Optimal control policies for an inventory system with commitment lead time

We consider a firm which faces a Poisson customer demand and uses a base‐stock policy to replenish its inventories from an outside supplier with a fixed lead time. The firm can use a preorder strategy which allows the customers to place their orders before their actual need. The time from a customer's order until the date a product is actually needed is called commitment lead time. The firm pays a commitment cost which is strictly increasing and convex in the length of the commitment lead time. For such a system, we prove the optimality of bang‐bang and all‐or‐nothing policies for the commitment lead time and the base‐stock policy, respectively. We study the case where the commitment cost is linear in the length of the commitment lead time in detail. We show that there exists a unit commitment cost threshold which dictates the optimality of either a buy‐to‐order (BTO) or a buy‐to‐stock strategy. The unit commitment cost threshold is increasing in the unit holding and backordering costs and decreasing in the mean lead time demand. We determine the conditions on the unit commitment cost for profitability of the BTO strategy and study the case with a compound Poisson customer demand.     

Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions

We study a multi‐item capacitated lot‐sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot‐sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch‐and‐price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Coordination of pricing and inventory control across products

We consider the joint pricing and inventory‐control problem for a retailer who orders, stocks, and sells two products. Cross‐price effects exist between the two products, which means that the demand of each product depends on the prices of both products. We derive the optimal pricing and inventory‐control policy and show that this policy differs from the base‐stock list‐price policy, which is optimal for the one‐product problem. We find that the retailer can significantly improve profits by managing the two products jointly as opposed to independently, especially when the cross‐price demand elasticity is high. We also find that the retailer can considerably improve profits by using dynamic pricing as opposed to static pricing, especially when the demand is nonstationary. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

An exact analysis of a joint production‐inventory problem in two‐echelon inventory systems

We consider a two‐echelon inventory system with a manufacturer operating from a warehouse supplying multiple distribution centers (DCs) that satisfy the demand originating from multiple sources. The manufacturer has a finite production capacity and production times are stochastic. Demand from each source follows an independent Poisson process. We assume that the transportation times between the warehouse and DCs may be positive which may require keeping inventory at both the warehouse and DCs. Inventory in both echelons is managed using the base‐stock policy. Each demand source can procure the product from one or more DCs, each incurring a different fulfilment cost. The objective is to determine the optimal base‐stock levels at the warehouse and DCs as well as the assignment of the demand sources to the DCs so that the sum of inventory holding, backlog, and transportation costs is minimized. We obtain a simple equation for finding the optimal base‐stock level at each DC and an upper bound for the optimal base‐stock level at the warehouse. We demonstrate several managerial insights including that the demand from each source is optimally fulfilled entirely from a single distribution center, and as the system's utilization approaches 1, the optimal base‐stock level increases in the transportation time at a rate equal to the demand rate arriving at the DC. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Resale price maintenance contracts with retailer sales effort: Effect of flexibility and competition

In Resale Price Maintenance (RPM) contracts, the manufacturer specifies the resale price that retailers must charge to consumers. We study the role of using a RPM contract in a market where demand is influenced by retailer sales effort. First, it is well known that RPM alone does not provide incentive for the retailer to use adequate sales effort and some form of quantity fixing may be needed to achieve channel coordination. However, when the market potential of the product is uncertain, RPM with quantity fixing is a rigid contract form. We propose and study a variety of RPM contracts with quantity fixing that offer different forms of flexibility including pricing flexibility and quantity flexibility. Second, we address a long‐time debate in both academia and practice on whether RPM is anti‐competitive in a market when two retailers compete on both price and sales effort. We show that depending on the relative intensity of price competition and sales effort competition, RPM may lead to higher or lower retail prices compared to a two‐part tariff contract, which specifies a wholesale price and a fixed fee. Further, the impact of RPM on price competition and sales effort competition is always opposite to each other. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

To wait or not to wait: Optimal ordering under lead time uncertainty and forecast updating

There has been a dramatic increase over the past decade in the number of firms that source finished product from overseas. Although this has reduced procurement costs, it has increased supply risk; procurement lead times are longer and are often unreliable. In deciding when and how much to order, firms must consider the lead time risk and the demand risk, i.e., the accuracy of their demand forecast. To improve the accuracy of its demand forecast, a firm may update its forecast as the selling season approaches. In this article we consider both forecast updating and lead time uncertainty. We characterize the firm's optimal procurement policy, and we prove that, with multiplicative forecast revisions, the firm's optimal procurement time is independent of the demand forecast evolution but that the optimal procurement quantity is not. This leads to a number of important managerial insights into the firm's planning process. We show that the firm becomes less sensitive to lead time variability as the forecast updating process becomes more efficient. Interestingly, a forecast‐updating firm might procure earlier than a firm with no forecast updating. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Disruption‐management strategies for short life‐cycle products

Supplier diversification, contingent sourcing, and demand switching (whereby a firm shifts customers to a different product if their preferred product is unavailable), are key building blocks of a disruption‐management strategy for firms that sell multiple products over a single season. In this article, we evaluate 12 possible disruption‐management strategies (combinations of the basic building‐block tactics) in the context of a two‐product newsvendor. We investigate the influence of nine attributes of the firm, its supplier(s), and its products on the firs preference for the various strategies. These attributes include supplier reliability, supplier failure correlation, payment responsibility in the event of a supply failure, product contribution margin, product substitutability, demand uncertainties and correlation, and the decision makes risk aversion. Our results show that contingent sourcing is preferred to supplier diversification as the supply risk (failure probability) increases, but diversification is preferred to contingent sourcing as the demand risk (demand uncertainty) increases. We find that demand switching is not effective at managing supply risk if the products are sourced from the same set of suppliers. Demand switching is effective at managing demand risk and so can be preferred to the other tactics if supply risk is low. Risk aversion makes contingent sourcing preferable over a wider set of supply and demand‐risk combinations. We also find a two‐tactic strategy provides almost the same benefit as a three‐tactic strategy for most reasonable supply and demand‐risk combinations. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Dynamic pricing in a dual‐market environment

This article is concerned with the determination of pricing strategies for a firm that in each period of a finite horizon receives replenishment quantities of a single product which it sells in two markets, for example, a long‐distance market and an on‐site market. The key difference between the two markets is that the long‐distance market provides for a one period delay in demand fulfillment. In contrast, on‐site orders must be filled immediately as the customer is at the physical on‐site location. We model the demands in consecutive periods as independent random variables and their distributions depend on the item's price in accordance with two general stochastic demand functions: additive or multiplicative. The firm uses a single pool of inventory to fulfill demands from both markets. We investigate properties of the structure of the dynamic pricing strategy that maximizes the total expected discounted profit over the finite time horizon, under fixed or controlled replenishment conditions. Further, we provide conditions under which one market may be the preferred outlet to sale over the other. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 531–549, 2015     

The impact of operational decisions on the design of salesforce incentives

When facing high levels of overstock inventories, firms often push their salesforce to work harder than usual to attract more demand, and one way to achieve that is to offer attractive incentives. However, most research on the optimal design of salesforce incentives ignores this dependency and assumes that operational decisions of production/inventory management are separable from design of salesforce incentives. We investigate this dependency in the problem of joint salesforce incentive design and inventory/production control. We develop a dynamic Principal‐Agent model with both Moral Hazard and Adverse Selection in which the principal is strategic and risk‐neutral but the agent is myopic and risk‐averse. We find the optimal joint incentive design and inventory control strategy, and demonstrate the impact of operational decisions on the design of a compensation package. The optimal strategy is characterized by a menu of inventory‐dependent salesforce compensation contracts. We show that the optimal compensation package depends highly on the operational decisions; when inventory levels are high, (a) the firm offers a more attractive contract and (b) the contract is effective in inducing the salesforce to work harder than usual. In contrast, when inventory levels are low, the firm can offer a less attractive compensation package, but still expect the salesforce to work hard enough. In addition, we show that although the inventory/production management and the design of salesforce compensation package are highly correlated, information acquisition through contract design allows the firm to implement traditional inventory control policies: a market‐based state‐dependent policy (with a constant base‐stock level when the inventory is low) that makes use of the extracted market condition from the agent is optimal. This work appears to be the first article on operations that addresses the important interplay between inventory/production control and salesforce compensation decisions in a dynamic setting. Our findings shed light on the effective integration of these two significant aspects for the successful operation of a firm. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 320–340, 2014     

Supply contracts in manufacturer‐retailer interactions with manufacturer‐quality and retailer effort‐induced demand

We consider a decentralized distribution channel where demand depends on the manufacturer‐chosen quality of the product and the selling effort chosen by the retailer. The cost of selling effort is private information for the retailer. We consider three different types of supply contracts in this article: price‐only contract where the manufacturer sets a wholesale price; fixed‐fee contract where manufacturer sells at marginal cost but charges a fixed (transfer) fee; and, general franchise contract where manufacturer sets a wholesale price and charges a fixed fee as well. The fixed‐fee and general franchise contracts are referred to as two‐part tariff contracts. For each contract type, we study different contract forms including individual, menu, and pooling contracts. In the analysis of the different types and forms of contracts, we show that the price only contract is dominated by the general franchise menu contract. However, the manufacturer may prefer to offer the fixed‐fee individual contract as compared to the general franchise contract when the retailer's reservation utility and degree of information asymmetry in costs are high. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Revenue sharing contracts in a supply chain with uncontractible actions

We consider a supplier–customer relationship where the customer faces a typical Newsvendor problem of determining perishable capacity to meet uncertain demand. The customer outsources a critical, demand‐enhancing service to an outside supplier, who receives a fixed share of the revenue from the customer. Given such a linear sharing contract, the customer chooses capacity and the service supplier chooses service effort level before demand is realized. We consider the two cases when these decisions are made simultaneously (simultaneous game) or sequentially (sequential game). For each game, we analyze how the equilibrium solutions vary with the parameters of the problem. We show that in the equilibrium, it is possible that either the customer's capacity increases or the service supplier's effort level decreases when the supplier receives a larger share of the revenue. We also show that given the same sharing contract, the sequential game always induces a higher capacity and more effort. For the case of additive effort effect and uniform demand distribution, we consider the customer's problem of designing the optimal contract with or without a fixed payment in the contract, and obtain sensitivity results on how the optimal contract depends on the problem parameters. For the case of fixed payment, it is optimal to allocate more revenue to the supplier to induce more service effort when the profit margin is higher, the cost of effort is lower, effort is more effective in stimulating demand, the variability of demand is smaller or the supplier makes the first move in the sequential game. For the case of no fixed payment, however, it is optimal to allocate more revenue to the supplier when the variability of demand is larger or its mean is smaller. Numerical examples are analyzed to validate the sensitivity results for the case of normal demand distribution and to provide more managerial insights. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Competition under time‐varying demands and dynamic lot sizing costs

We develop a competitive pricing model which combines the complexity of time‐varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. Each firm adopts, at the beginning of the planning horizon, a (single) price to be employed throughout the horizon. On the basis of each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan. We establish the existence of a price equilibrium and associated optimal dynamic lotsizing plans, under mild conditions. We also design efficient procedures to compute the equilibrium prices and dynamic lotsizing plans.© 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

A two‐echelon inventory‐location problem with service considerations

We study the problem of designing a two‐echelon spare parts inventory system consisting of a central plant and a number of service centers each serving a set of customers with stochastic demand. Processing and storage capacities at both levels of facilities are limited. The manufacturing process is modeled as a queuing system at the plant. The goal is to optimize the base‐stock levels at both echelons, the location of service centers, and the allocation of customers to centers simultaneously, subject to service constraints. A mixed integer nonlinear programming model (MINLP) is formulated to minimize the total expected cost of the system. The problem is NP‐hard and a Lagrangian heuristic is proposed. We present computational results and discuss the trade‐off between cost and service. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Resource allocation with lumpy demand: To speed or not to speed?

In the classical EPQ model with continuous and constant demand, holding and setup costs are minimized when the production rate is no larger than the demand rate. However, the situation may change when demand is lumpy. We consider a firm that produces multiple products, each having a unique lumpy demand pattern. The decision involves determining both the lot size for each product and the allocation of resources for production rate improvements among the products. We find that each product's optimal production policy will take on only one of two forms: either continuous production or lot‐for‐lot production. The problem is then formulated as a nonlinear nonsmooth knapsack problem among products determined to be candidates for resource allocation. A heuristic procedure is developed to determine allocation amounts. The procedure decomposes the problem into a mixed integer program and a nonlinear convex resource allocation problem. Numerical tests suggest that the heuristic performs very well on average compared to the optimal solution. Both the model and the heuristic procedure can be extended to allow the company to simultaneously alter both the production rates and the incoming demand lot sizes through quantity discounts. Extensions can also be made to address the case where a single investment increases the production rate of multiple products. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Delivery‐date and capacity management in a decentralized internal market

We study competitive due‐date and capacity management between the marketing and engineering divisions within an engineer‐to‐order (ETO) firm. Marketing interacts directly with the customers and quotes due‐dates for their orders. Engineering is primarily concerned with the efficient utilization of resources and is willing to increase capacity if the cost is compensated. The two divisions share the responsibility for timely delivery of the jobs. We model the interaction between marketing and engineering as a Nash game and investigate the effect of internal competition on the equilibrium decisions. We observe that the internal competition not only degrades the firm's overall profitability but also the serviceability. Finally, we extend our analysis to multiple‐job settings that consider both flexible and inflexible capacity. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Optimal inventory control policy for periodic‐review inventory systems with inventory‐level‐dependent demand

We consider a setting in which inventory plays both promotional and service roles; that is, higher inventories not only improve service levels but also stimulate demand by serving as a promotional tool (e.g., as the result of advertising effect by the enhanced product visibility). Specifically, we study the periodic‐review inventory systems in which the demand in each period is uncertain but increases with the inventory level. We investigate the multiperiod model with normal and expediting orders in each period, that is, any shortage will be met through emergency replenishment. Such a model takes the lost sales model as a special case. For the cases without and with fixed order costs, the optimal inventory replenishment policy is shown to be of the base‐stock type and of the (s,S) type, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Base‐stock policies in capacitated assembly systems: Convexity properties

We study an assembly system with a single finished product managed using an echelon base‐stock or order‐up‐to policy. Some or all operations have capacity constraints. Excess demand is either backordered in every period or lost in every period. We show that the shortage penalty cost over any horizon is jointly convex with respect to the base‐stock levels and capacity levels. When the holding costs are also included in the objective function, we show that the cost function can be written as a sum of a convex function and a concave function. Throughout the article, we discuss algorithmic implications of our results for making optimal inventory and capacity decisions in such systems.© 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Selling to strategic and loss‐averse consumers: Stocking,procurement, and product design policies

Motivated by the presence of loss‐averse decision making behavior in practice, this article considers a supply chain consisting of a firm and strategic consumers who possess an S‐shaped loss‐averse utility function. In the model, consumers decide the purchase timing and the firm chooses the inventory level. We find that the loss‐averse consumers' strategic purchasing behavior is determined by their perceived gain and loss from strategic purchase delay, and the given rationing risk. Thus, the firm that is cognizant of this property tailors its inventory stocking policy based on the consumers' loss‐averse behavior such as their perceived values of gain and loss, and their sensitivity to them. We also demonstrate that the firm's equilibrium inventory stocking policy reflects both the economic logic of the traditional newsvendor inventory model, and the loss‐averse behavior of consumers. The equilibrium order quantity is significantly different from those derived from models that assume that the consumers are risk neutral and homogeneous in their valuations. We show that the firm that ignores strategic consumer's loss‐aversion behavior tends to keep an unnecessarily high inventory level that leads to excessive leftovers. Our numerical experiments further reveal that in some extreme cases the firm that ignores strategic consumer's loss‐aversion behavior generates almost 92% more leftovers than the firm that possesses consumers’ loss‐aversion information and takes it into account when making managerial decisions. To mitigate the consumer's forward‐looking behavior, we propose the adoption of the practice of agile supply chain management, which possesses the following attributes: (i) procuring inventory after observing real‐time demand information, (ii) enhanced design (which maintains the current production mix but improves the product performance to a higher level), and (iii) customized design (which maintains the current performance level but increases the variety of the current production line to meet consumers’ specific demands). We show that such a practice can induce the consumer to make early purchases by increasing their rationing risk, increasing the product value, or diversifying the product line. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 435–453, 2015     

The continuous‐time single‐sourcing problem with capacity expansion opportunities

This paper develops a new model for allocating demand from retailers (or customers) to a set of production/storage facilities. A producer manufactures a product in multiple production facilities, and faces demand from a set of retailers. The objective is to decide which of the production facilities should satisfy each retailer's demand, in order minimize total production, inventory holding, and assignment costs (where the latter may include, for instance, variable production costs and transportation costs). Demand occurs continuously in time at a deterministic rate at each retailer, while each production facility faces fixed‐charge production costs and linear holding costs. We first consider an uncapacitated model, which we generalize to allow for production or storage capacities. We then explore situations with capacity expansion opportunities. Our solution approach employs a column generation procedure, as well as greedy and local improvement heuristic approaches. A broad class of randomly generated test problems demonstrates that these heuristics find high quality solutions for this large‐scale cross‐facility planning problem using a modest amount of computation time. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Analysis of decentralized multi‐product pull systems with lost sales

We study a pull‐type, flexible, multi‐product, and multi‐stage production/inventory system with decentralized two‐card kanban control policies. Each stage involves a processor and two buffers with finite target levels. Production stages, arranged in series, can process several product types one at a time. Transportation of semi‐finished parts from one stage to another is performed in fixed lot sizes. The exact analysis is mathematically intractable even for smaller systems. We present a robust approximation algorithm to model two‐card kanban systems with batch transfers under arbitrary complexity. The algorithm uses phase‐type modeling to find effective processing times and busy period analysis to identify delays among product types in resource contention. Our algorithm reduces the effort required for estimating performance measures by a considerable margin and resolves the state–space explosion problem of analytical approaches. Using this analytical tool, we present new findings for a better understanding of some tactical and operational issues. We show that flow of material in small procurement sizes smoothes flow of information within the system, but also necessitates more frequent shipments between stages, raising the risk of late delivery. Balancing the risk of information delays vis‐à‐vis shipment delays is critical for the success of two‐card kanban systems. Although product variety causes time wasted in setup operations, it also facilitates relatively short production cycles enabling processors to switch from one product type to another more rapidly. The latter point is crucial especially in high‐demand environments. Increasing production line size prevents quick response to customer demand, but it may improve system performance if the vendor lead‐time is long or subject to high variation. Finally, variability in transportation and processing times causes the most damage if it arises at stages closer to the customer. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007