uncertainty has a more complicated effect and numerical examples show that it may even encourage the adoption of the current technology relative to the deterministic equilibrium.     

Dynamic Control and Optimization of Capital-Constrained Stochastic Inventory Systems

For most firms,especially the small-and medium-sized ones,the operational decisions are affected by their internal capital and ability to obtain external capital.However,the majority of the current studies on dynamic inventory control ignore the firm’s financial status and financing issues completely.An important question that arises is:what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital?In this paper,we review some of the latest developments in this area.After a brief review of single period models,we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth.Two cases are discussed in detail:self-finance and short term finance.In the first case,the firm has to rely on its own capital for all ordering decisions,while in the second,the firm can borrow short term loan from lenders.A detailed characterization of the optimal policy is presented and its managerial insights are discussed.Several possible extensions are suggested.