Optimal Sequencing of Unpunctual Patients in High‐Service‐Level Clinics

Even though patients often arrive early and out of turn for scheduled appointments in outpatient clinics, no research has been undertaken to establish whether an available provider should see an early patient right away (preempt) or wait for the patient scheduled next. This problem, which we call the “Wait‐Preempt Dilemma,” is particularly relevant for “high‐service‐level” clinics (such as psychotherapy, chiropractic, acupuncture), where preempting may cause the missing patient to wait for an excessively long time, should she show up soon. Typically, the dilemma is resolved by preemption, where the provider starts serving the patient who has already arrived to avoid staying idle. By contrast, we analytically determine the time intervals where it is optimal to preempt and those where it is optimal to wait, and find that in some cases the provider should in fact stay idle, even in the presence of waiting patients. Our results suggest that the proposed analytical method outperforms the always‐preempt policy in clinics that do not overbook and have service times longer than 30 minutes. In these cases, the analytical method dramatically reduces patient waiting times at the cost of a modest increase in overtime. By contrast, in clinics that overbook or have short service times, the two policies perform similarly, and hence the always‐preempt policy is preferable due to its simplicity. A software application is provided that clinics can readily use to solve the wait‐preempt dilemma.     

Algorithms for storage allocation based on client preferences

We consider a packing problem arising in storage management of Video on Demand (VoD) systems. The system consists of a set of video files (movies) and several servers (disks), each having a limited storage capacity, C, and a limited bandwidth (load capacity), L. The goal in the storage allocation problem is to assign the video files to the servers and the bandwidth to the clients. The induced class-constrained packing problem was studied in the past assuming each client provides a single request for a single movie. This paper considers a more general and realistic model—in which each client ranks all the movies in the system. Specifically, for each client j and movie i, it is known how much client j is willing to pay in order to watch movie i. The goal is to maximize the system’s profit. Alternatively, the client might provide a ranking of the movies and the goal is to maximize the lexicographic profile of the solution.     

An Analysis of Scoring and Buyer‐Determined Procurement Auctions

In procurement auctions, the object for sale is a contract, bidders are suppliers, and the bid taker is a buyer. The suppliers bidding for the contract are usually the current supplier (the incumbent) and a group of potential new suppliers (the entrants). As the buyer has an ongoing relationship with the incumbent, he needs to adjust the bids of the entrants to include non‐price attributes, such as the switching costs. The buyer can run a scoring auction, in which suppliers compete on the adjusted bids or scores, or, he can run a buyer‐determined auction, in which suppliers compete on the price, and the buyer adjusts a certain number of the bids with the non‐price attributes after the auction to determine the winner. Unless the incumbent has a significant cost advantage over the entrants, I find that the scoring auction yields a lower average cost for the buyer, if the non‐price attributes are available. If the non‐price attributes are difficult or expensive to obtain, the buyer could run a buyer‐determined auction adjusting only the lowest price bid.     

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

Joint Inventory and Pricing Coordination with Incomplete Demand Information

In retailing operations, retailers face the challenge of incomplete demand information. We develop a new concept named K‐approximate convexity, which is shown to be a generalization of K‐convexity, to address this challenge. This idea is applied to obtain a base‐stock list‐price policy for the joint inventory and pricing control problem with incomplete demand information and even non‐concave revenue function. A worst‐case performance bound of the policy is established. In a numerical study where demand is driven from real sales data, we find that the average gap between the profits of our proposed policy and the optimal policy is 0.27%, and the maximum gap is 4.6%.     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

Myopic Analysis for Multi‐Echelon Inventory Systems with Batch Ordering and Nonstationary/Time‐Correlated Demands

We provide an exact myopic analysis for an N‐stage serial inventory system with batch ordering, linear ordering costs, and nonstationary demands under a finite planning horizon. We characterize the optimality conditions of the myopic nested batching newsvendor (NBN) policy and the myopic independent batching newsvendor (IBN) policy, which is a single‐stage approximation. We show that echelon reorder levels under the NBN policy are upper bounds of the counterparts under both the optimal policy and the IBN policy. In particular, we find that the IBN policy has bounded deviations from the optimal policy. We further extend our results to systems with martingale model of forecast evolution (MMFE) and advance demand information. Moreover, we provide a recursive computing procedure and optimality conditions for both heuristics which dramatically reduces computational complexity. We also find that the NBN problem under the MMFE faced by one stage has one more dimension for the forecast demand than the one faced by its downstream stage and that the NBN policy is optimal for systems with advance demand information and stationary problem data. Numerical studies demonstrate that the IBN policy outperforms on average the NBN policy over all tested instances when their optimality conditions are violated.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

A Framework for Facilitating Sourcing and Allocation Decisions for Make‐to‐Order Items

This paper provides a fundamental building block to facilitate sourcing and allocation decisions for make‐to‐order items. We specifically address the buyer's vendor selection problem for make‐to‐order items where the goal is to minimize sourcing and purchasing costs in the presence of fixed costs, shared capacity constraints, and volume‐based discounts for bundles of items. The potential suppliers for make‐to‐order items provide quotes in the form of single sealed bids or participate in a dynamic auction involving open bids. A solution to our problem can be used to determine winning bids amongst the single sealed bids or winners at each stage of a dynamic auction. Due to the computational complexity of this problem, we develop a heuristic procedure based on Lagrangian relaxation technique to solve the problem. The computational results show that the procedure is effective under a variety of scenarios. The average gap across 2,250 problem instances is 4.65%.     

Optimal Inventory Control with Retail Pre‐Packs

A pre‐pack is a collection of items used in retail distribution. By grouping multiple units of one or more stock keeping units (SKU), distribution and handling costs can be reduced; however, ordering flexibility at the retail outlet is limited. This paper studies an inventory system at a retail level where both pre‐packs and individual items (at additional handling cost) can be ordered. For a single‐SKU, single‐period problem, we show that the optimal policy is to order into a “band” with as few individual units as possible. For the multi‐period problem with modular demand, the band policy is still optimal, and the steady‐state distribution of the target inventory position possesses a semi‐uniform structure, which greatly facilitates the computation of optimal policies and approximations under general demand. For the multi‐SKU case, the optimal policy has a generalized band structure. Our numerical results show that pre‐pack use is beneficial when facing stable and complementary demands, and substantial handling savings at the distribution center. The cost premium of using simple policies, such as strict base‐stock and batch‐ordering (pre‐packs only), can be substantial for medium parameter ranges.     

Priority Rules for Multi‐Task Due‐Date Scheduling under Varying Processing Costs

We study the scheduling of multiple tasks under varying processing costs and derive a priority rule for optimal scheduling policies. Each task has a due date, and a non‐completion penalty cost is incurred if the task is not completely processed before its due date. We assume that the task arrival process is stochastic and the processing rate is capacitated. Our work is motivated by both traditional and emerging application domains, such as construction industry and freelance consulting industry. We establish the optimality of Shorter Slack time and Longer remaining Processing time (SSLP) principle that determines the priority among active tasks. Based on the derived structural properties, we also propose an effective cost‐balancing heuristic policy and demonstrate the efficacy of the proposed policy through extensive numerical experiments. We believe our results provide operators/managers valuable insights on how to devise effective service scheduling policies under varying costs.     

Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.     

Transparency in Buyer‐Determined Auctions: Should Quality be Private or Public?

We study buyer‐determined procurement auctions where both price and non‐price characteristics of bidders matter for being awarded a contract. Although, in scoring auctions bidders perfectly know how price and non‐price attributes determine the awarding of the contract, this remains uncertain in buyer‐determined auctions where the buyer is free to choose once all bids have been submitted. We analyze the impact of information bidders have with respect to the buyer's awarding decision. As we show theoretically whether it is in the buyer's interest to conceal the impact of non‐price characteristics depends on how important the quality aspects of the procured good are to the buyer: The more important quality aspects are, the more interesting concealment becomes. In a counterfactual analysis using data from a large European procurement platform, we analyze the reduction of non‐price information available to the bidders. Confirming our hypothesis, for auction categories where bidders’ non‐price characteristics strongly influence buyers’ decisions concealment of non‐price information leads to an increase in buyers’ surplus of up to 15% due to higher competitive pressure and lower bids. Conversely, for categories where bidders’ non‐price characteristics are of little importance concealment of non‐price information leads to a decrease in buyers’ surplus of up to 6%.     

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.     

Safety Stock,Excess Capacity or Diversification: Trade‐Offs under Supply and Demand Uncertainty

Firms mitigate uncertainty in demand and supply by carrying safety stock, planning for excess capacity and diversifying supply sources. In this study, we provide a framework to jointly optimize these three levers in a periodic review infinite horizon setting, and in particular we examine how one can reduce inventory and capacity investments through proper diversification strategies. Observing that a modified base‐stock inventory policy is optimal, we find that the capacity‐diversification problem is well behaved and characterize the optimal mix of safety stock, excess capacity and extra number of supply sources. We find that higher supply uncertainty results in higher safety stock, more excess capacity, and higher diversification. But safety stock and diversification are non‐monotonic in demand uncertainty. Our results can be extended to situations in which suppliers are heterogeneous, and can be used to develop effective heuristics.     

Integrality in Stochastic Inventory Models

We study several finite‐horizon, discrete‐time, dynamic, stochastic inventory control models with integer demands: the newsvendor model, its multi‐period extension, and a single‐product, multi‐echelon assembly model. Equivalent linear programs are formulated for the corresponding stochastic dynamic programs, and integrality results are derived based on the total unimodularity of the constraint matrices. Specifically, for all these models, starting with integer inventory levels, we show that there exist optimal policies that are integral. For the most general single‐product, multi‐echelon assembly system model, integrality results are also derived for a practical alternative to stochastic dynamic programming, namely, rolling‐horizon optimization by a similar argument. We also present a different approach to prove integrality results for stochastic inventory models. This new approach is based on a generalization we propose for the one‐dimensional notion of piecewise linearity with integer breakpoints to higher dimensions. The usefulness of this new approach is illustrated by establishing the integrality of both the dynamic programming and rolling‐horizon optimization models of a two‐product capacitated stochastic inventory control system.     

The benefit of receding horizon control: Near-optimal policies for stochastic inventory control

In this paper we address the single-item, single-stocking point, non-stationary stochastic lot-sizing problem under backorder costs. It is well known that the (s, S) policy provides the optimal control for such inventory systems. However the computational difficulties and the nervousness inherent in (s, S) paved the way for the development of various near-optimal inventory control policies. We provide a systematic comparison of these policies and present their expected cost performances. We further show that when these policies are used in a receding horizon framework the cost performances improve considerably and differences among policies become insignificant.     

Hierarchical Screening for Capacity Allocation in Supply Chains: The Role of Distributors

We consider a two‐stage principal–agent screening environment in a decentralized supply chain with retailers, distributors, and a supplier. The retailers possess private information regarding their local market profitabilities. The distributors can partially observe the retailers' profitabilities and are heterogeneous with regard to the precision of that information. The supplier determines the level of production, but knows neither the local market profitabilities nor the precision of the distributors' information. The supplier first allocates finished products to distributors, and the distributors then contract with local retailers with a capacity constraint. We find that due to the distributors' superior information, the quantity distortion on the retailers' side is mitigated, and the upstream information asymmetry subsequently affects the quantity allocation among the downstream retailers. The supplier may not benefit from contracting with the distributors. In addition, no distributor is excluded based on the heterogeneity of the information precision, even though some distributors do not have better information than the supplier. In the numerical examples, we further analyze how the local market heterogeneity and inventory costs affect the capacity allocation, the retailers' payoffs, and the supply chain profits. We document some counter‐intuitive quantity allocation rules that arise from the distributors' information advantage.