We consider a multi-echelon joint inventory-location (MJIL) problem that makes location, order assignment, and inventory decisions simultaneously. The model deals with the distribution of a single ...commodity from a single manufacturer to a set of retailers through a set of sites where distribution centers can be located. The retailers face deterministic demand and hold working inventory. The distribution centers order a single commodity from the manufacturer at regular intervals and distribute the product to the retailers. The distribution centers also hold working inventory representing product that has been ordered from the manufacturer but has not been yet requested by any of the retailers. Lateral supply among the distribution centers is not allowed. The problem is formulated as a nonlinear mixed-integer program, which is shown to be NP-hard. This problem has recently attracted attention, and a number of different solution approaches have been proposed to solve it. In this paper, we present a Lagrangian relaxation-based heuristic that is capable of efficiently solving large-size instances of the problem. A computational study demonstrates that our heuristic solution procedure is efficient and yields optimal or near-optimal solutions.
We introduce a measure of elasticity of stochastic demand, called the elasticity of the lost-sales rate, which offers a unifying perspective on the well-known newsvendor with pricing problem. This ...new concept provides a framework to characterize structural results for coordinated and uncoordinated pricing and inventory strategies. Concavity and submodularity of the profit function, as well as sensitivity properties of the optimal inventory and price policies, are characterized by monotonicity conditions, or bounds, on the elasticity of the lost-sales rate. These elasticity conditions are satisfied by most relevant demand models in the marketing and operations literature. Our results unify and complement previous work on price-setting newsvendor models and provide a new tool for researchers modeling stochastic price-sensitive demand in other contexts.
Lost-sales inventory theory: A review Bijvank, Marco; Vis, Iris F.A.
European journal of operational research,
11/2011, Letnik:
215, Številka:
1
Journal Article
Recenzirano
In classic inventory models it is common to assume that excess demand is backordered. However, studies analyzing customer behavior in practice show that most unfulfilled demand is lost or an ...alternative item/location is looked for in many retail environments. Inventory systems that include this lost-sales characteristic appear to be more difficult to analyze and to solve. Furthermore, lost-sales inventory systems require different replenishment policies to minimize costs compared to backorder systems. In this paper, we classify the models in the literature based on the characteristics of the inventory system and review the proposed replenishment policies. For each classification and type of replenishment policy we discuss the available models and their performance. Furthermore, directions for future research are proposed.
In this paper we experimentally investigate how the allocation of inventory risk in a two-stage supply chain affects channel efficiency and profit distribution. We first evaluate two common wholesale ...price contracts that differ in which party incurs the risk associated with unsold inventory: a push contract in which the retailer incurs the risk and a pull contract in which the supplier incurs the risk. Our experimental results show that a pull contract achieves higher channel efficiency than that of a push contract, and that behavior systematically deviates from the standard theory in three ways: (1) stocking quantities are set too low, (2) wholesale prices are more favorable to the party stocking the inventory, and (3) some contracts are erroneously accepted or rejected. To account for these systematic regularities, we extend the existing theory and structurally estimate a number of behavioral models. The estimates suggest that a combination of loss aversion with errors organizes our data remarkably well. We apply our behavioral model to the advance purchase discount (APD) contract, which combines features of push and pull by allowing both parties to share the inventory risk, in a separate experiment as an out-of-sample test, and we find that it accurately predicts channel efficiency and qualitatively matches decisions. Two practical implications of our work are that (1) the push contract performs close to standard theoretical benchmarks, which implies that it is robust to behavioral biases, and (2) the APD contract weakly Pareto dominates the push contract; retailers are better off and suppliers are no worse off under the APD contract.
Data, as supplemental material, are available at
http://dx.doi.org/10.1287/mnsc.2014.1940
.
This paper was accepted by Serguei Netessine, operations management.
We present an efficient dynamic programming algorithm to determine the optimal assortment and inventory levels in a single-period problem with stockout-based substitution. In our model, total ...customer demand is random and comprises
fixed proportion
of customers of different types. Customer preferences are modeled through the definition of these types. Each customer type corresponds to a specific preference ordering among products. A customer purchases the highest-ranked product, according to his type (if any), that is available at the time of his visit to the store (stockout-based substitution). We solve the optimal assortment problem using a dynamic programming formulation. We establish structural properties of the value function of the dynamic program that, in particular, help to characterize multiple local maxima. We use the properties of the optima to solve the problem in pseudopolynomial time. Our algorithm also gives a heuristic for the general case, i.e., when the proportion of customers of each type is random. In numerical tests, this heuristic performs better and faster than previously known methods, especially when the mean demand is large, the degree of substitutability is high, the population is homogeneous, or prices and/or costs vary across products.
We find that inventory productivity strongly predicts future stock returns among a sample of publicly listed U.S. retailers during the period from 1985 to 2010. A zero-cost portfolio investment ...strategy, which consists of buying from the two highest and selling from the two lowest quintiles formed on inventory turnover, earns more than 1% average monthly abnormal return benchmarked to the Fama-French-Carhart four-factor model. Our results are robust to different measures of inventory productivity, distinct from the well-known firm characteristics known to generate abnormal returns, and not driven by a particular subsample period. A longitudinal analysis of portfolio returns over longer holding periods shows that although inventory productivity is predictive of stock returns, its information dissipates about one to two years after release.
This paper was accepted by Serguei Netessine, operations management
.
Mathematical models of inventory typically include the three inventory associated costs of surplus, shortage and ordering. These classic inventory models are then analysed so as to choose inventory ...parameters that usually minimise the total cost of operating the inventory system being investigated.
Unfortunately, classic inventory models do not provide a meaningful basis for analysing many real and increasingly important practical inventory problems and situations. It is therefore not surprising that over recent years, several authors have discussed these issues in broad terms and suggested that a new paradigm needs to be developed.
This paper develops some specific aspects of this discussion. In particular, the paper identifies a range of inventory problems that are not covered appropriately by traditional inventory analysis. One of these is to design responsible inventory systems, i.e. systems that reflect the needs of the environment. The paper then examines the importance of inventory planning to the environment in greater detail. For example, packaging is important, not only because of its costs and the protection that it provides to the inventory items, but also because of its eventual effects on the environment in terms of the use of resources and potential landfill. For similar reasons, waste, which can result from poor inventory management, is highly important. The location of stores is important because location affects transport costs. Thus the influence of the secondary aspects of most inventory models; packaging, waste and location are important but, even more important are the inter-relations with the total system. In particular, the location of the manufacturing plants and the effect that inventory planning has on the logistics chain, potentially have considerable environmental implications. Inventory is part of a wider system.
However, until the cost charged for an activity reflects the true environmental cost of that activity, it is likely that decisions will be made on the basis of erroneous data. In that situation, we are faced with either determining the environmental cost of specific actions or to use environmental costs that are somewhat contrived; in which case it may be more sensible to use very different performance measures and models. The paper discusses these ideas and ways in which inventory policies may reassure us with our environmental concerns.
In this paper, an economic production quantity (EPQ) inventory model with interruption in process, scrap and rework is developed and analyzed. The inventory model is for multiple products and all ...products are manufactured in a unique machine. Obviously, the existence of only one machine results in limited production capacity and shortages. Therefore, shortages are permitted and fully backordered. In this EPQ inventory model, the decision variables are cycle length and backordered quantities of each product and the main objective is to minimize the expected total cost. An easy to use solution procedure is developed for finding the optimal solution. Numerical examples are provided to perform a sensitivity analysis. Finally, some conclusions and future researches are included.
•An EPQ model with interruption in process, scraped, rework and backorders is derived.•The EPQ model is developed for multi products-single machine system.•An easy to use procedure for finding the optimal solution is proposed.•Numerical examples are used to perform a sensitivity analysis of EPQ model.
We analyze a finite horizon periodic review joint pricing and inventory management model for a firm that replenishes and sells a product under the
scarcity effect
of inventory. The demand ...distribution in each period depends negatively on the sales price and customer-accessible inventory level at the beginning of the period. The firm can withhold or dispose of its on-hand inventory to deal with the scarcity effect. We show that a customer-accessible-inventory-dependent order-up-to/dispose-down-to/display-up-to list-price policy is optimal. Moreover, the optimal order-up-to/display-up-to and list-price levels are decreasing in the customer-accessible inventory level. When the scarcity effect of inventory is sufficiently strong, the firm should display no positive inventory and deliberately make every customer wait. The analysis of two important special cases wherein the firm cannot withhold (or dispose of) inventory delivers sharper insights showing that the inventory-dependent demand drives both optimal prices and order-up-to levels down. In addition, we demonstrate that an increase in the operational flexibility (e.g., a higher salvage value or the inventory withholding opportunity) mitigates the demand loss caused by high excess inventory and increases the optimal order-up-to levels and sales prices. We also generalize our model by incorporating responsive inventory reallocation after demand realizes. Finally, we perform extensive numerical studies to demonstrate that both the profit loss of ignoring the scarcity effect and the value of dynamic pricing under the scarcity effect are significant.
This paper considers a two-echelon dual-channel supply chain model with setup of production and delivery and develops a new inventory control policy for the supply chain. Previously, a two-echelon ...supply chain model without setup of production and delivery is considered and a one-for-one inventory control policy is applied to the supply chain. In the inventory control policy, production is stopped when the warehouse inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. Moreover, delivery to the retailer is stopped when the store inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. The total cost that consists of inventory holding costs and lost sales cost is considered, and setup costs are not considered in the total cost. Once setup costs are introduced, the one-for-one inventory control policy is no longer appropriate. Then, this paper develops a new control policy for the two-echelon dual-channel supply chain with setup of production and delivery. As performance measure, the total cost that consists of inventory holding costs, lost sales cost, and production and delivery setup costs is considered, and the total cost calculated on the basis of Markov analysis demonstrates the effectiveness of the proposed control policy.
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