Single-period Inventory Models Research Articles

Single-period ordering and pricing policies with markdown, multivariate demand and customer price sensitivity

Abstract This paper studies single-period ordering and markdown pricing policies for short lifecycle products (SLP) by considering differing customer price and time sensitivities. The SLP is assumed to have declining customer valuation (and price) over the selling season and multivariate demand, which is a function of the inventory level, price and time. Promotional markdown (in contrast to clearance markdown) becomes an indispensable part of a pricing policy in view of stock-dependent demand and isused as a mechanism for customer segmentation and price discrimination over time. To offer a realistic pricing, we consider the impact of highly price-sensitive customers who value the price of the product over its innovativeness and who act strategically by purchasing only during a‘sale’ at a markdown price. In this context, single-period inventory models are formulated to include markdown under two market scenarios, namely the homogenous market and thetwo-segment market – a price insensitive (PI) segment, and a price-sensitive (PS) segment. The assumption of non-overlapping segments is relaxed later, and PI customers are allowed to buy later on at a markdown price. The proposed profit-maximising models determine the optimal order size, initial price, markdown time, and price. The solution methods along with the optimality conditions are specified in detail. The results are discussed by using numerical examples, and model behavior with respect to parameters is presented along with the sensitivity analysis.The study reveals the benefits of market segmentation and markdown pricing which recognise high price-sensitive ‘bargain hunter’ customers and offers deeper discounts that yield greater profits. It also demonstrates the superiority of a markdown policy to a single pricing policy, and the benefits of considering the demand stimulating-effect of inventory.

Seasonal Inventory Decisions (Single-Period Inventory Models)

<p>One of the dilemmas facing many retailers is how to handle seasonal goods, such as sarung dress or batik dress, biscuits and syrups during Idul Fitri celebration. Often they cannot be sold at full markup next year because of changes in styles, and expiry dates for foods and beverages. Furthermore, the lead time can be longer than the selling season, allowing no second chance to rush through another order to cover unexpectedly high demand. At the end of the period the product has either sold out or there is a surplus of unsold items to sell for a salvage value. The single-period inventory models are used in situations involving seasonal or perishable items that cannot be carried in inventory and sold in future periods.<br />This type of situation is often called the newsboy problem. If the newspaper seller does not buy enough newspapers to resell on the street corner, sales opportunities are lost. If the seller buys too many newspapers, the overage cannot be sold because nobody wants yesterday’s newspaper.<br />At this opportunity, we will use the single-period inventory models decisions to create an optimal order quantity decision with the highest expected payoff. We will be able to use this decision process for all such items over many selling seasons to maximize profits.<br />However, it is not a foolproof, and it can result in an occasional bad outcome. It will depend on the situation, if the probability of demand follows the demand probability planning, then you will be able to get the best decision to prepare and execute an order.<br />Kata kunci:<br />Seasonal Inventory, Single-Period Inventory Models, Probability of Demand.</p>

A novel single-period inventory problem with uncertain random demand and its application

In many real inventory situations of short life-cycle products the decision maker often has to provide a subjective estimate of new demand distribution due to the lack of historical data. Thus, both randomness and uncertainty simultaneously appear in a single-period inventory (newsboy) problem. In this paper, we develop both single-item and multi-item single-period inventory models when market demands are assumed to be uncertain random variables. The objective of this study is to provide theoretical analysis of the models that attains optimality when demand information availability in subjective judgments leading to uncertainty along with random variation. The uncertain random models are transferred to equivalent deterministic forms by considering expected profit and providing more information of chance distributions. Finally, the numerical examples of ordering pharmaceutical reference standard materials are presented to illustrate the models.

Single-Period Inventory Models with multiple ordering opportunities: a review

Single-Period Inventory Models (SPIMs) or else referred as newsboy model are used to acquire optimal ordering decisions of short life-cycle products facing uncertain demand. Due to longer production and delivery lead-time, SPIM have single-ordering opportunity. To reduce the higher demand variability, the concept of SPIM with multiple ordering opportunities has been adopted in the recent literatures and has proved that the supply chain performance is better than SPIM. This paper broadly studies the literature discussing the SPIM with multiple ordering opportunities under three major classifications such as This paper identifies several research gaps from the existing literatures and proposes a conceptual model based on those gaps. This study also suggests some potential scope for research.

A multi-period inventory model with multi-dimensional procurement bidding

We consider a multi-period inventory model with raw material procurements carried out via a reverse auction. Bids are multi-dimensional, and they consist of supplier information of price, shortage quantity and lead time. This work is an extension of our earlier work that has focused on multi-dimensional procurement auctions in single-period inventory models, to multi-period settings. The new model is based on a hybrid approach combining stochastic dynamic programming and simulation.

Optimal newsvendor policies for dual-sourcing supply chains: A disruption risk management framework

We propose generic single period (newsvendor-type) inventory models for capturing the trade-off between inventory policies and disruption risks in a dual-sourcing supply chain network both unconstrained and under service level constraints, where both supply channels are susceptible to disruption risks. The models are developed for both risk neutral and risk-averse decision-makers and can be applicable for different types of disruptions related among others to the supply of raw materials, the production process, and the distribution system, as well as security breaches and natural disasters. Analytical closed-form solutions are obtained and interesting managerial insights on the merit of contingency strategies in managing uncertainties and risks in dual-sourcing supply chains are discussed.

Application of multi-dimensional procurement auction in single-period inventory models

Procurement is one of the major activities in the Manufacturing Resource Planning (MRP II), which is closely coupled with inventory management. Any improvement in this area will have a direct impact on the performance of the entire supply chain. Auction mechanism can be a successful procurement method when there are several potential suppliers available. In this paper, we consider a single-period inventory model when the selection of the supplier is done through a reverse auction with bids consisting of several attributes, namely price, shortage quantity, and lead time. The multi-dimensionality of the bid increases the complexity of the underlying problem creating a need for an approach to determine an approximate optimal target level. This is needed for the initiation of the auction and the procurement process. Monte-Carlo simulation method was used to investigate the performance of the approximation. Simulation results show that the analytical method provides an acceptable approximation for the optimal target inventory level.

Inventory systems with random arrival of shipments

In single-period inventory models, neither excess demand nor excess inventory can be carried forward to the next period. In stochastic multi-period models, an order is placed at some point in time during the cycle, and lead-time is considered to be either constant or random. Lead-time demand, however, is assumed to be probabilistic. At the time an order is placed, the amount of inventory which will be on hand when replenishment arrives is unknown. In this paper, we propose a variation of these models to determine the optimal economic order quantity. Shipments arrive according to a Poisson process. The status of the inventory becomes known at the time of the arrival of the shipment, and the selection of order quantity is made at that time. However, the arrival time of future shipments is uncertain. It is also demonstrated that traditional single- and multi-period inventory models can be obtained as special cases of the proposed model.

Optimizing centralized inventory operations in a cooperative game theory setting

For single period inventory models with normally distributed, correlated individual demands we examine the problem of minimizing the cost of inventory centralization as a function of the covariance matrix. In a stable centralized setting there are no incentives for any party to break-away -- referred to as nonempty core conditions. For the allocated benefits in inventory centralization, nonempty core conditions are always satisfied. In this paper we discuss a step by step greedy optimization procedure which computes an optimal centralization solution. The procedure manipulates the correlations without changing the mean or the variance at each store. We do not just accept that in the centralized setting the parties are better-off but for the first time provide the analysis of how to maximize their collective benefits.

A single-period inventory model with fuzzy demand

The single-period inventory models have wide applications in the real world in assisting the decision maker to determine the optimal quantity to order. Due to lack of historical data, the demand has to be subjectively determined in many cases. In this paper, a single-period inventory model for cases of fuzzy demand is constructed. The costs considered include the procurement cost, shortage cost, and holding cost. For different fuzzy total cost resulted from different order quantity, a method for ranking fuzzy numbers is adopted to find the optimal order quantity in terms of the cost. When the profit gained from selling one item is less (greater) than the loss incurred due to one unsold item, the optimal order quantity lies in the range defined for the left-shape (right-shape) function of the fuzzy demand. If the unit profit is equal to the unit loss, then all quantities with a membership grade 1 are optimal to be ordered. The methodology of this paper can be applied to construct other inventory models with fuzzy demand.

Single period inventory models with two levels of storage

It is common practice in most inventory systems to hold excess stocks in a rented warehouse (RW) whenever the storage capacity of the owned warehouse (OW) is insufficient. Therefore, the purpose of this paper is to study the effect of renting more storage space on the optimal ordering policy in a stochastic single-period setting. We show that the optimal ordering quantity obtained from the single-period, two-warehouse model is smaller than the ordering quantity of the unconstrained classical newsboy problem. We additionally present various properties of the optimal ordering policy. The model is also extended to the fixed cost case, where depending on the level of the initial inventory, a fixed ordering charge is incurred at the start of the period. In addition, we analyse both models with and without fixed ordering cost under the distribution-free approach in which the form of the demand distribution is not required to be specified. Numerical examples are also included to illustrate the developed models in this paper.