Inventory management with random supply and imperfect information: A hidden Markov model

In most of the papers on inventory models operating in a random environment, the state of the environment in each period is assumed to be fully observed with perfect information. However, this assumption is not realistic in most real-life situations and we provide a remedy in this paper by assuming that the environment is only partially observed with imperfect information. We accomplish this by analyzing two formulations of single-item models with periodic-review and random supply in a random environment. In the first one, supply is random due to random capacity of production and random availability of transportation. We show that state-dependent base-stock policy is optimal if the capacity and all costs are observed, while demand and availability are unobserved. In the second model, we consider a model with random availability only with fixed-ordering cost. We show that state-dependent (s,S) policy is optimal if the availability process is observable.     

The uniform distribution as a first practical approach to new product inventory management

It is common sense that the premises usually considered in inventory models have little applicability to new product inventory management. This paper develops a first practical approach to deal with this issue: the solution to the (Q, r) inventory model for uniform demand forecasts and lead-times. Based on the fact that the uniform distribution is defined by two parameters that are easy to estimate—maximum and minimum—this paper shows that such a premise may comprise a helpful and accurate decision support tool for managers until they begin to learn about the distribution characteristics of the demand during the lead-time.     

Replenish-up-to inventory control policy with random replenishment intervals

The multi period inventory problems have been studied under two main assumptions. Continuous review assumption where an order can be made at any time depending on inventory position and periodic review assumption where an order can be initiated only at discrete time epochs. In this study, we analyze a multi period inventory problem that falls under neither of these two assumptions. In the case we consider, there are periodic replenishments but the replenishment intervals are taken to be i.i.d. random variables. This setting represents the real life cases where a supplier visits a retailer with random inter arrival times and the retailer replenishes his inventories based on a replenish-up-to-level inventory control policy. We also assume that only a certain fraction of unmet demand is backordered and the rest of it is lost.In this setting under general distribution between replenishment epochs, we show the concavity of the expected profit function and give the condition that must hold for the optimal replenish-up-to-level. We also present the specific solutions and analysis under two different distributions, namely, uniform and exponential distributions, together with some numerical examples.     

Optimal inventory policy with noninstantaneous receipt under trade credit

In the last two decades, the models for inventory replenishment policies under trade credit have been widely studied by several researchers. However, the extant papers only consider the effects of permissible delay in payments in the inventory systems. In some situations, the supplier also may offer a cash discount to encourage retailer to pay for his purchases quickly. On the other hand, an inventory model with instantaneous receipt is not a common feature in actual practice. For generality, this study develops an inventory model with noninstantaneous receipt under trade credit, in which the supplier provides not only a permissible delay but also a cash discount to the retailer. We then characterize the optimal solution and provide an easy-to-use criterion to find the optimal order strategies. Finally, several numerical examples are presented to illustrate the theoretical results.     

Inter-temporal inventory competition and the effects of capacity constraints

This paper addresses an intertemporal inventory competition between a supplier (a provider, manufacturer) and a retailer engaged in a supply chain. The paper's focus is on the effect of capacity constraints on both parties when demands are seasonal. The paper provides a comparative study of two solution approaches, one is based on supply chain competition and the other is based on system wide optimization. Our results demonstrate that with dynamic inventory competition, the retailer reduces inventory costs by reducing the response period to higher demands while increasing the supply requests compared to the system-wide optimal approach. As a result, the supplier's inventory costs increase. An example illustrating these particular facets of the problem and its application is presented and discussed in light of the supplier and the retailer coordinating policies.     

Evaluating the robustness of lead time demand models

This paper examines the robustness of lead time demand models for the continuous review (r, Q) inventory policy. A number of classic distributions, (e.g. normal, lognormal, gamma, Poisson and negative binomial) as well as distribution selection rules are examined under a wide variety of demand conditions. First, the models are compared to each other by assuming a known demand process and evaluating the errors associated with using a different model. Then, the models are examined using a large sample of simulated demand conditions. Approximation results of inventory performance measures—ready rate, expected number of backorders and on-hand inventory levels are reported. Results indicate that distribution selection rules have great potential for modeling the lead time demand.     

Optimal economic ordering policy with deteriorating items under different supplier trade credits for finite horizon case

This paper develops and solves a general finite horizon trade credit economic ordering policy for an inventory model with deteriorating items under inflation and time value of money when shortages are not allowed. The time horizon is divided into different cycles each of which has its own demand rate and its own trade credit period offered from the supplier to his retailer so that the retailer should pay his supplier before or after the end of the permissible trade credit of that cycle. Up to the end of the trade credit of a cycle, the retailer is free of charge, but he is charged on an interest for those items not being sold before this end. The retailer can also earn the interest of the money from the generated sales revenue in any cycle by depositing such revenue into an interest bearing account. The objective of the retailer is then to minimize his net total relevant costs. A closed form of this net total cost is derived and the resulting model is solved. Then rigorous mathematical methods are used to show that, under some seemingly possible conditions, there exist a unique vector of the relevant decision variables that solve the underlying inventory system. A numerical example which shows the applicability of the theoretical results is given.     

A perishable inventory model with Markovian renewal demands

In the inventory model, people usually assume that the inter-demand time is independently identical distributed which may not be true in reality. Here we study an (s,S) continuous review model for items with an exponential random lifetime and a general Markovian renewal demand process. By constructing Markovian renewal equations, we derive the mean and the variance of the reorder cycle time and lead to a simple expression for the total expected long run cost rate. The numerical results illustrate the system behavior and lead to managerial insights into controlling such inventory systems.     

Impact of demand uncertainty on supply chain cooperation of single-period products

Cooperation is an approach of improving competitive advantages of a supply chain. A two-echelon supply chain consisting of a manufacturer and a retailer for a single-period product is studied, and retail-market demand uncertainty is described by coefficient of variation. We develop a cooperation mechanism to address the cooperation and its implementation between the manufacturer and the retailer, two market situations are considered: (i) the wholesale price and the order quantity are decision variables, (ii) the wholesale and the retail prices as well as the order quantity are decision variables. In both market situations, our research shows that: (1) the cooperation mechanism can improve the overall channel profits and the supply chain members’ allocated profits, (2) the described cooperation is conditional on retail-market demand uncertainty: it can be implemented if, and only if, the fluctuation of retail-market demand is relatively small and coefficient of variation of retail-market demand does not exceed an upper bound. Impacts of retail-market demand uncertainty on wholesale price, order quantity and/or retail price have also been investigated through analytical and numerical analyses. Although our research is based on the assumption that the manufacturer dominates the supply chain in the non-cooperative situation, which is not the case for most retailer-driven supply chains, this research is still significant on providing guidelines for practitioners in current China mid-level car market that is similar to situations described in the paper.     

Coordination in retailer-carrier channels for long term planning

We study a retailer-carrier channel for the purpose of long term planning and coordination. Here, the term channel represents the business interaction between the retailer and the carrier. The retailer sells a particular item with price-dependent demand, whereas the carrier is responsible for transporting the item to the retailer's site. We characterize the profit functions of each channel member as well as the total channel profit. We consider two specific channel structures: (i) the centralized channel and (ii) the decentralized channel. Under the first channel structure, the goal is to set the retail price so as to maximize the total channel profit. Under the latter, the carrier and the retailer choose their own policy parameters, i.e., the freight rate for the carrier and the retail price for the retailer, so as to maximize their individual profits. We model the decentralized channel as a Stackelberg Game and propose a coordination mechanism between the retailer and the carrier in which the retailer signals a price multiplier to the carrier. We illustrate that this mechanism could provide win-win solutions for both parties and present analytical and numerical results on the efficiency of channel coordination. We demonstrate that coordination in retailer-carrier channels can be as promising as supplier-retailer channels. We also discuss the effects of retailer-carrier coordination on inventory levels.     

Introduction to design and analysis of production systems

In a two-party VMI channel, the vendor operates the basic stocking and delivery functions and makes inventory replenishment decisions while the retailer is responsible for customer acquisition and in-store services. This paper focuses on such retail channel and proposes an analytical model for the partners in supply channel to determine the inventory policy with the objective of optimizing system net profit. The model explicitly incorporates issues from both the vendor and the retailer in order to derive a policy for mutual benefits. To illustrate and obtain insights from the proposed solution procedure, we devise a set of numerical analyses based on various scenarios. Factors such as shelf-space-dependent demand, shelf-space capacity, demand pattern, logistics characteristics, and disparity between holding costs of the warehouse and the retail store are also investigated.     

Inventory decisions for substitutable products with stock-dependent demand

We study a retailer’s inventory policy for two products. The products are substitutable and have inventory dependent demand, so a higher inventory level of a product increases its sales. We model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single-period, stochastic demand setting. We provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis. We also consider two heuristic solutions that separately account for either demand stimulation or product substitution. Our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits. The profit benefits are lessened under certain circumstances, such as when the two products have similar critical fractile values, suggesting that in such instances the heuristics may be used effectively.     

Determination of an order-up-to policy in the stochastic economic lot scheduling model

We consider a production–inventory problem with compound renewal item demand. The model consists of stockpoints, one for each item, controlled according to (R,S)-policies and one machine which replenishes them. The replenishment orders are produced with a fixed rate on the machine with significant setup times and costs, which are stochastic and sequence dependent. The time between the release and the production of the replenishment order is called the waiting time. We develop analytical approximations for the first two moments of this waiting time, the order-up-to levels and the average physical inventory levels for all stockpoints, given the target fill rates. These analytical approximations allows for a quick evaluation of the waiting time which is important when optimization of the system is considered.     

Retailer policy, uncertainty reduction, and supply chain performance

We investigate how the retailer’s inventory policy affects the total cost of a serial supply chain. When the retailer uses the locally optimal (s,S) policy, there is randomness in order time and order quantity to the supplier whereas the supplier sees randomness only in order quantity for the suboptimal (R,T) policy and only in order time for another suboptimal (Q,r) policy. Using an extensive computational study, we find that the suboptimal policies perform better from the total supply chain perspective. The benefit of policy changes is magnified when the retailer costs are low, when the supplier costs are high, and when there is information sharing.     

A production/remanufacture model with returns’ subassemblies managed differently

This paper considers a production-remanufacturing inventory model for a single product, where constant demand is satisfied from the inventory of newly produced and remanufactured items. Although the available models in the literature imply that collected used units (or returns) are disassembled for recovery purposes, these models really do not treat them as such. Contrary, the returns are assumed to be recovered as whole units, perhaps, for simplicity. This assumption may not capture the benefits reaped from product recovery programs. This paper addresses this limitation in the literature and assumes that each unit of a used product is collected and disassembled into components, where these components are sorted into subassemblies, which are fed back into the production-remanufacturing process. The returned subassemblies are remanufactured and reassembled to represent a second source of as-good-as-new units of the end-product. For this multi-component inventory problem, the question that needs to be answered is whether, or not, extreme strategies of either pure remanufacturing or pure production are more economical than a mixed strategy (one that combines both strategies). A mathematical model is developed that accounts for the inventories of subassemblies. The results suggested that not accounting for the disassembled components of a product leads to inappropriate inventory decisions that are not environmentally sound.     

Integer-ratio policies for distribution/inventory systems

We study a multistage distribution/inventory system with a central warehouse and N retailers. Customer demand arrives at each retailer at a constant rate. The retailers replenish their inventories from the warehouse, which in turn orders from an outside supplier. It is assumed that shortages are not allowed and lead times are negligible. The goal is to determine policies which minimize the overall cost in the system, that is, the sum of the costs at each facility consisting of a fixed charge per order and a holding unit cost. We propose a heuristic procedure to compute near-optimal policies. Computational results on several randomly generated problems are reported.     

Inventory performance under pack size constraints and spatially-correlated demand

Motivated by a problem facing a large retailer, we consider the impact of pack size on the performance of a periodic review inventory system in the presence of spatial (i.e., between retailers) correlation of demand—which we model using an equicorrelated multivariate Poisson distribution. Employing simulation, we utilise a full factorial experiment to provide support for decisions on product and supplier selection, and whether or not packs should be split during distribution. We consider variables such as pack size, correlation, and the number of branches, and discuss how they and their interactions impact performance metrics such as inventory and shortage levels and the bullwhip effect.     

An investigation of setup instability in non-stationary stochastic inventory systems

In stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so-called system nervousness. In this paper, we provide the grounds for measuring system nervousness in non-stationary demand environments, and gauge the stability and the cost performances of (R,S) and (s,S) inventory policies. Our results reveal that, both the stability and the cost performance of inventory policies are affected by the demand pattern as well as the cost parameters, and the (R,S) policy has the potential to replace the cost-optimal (s,S) policy for systems with limited flexibility.     

Consolidating distribution centers can reduce lost sales

In many industries, products are sold out of inventory. When inventory shortages are possible, expected product sales will fall short of expected product demand. We find that this shortfall is proportional to the standard deviation of demand. As we show, this implies that consolidating retailer units – which leads to a lower standard deviation for the aggregate demand – can increase sales.     

Inventory inaccuracies in the wholesale supply chain

The inventory level shown in the Information System contrary to popular belief and assumptions in most academic papers and in spite of the considerable amounts invested in information technology, is often inaccurate. The inventory inaccuracy occurs when the inventory shown in the Information System is not in agreement with the actually available inventory. In this paper, we first describe the major factors generating inventory inaccuracy. Then, we provide situations permitting to manage an inventory system subject to errors. We provide a general framework permitting to model the inventory inaccuracy issue. In particular, we link the inaccuracy issue with the well known random yield problem. The shown link permits us to derive the optimal ordering policy of an inventory framework where demand satisfaction is done based on the inventory records (which are subject to inaccuracies). We also propose an analysis permitting to show the added value of an advanced identification system such as the RFID technology.