Revenue Management in Order‐Driven Production Systems

This article investigates the effectiveness of a tactical demand‐capacity management policy to guide operational decisions in order‐driven production systems. The policy is implemented via a heuristic that attempts to maximize revenue by selectively accepting or rejecting customer orders for multiple product classes when demand exceeds capacity constantly over the short term. The performance of the heuristic is evaluated in terms of its ability to generate a higher profit compared to a first‐come‐first‐served (FCFS) policy. The policies are compared over a wide range of conditions characterized by variations in both internal (firm) and external (market) factors. The heuristic, when used with a Whole Lot order‐processing approach, produces higher profit compared to FCFS when profit margins of products are substantially different from each other and demand exceeds capacity by a large amount. In other cases it is better to use the heuristic in conjunction with the Split Lot order‐processing approach.     

Demand switching criteria for multiple products: An inventory cost analysis

In this paper, we consider the problem of demand switching and show how a firm can take advantage of the risk-pooling effect to gain more profit. We examine the case of three products under various switching criteria; a model based on the heuristic approach is developed to determine the switching paths and the corresponding switching rates that yield the optimal profit. A constrained model with limited amount of the switched demand is also developed. In general, the profit increases as a result of higher profit margin or smaller demand variation and correlation. Our result indicates that the profit does not necessarily increase as the switching rate increases; in some cases the profit may even decrease as a result of demand switching. Numerical examples are also included to illustrate the derived models. The developed analytical approach may help practitioners to gain more insight in demand switching and facilitate inventory related decision-making process as well.     

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.     

A hybrid approach to sequencing jobs using heuristic rules and neural networks

A hybrid approach to solve job sequencing problems using heuristic rules and artificial neural networks is proposed. The problem is to find a job sequence for a single machine that minimizes the total weighted tardiness of the jobs. Two different cases are considered: (1) when there are no setups, and (2) when there are sequence-dependent setup times. So far, successful heuristic rules for these cases are: apparent tardiness cost (ATC) rule proposed by Vepsalainen and Morton for the former case, and an extended version of the ATC rule (ATCS) proposed by Lee, Bhaskaran, and Pinedo for the latter. Both approaches utilize some look-ahead parameters for calculating the priority index of each job. As reported by Bhaskaran and Pinedo, the proper value of the look-ahead parameter depends upon certain problem characteristics, such as due-date tightness and due-date range. Thus, an obvious extension of the ATC or the ATCS rule is to adjust the parameter values depending upon the problem characteristics: this is known to be a difficult task. In this paper, we propose an application of a neural network as a tool to ‘predict’ proper values of the look-ahead parameters. Our computational tests show that the proposed hybrid approach outperforms both the ATC rule with a fixed parameter value and the ATCS using the heuristic curve-fitting method.     

The Role of Contract Expirations in Service Parts Management

The majority of after‐sales service providers manage their service parts inventory by focusing on the availability of service parts. This approach, combined with automatic replenishment systems, leads to reactive inventory control policies where base stock levels are adjusted only after a service contract expires. Consequently, service providers often face excess stock of critical service parts that are difficult to dispose due to their specificity. In this study, we address this problem by developing inventory control policies taking into account contract expirations. Our key idea is to reduce the base stock level of the one‐for‐one policy before obsolescence (a full or partial drop in demand rate) occurs and let demand take away excess stock. We refer to this policy as the single‐adjustment policy. We benchmark the single‐adjustment policy with the multiple‐adjustment policy (allowing multiple base stock adjustments) formulated as a dynamic program and verify that for a wide range of instances the single‐adjustment policy is an effective heuristic for the multiple‐adjustment policy. We also compare the single‐adjustment policy with the world‐dependent base stock policy offered by Song and Zipkin (1993) and identify the parameter combinations where both policies yield similar costs. We consider two special cases of the single‐adjustment policy where the base stock level is kept fixed or the base stock adjustment is postponed to the contract expiration time. We find that the initial demand rate, contract expiration time, and size of the drop in demand rate are the three key parameters driving the choice between the single‐adjustment policy and its special cases.     

Bayesian Inventory Management with Potential Change‐Points in Demand

We consider the inventory management problem of a firm reacting to potential change points in demand, which we define as known epochs at which the demand distribution may (or may not) abruptly change. Motivating examples include global news events (e.g., the 9/11 terrorist attacks), local events (e.g., the opening of a nearby attraction), or internal events (e.g., a product redesign). In the periods following such a potential change point in demand, a manager is torn between using a possibly obsolete demand model estimated from a long data history and using a model estimated from a short, recent history. We formulate a Bayesian inventory problem just after a potential change point. We pursue heuristic policies coupled with cost lower bounds, including a new lower bounding approach to non‐perishable Bayesian inventory problems that relaxes the dependence between physical demand and demand signals and that can be applied for a broad set of belief and demand distributions. Our numerical studies reveal small gaps between the costs implied by our heuristic solutions and our lower bounds. We also provide analytical and numerical sensitivity results suggesting that a manager worried about downside profit risk should err on the side of underestimating demand at a potential change point.     

Optimal Control of Replenishment and Substitution in an Inventory System with Nonstationary Batch Demand

We study an inventory system in which a supplier supplies demand using two mutually substitutable products over a selling season of T periods, with a single replenishment opportunity at the beginning of the season. As the season starts, customer orders arrive in each period, for either type of products, following a nonstationary Poisson process with random batch sizes. The substitution model we consider combines the usual supplier‐driven and customer‐driven schemes, in that the supplier may choose to offer substitution, at a discount price, or may choose not to; whereas the customer may or may not accept the substitution when it is offered. The supplier's decisions are the supply and substitution rules in each period throughout the season, and the replenishment quantities for both products at the beginning of the season. With a stochastic dynamic programming formulation, we first prove the concavity of the value function, which facilitates the solution to the optimal replenishment quantities. We then show that the optimal substitution follows a threshold rule, and establish the monotonicity of the thresholds over time and with respect to key cost parameters. We also propose a heuristic exhaustive policy, and illustrate its performance through numerical examples.     

A Single‐Period Assortment Optimization Model

This paper studies a single‐period assortment optimization problem with unequal cost parameters. The consumer choice process is characterized by a Multinomial Logit (MNL) model. When the store traffic is a continuous random variable, we explicitly derive the structure of the optimal assortment. Our approach is to use a comprehensive measure–profit rate to evaluate the profitability of each variant and then determine which product should be offered. We demonstrate that the optimal assortment contains the few items that have the highest profit rate. When the store traffic is discrete, the optimal solution is difficult to obtain. We propose a “profit rate” heuristic, which is inspired by the result for the case of continuous store traffic. In a special case with equal cost parameters and normal demand distribution, the profit rate heuristic is indeed optimal. Using randomly generated data, we test the effectiveness of the heuristic and find that the average percentage error is less than 0.1% and that the hit rate is above 90%. Our research provides managerial insights on assortment planning and accentuates the importance of measuring the profitability of each product when the demand is random and cannibalization among different products exists.     

Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.     

A two-stage stochastic programming approach for identifying optimal postponement strategies in supply chains with uncertain demand

In the course of globalization, applying mass-customization strategies has led to a high diversity of variants in many economic sectors. Thus, customer demands are often less predictable, and handling increasing inventory stocks as well as avoiding shortfalls have become particularly important. All these complexity drivers result in higher supply chain risks. Postponement strategies have been proposed as a suitable approach to address these problems. Although the concept of postponement and its impact on the supply chain are theoretically well discussed, optimally configuring the entire production and distribution activities is still challenging. We present a two-stage stochastic mixed-integer linear programming model, which comprises an integrated production and distribution planning approach, and considers postponement concepts. In comparison to earlier approaches that examine postponement strategies, our model supports the decision maker under demand uncertainty and considers lead times, penalty costs for shortfalls, as well as inventory-keeping decisions over a tactical planning horizon. This allows an integrated investigation of both form and logistics postponement concepts. Moreover, we consider the decision maker’s risk attitude identifying non-dominated profitable and risk-averse strategies. We illustrate the benefits of the model by using a case study from the apparel industry, and present the results of a sensitivity analysis with respect to varying demand uncertainty and demand correlations as well as different preferences regarding risk aversion. Furthermore, we carry out performance and quality benchmarks and compare the results of a standard mixed-integer linear programming solver, a parallel nested Benders approach and a sample average approximation technique.     

The Effect of Distribution Processes on Replenishment Lead Time and Inventory

We investigate the interrelationship of distribution center picking policies and supply chain inventory performance. In particular, we show how the picking sequence in the upstream supply chain link affects the inventory levels of items being replenished to a downstream link for a common “ship‐when‐full” trailer dispatching policy. Perturbing the picking sequence affects items’ inventory levels asymmetrically which causes the aggregate system inventory to vary. We separate the items in replenishment into those units in transit and those awaiting shipment from the upstream distribution step: we call the latter the residual replenishment. We show that the process governing aggregate residual replenishment is Markov and has a stationary distribution that is discrete uniform. Computing the item‐level residual distribution is intractable and so we develop analytical models from which we derive hypotheses for the effectiveness of stable vs. random picking sequences, how item residual replenishment varies with stable picking sequences, and how the aggregate inventory level changes with picking sequence. These suggest a heuristic sequencing algorithm for minimizing inventory, which performs well in simulation tests over a large testbed of parameter sets.     

Characterizing order processes of using inventory policies in supply chains

This study characterizes order processes under (R,nQ) inventory policies. We show first that the order distribution at an installation is stationary when it uses an (R,nQ) control policy, for any arbitrary stationary distribution of customer demand. We then quantify variance amplification and show that variance of orders is never less than the demand variance. Finally, we extend the analysis to the case where the supply chain comprises of one distributor and N retailers serving customers.     

Assortment optimisation problem: A distribution-free approach

Assortment optimisation is a critical decision that is regularly made by retailers. The decision involves a trade-off between offering a larger assortment of products but smaller inventories of each product and offering a smaller number of varieties with more inventory of each product. We propose a robust, distribution-free formulation of the assortment optimisation problem such that the assortment and inventory levels can be jointly optimised without making specific assumptions on the demand distributions of each product. We take a max-min approach to the problem that provides a guaranteed lower bound to the expected profit when only the mean and variance of the demand distribution are known. We propose and test three heuristic algorithms that provide solutions in O(nlog (n)) time and identify two cases where one of the heuristics is guaranteed to return optimal policies. Through numerical studies, we demonstrate that one of the heuristics performs extremely well, with an average optimality gap of 0.07% when simulated under varying conditions. We perform a sensitivity analysis of product and store demand attributes on the performance of the heuristic. Finally, we extend the problem by including maximum cardinality constraints on the assortment size and perform numerical studies to test the performance of the heuristics.     

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.     

Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms

Due to their importance in industry and mathematical complexity, dynamic demand lot-sizing problems are frequently studied. In this article, we consider coordinated lot-size problems, their variants and exact and heuristic solutions approaches. The problem class provides a comprehensive approach for representing single and multiple items, coordinated and uncoordinated setup cost structures, and capacitated and uncapacitated problem characteristics. While efficient solution approaches have eluded researchers, recent advances in problem formulation and algorithms are enabling large-scale problems to be effectively solved. This paper updates a 1988 review of the coordinated lot-sizing problem and complements recent reviews on the single-item lot-sizing problem and the capacitated lot-sizing problem. It provides a state-of-the-art review of the research and future research projections. It is a starting point for anyone conducting research in the deterministic dynamic demand lot-sizing field.     

Impact of investing in quality improvement on (Q,r, L) model involving the imperfect production process

This paper investigates the impact of quality improvement on the modified lot size reorder point models involving variable lead time and partial backorders. The formulated models include the imperfect production process and an investing option of improving the process quality. The objective is simultaneously optimizing the lot size, reorder point, process quality level and lead time. We first assume that the lead time demand follows a normal distribution, then relax this assumption to consider the distribution-free case where only the mean and standard deviation of lead time demand are known. An algorithm procedure of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.     

Sign Restrictions,Structural Vector Autoregressions,and Useful Prior Information

This paper makes the following original contributions to the literature. (i) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions (VARs) that can be used for models that are overidentified, just‐identified, or underidentified. (ii) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n‐variable VAR is confined to the set of values that orthogonalize the population variance–covariance matrix of ordinary least squares residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (iii) We provide analytical characterizations of the informative prior distributions for impulse‐response functions that are implicit in the traditional sign‐restriction approach to VARs, and we note, as a special case of result (ii), that the influence of these priors does not vanish asymptotically. (iv) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just‐identified models. (v) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the U.S. labor market.     

Hedging strategic flexibility in the distribution optimization problem

Motivated by the increasing prevalence of flexibility hedging in corporate-level risk management programs, this paper focuses on the treatment of hedging operational risks in the coordinated replenishment and shipment for distribution systems. The forward option pricing model with the generalized autoregressive conditional heteroskedasticity (GARCH) model for stochastic demand forecasting is adopted for constructing inventory volume flexibility. We therefore propose a hedge-based coordinated inventory replenishment and shipment (HCIRS) methodology for flexibly making inventory hedging and optimal routing assignment decisions as well as coordinating replenishment and shipment policies. The HCIRS methodology provides insight into strategic flexibility adopted for a real-life inventory–distribution problem faced by one of the major East Asia food supply networks and turns out to be very efficient. The proposed HCIRS methodology has provided evidence of better results than the traditional operational techniques for the presented case in this paper.     

On the benefits of operational flexibility in a distribution network with transshipment

We consider a centralized distribution network with multiple retailers who receive replenishment inventory to satisfy customer demand of the local markets. The operational flexibility of the network is defined as the opportunity that one retailer's excess inventory can be transferred to satisfy other retailers’ unmet customer demand due to stock-outs. A general modeling framework is developed to optimize retailers’ order quantities under any possible flexibility level of a stylized two-stage distribution network. We apply the framework to formulate and solve the transshipment problem of a distribution network with three retailers. Six typical flexibility levels are investigated to make the comparison study on the firm's profit performance under three ordering quantity policies: average demand, newsvendor order quantity, and optimal order quantity. We find that the operational flexibility and system optimization are complements to the firm's performance. The ordering policy with newsvendor ordering quantity can perform fairly well with moderate flexibility level when compared with the optimized ordering policy with full flexibility.     

Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs

We develop a new, unified approach to treating continuous‐time stochastic inventory problems with both the average and discounted cost criteria. The approach involves the development of an adjusted discounted cycle cost formula, which has an appealing intuitive interpretation. We show for the first time that an (s, S) policy is optimal in the case of demand having a compound Poisson component as well as a constant rate component. Our demand structure simultaneously generalizes the classical EOQ model and the inventory models with Poisson demand, and we indicate the reasons why this task has been a difficult one. We do not require the surplus cost function to be convex or quasi‐convex as has been assumed in the literature. Finally, we show that the optimal s is unique, but we do not know if optimal S is unique.