Inventory Model with Seasonal Demand: A Specific Application to Haute Couture

In the stochastic multiperiod inventory problem, a vast majority of the literature deals with demand volume uncertainty. Other dimensions of uncertainty have generally been overlooked. In this paper, we develop a newsboy formulation for the aggregate multiperiod inventory problem intended for products of short sales season and without replenishments. A distinguishing characteristic of our formulation is that it takes a time dimension of demand uncertainty into account. The proposed model is particularly suitable for applications in haute couture, i.e., high fashion industry. The model determines the time of switching primary sales effort from one season to the next as well as optimal order quantity for each season with the objective of maximizing expected profit over the planning horizon. We also derive the optimality conditions for the time of switching primary sales effort and order quantity. Furthermore, we show that if time uncertainty and volume uncertainty are independent, order quantity becomes the main decision over the interval of the primary selling season. Finally, we demonstrate that the results from the two-season case can be directly extended to the multi-season case and the limited resource multiple-item case

Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand

This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and Log-Normal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through Monte-Carlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace non-normality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise.Inventory Control; Newsboy Problem; Skewed Demand; Exact and Asymptotic Confidence Intervals; Monte-Carlo Simulations

Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand

In this paper we consider the classical newsvendor model with profit maximization. When demand is fully observed in each period and follows either the Rayleigh or the exponential distribution, appropriate estimators for the optimal order quantity and the maximum expected profit are established and their distributions are derived. Measuring validity and precision of the corresponding generated confidence intervals by respectively the actual confidence level and the expected half-length divided by the true quantity (optimal order quantity or maximum expected profit), we prove that the intervals are characterized by a very important and useful property. Either referring to confidence intervals for the optimal order quantity or the maximum expected profit, measurements for validity and precision take on exactly the same values. Furthermore, validity and precision do not depend upon the values assigned to the revenue and cost parameters of the model. To offer, therefore, a-priori knowledge for levels of precision and validity, values for the two statistical criteria, that is, the actual confidence level and the relative expected half-length are provided for different combinations of sample size and nominal confidence levels 90%, 95% and 99%. The values for the two criteria have been estimated by developing appropriate Monte-Carlo simulations. For the relative-expected half-length, values are computed also analytically.Inventory Control; Classical newsvendor model; Exponential and Rayleigh Distributions; Confidence Intervals; Monte-Carlo Simulations

A Finite Horizon Inventory Model: An Operational Framework

We present a simulation based decision support system to decide the inventory ordering policy in the context of a single commodity, multi pack, and finite horizon situation. The multiple objectives include (a) Minimizing the end of the season inventory, (b) Maximizing the operating profit, (c) Minimizing the peak working capital requirements during the season. Stochastic demand and positive lead time add to the complexity of the problem context. In addition multiple partners in the supply chain with distinct and conflicting set of objectives necessitate the need for a formal approach. The motivation for this model is based on a real life situation. The model addresses the decision choices faced by the distributor in a specific logistics chain. In this chain, a typical distributor has to balance between the stochastic nature of the demand and the attractive nature of financial incentives (order quantity based) proposed by the manufacturer. The problem can be formulated as a multi-period dynamic programming problem with stochastic demand with an objective to optimize the expected operating profit, subject to specific constraints on working capital requirement, service level, order fill rate and end of the season inventory. Such a formulation is hard to solve and does not lend itself to analyze several ordering policies. Based on simulation experiments, we propose an ordering policy which optimizes the overall objectives of supply chain partners and hence demonstrated the possibility of jointly managing the uncertain demand by supply chain partners. The model is simple and easy to use. It is implemented by using spreadsheet. It provides adequate flexibility to conduct what-if analysis. The model has a potential to be useful in a wide range of situations.

The distribution-free newsboy problem with resalable returns

We study the case of a catalogue/internet mail order retailer selling seasonal productsand receiving large numbers of commercial returns. Returned products arriving beforethe end of the selling season can be resold if there is sufficient demand. A single orderis placed before the season starts. Excess inventory at the end of the season is salvagedand all demands not met directly are lost. Since little historical information is available,it is impossible to determine the shape of the distribution of demand. Therefore, weanalyze the distribution-free newsboy problem with returns, in which only the mean andvariance of demand are assumed to be known. We derive a simple closed-form expressionfor the distribution-free order quantity, which we compare to the optimal order quantities whengross demand is assumed to be normal, lognormal or uniform. We find that the distribution-freeorder rule performs well in most realistic cases.inventory;product returns;distribution-free newsboy problem

Multiple products, multiple constraints, single period inventory problem: A Hierarchical solution procedure

This paper presents the formulation and a hierarchical solution procedure of multiple products, multiple constraints, single period inventory problem. The hierarchical procedure decomposes the problem into a number of sub-problems equal to the number of constraints sets. Each sub-problem is solved optimally by applying Lagrange multipliers and satisfying Kuhn-Tucker conditions. The experimental results show that the hierarchical procedure performs well even when there are large a number of products and constraints.

The Newsboy Problem with Resalable Returns

We analyze a newsboy problem with resalable returns. A single order isplaced before the selling season starts. Purchased products may bereturned by the customer for a full refund within a certain timeinterval. Returned products are resalable, provided they arrive backbefore the end of the season and are undamaged. Products remaining atthe end of the season are salvaged. All demands not met directly arelost. We derive a simple closed-form equation that determines theoptimal order quantity given the demand distribution, the probabilitythat a sold product is returned, and all relevant revenues and costs.We illustrate its use with real data from a large catalogue/internetmail order retailer.inventory;reverse logistics;product returns;mail order retailer;newsboy problem

Using system simulation to search for the optimal multi-ordering policy for perishable goods

[EN] This paper explores the possibility that perishable goods can be ordered several times in a single period after considering the cost of Marginal contribution, Marginal loss, Shortage, and Purchasing under stochastic demand. In order to determine the optimal ordering quantity to improve the traditional newsvendor and maximize the total expected profits, and then sensitivity analysis is taken to realize the influence of the parameters on total expected profits and decision variables respectively. In addition, this paper designed a multi-order computerized system with Monte Carlo method to solve the optimal solution under stochastic demand. Based on numerical examples, this paper verified the feasibility and efficiency of the proposed model. Finally, several specific conclusions are drawn for practical applications and future studies.Huang, Y.; Chang, X.; Ding, Y. (2019). Using system simulation to search for the optimal multi-ordering policy for perishable goods. International Journal of Production Management and Engineering. 7(1):49-62. https://doi.org/10.4995/ijpme.2019.10745SWORD496271Azoury, K.S., Miller, B.L. (1984). A comparison of the optimal ordering levels of bayesian and non-bayesian inventory models, Management Science, 30(8), 993-1003. https://doi.org/10.1287/mnsc.30.8.993Alfares, H.K., Elmorra, H.H. (2005). The distribution-free newsboy problem: extensions to the shortage penalty case, International Journal of Production Economics, 93-94(8), 465-477. https://doi.org/10.1016/j.ijpe.2004.06.043Chung, C.S., Flynn, J. (2001). A newsboy problem with reactive production, Computers & Operations Research, 28(8), 751-765. https://doi.org/10.1016/S0305-0548(00)00006-XChun, Y.H. (2003). Optimal pricing and ordering policies for perishable commodities, European Journal of Operational Research, 144(1), 68-82. https://doi.org/10.1016/S0377-2217(01)00351-4Chen, L.H., Chen, Y.C. (2009). A newsboy problem with a simple reservation arrangement. Computers & Industrial Engineering, 56(1), 157-160. https://doi.org/10.1016/j.cie.2008.04.010Dian, J.R. (1990). A high-low search algorithm for a newsboy problem with delayed information feedback. Operations Research, 38(5), 838-846. https://doi.org/10.1287/opre.38.5.838Dye, C.Y., Ouyang, L.Y. (2005). An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging. European Journal of Operational Research, 163(3), 776-783. https://doi.org/10.1016/j.ejor.2003.09.027Fujiwara, O., Soewandi, H., Sedarage, D. (1997). An optimal ordering and issuing policy for a two-stage inventory system for perishable products. European Journal of Operational Research, 99(2), 412-424. https://doi.org/10.1016/S0377-2217(95)00365-7Gallego, G., Moon, I. (1993). The distribution free newsboy problem: review and extensions. Journal of the Operational Research Society, 44(8), 825-834. https://doi.org/10.1057/jors.1993.141Khouja, M. (1999). The single-period (news-vendor) problem: literature review and suggestions for future research. Omega, 27(5), 537-553. https://doi.org/10.1016/S0305-0483(99)00017-1Khouja, M.J. (2000). Optimal ordering, discounting, and pricing in the single-period problem. International Journal of Production Economics, 65(2), 201-216. https://doi.org/10.1016/S0925-5273(99)00027-4Lau, H., Lau, H. (1998). Decision models for single-period products with two ordering opportunities. International Journal of Production Economics, 55(1), 57-70. https://doi.org/10.1016/S0925-5273(98)00040-1Padmanabhan, G., Vrat, P. (1995). EOQ models for perishable items under stock dependent selling rate. European Journal of Operational Research, 86(2), 281-292. https://doi.org/10.1016/0377-2217(94)00103-JPando, V., Luis, A.S.J., Juan, G.L., Sicilia, J. (2013). A newsboy problem with an emergency order under a general backorder rate function. Omega, 41(6), 1020-1028. https://doi.org/10.1016/j.omega.2013.01.003Zheng, M., Wu, K., Shu, Y. (2016). Newsvendor problems with demand forecast updating and supply constraints. Computers & Operations Research, 67, 193-206. https://doi.org/10.1016/j.cor.2015.10.00

Optimal control of a divergent N-echelon inventory system

Consider a divergent multi-echelon inventory system, e.g. a distribution system or a production system. At every facility in the system orders are placed (or production is initiated) periodically. The order arrives after a fixed lead time. At the end of each period linear costs are incurred at each facility for holding inventory. Also, linear penalty costs are incurred at the most downstream facilities for backorders. The objective is to minimize the expected holding and penalty costs per period. We prove that under the balance assumption it is cost-optimal to control every facility by an order-up-to-policy. The optimal replenishment policy, i.e., the order-up-to-level and the rationing functions at each facility, can be determined by decomposition of the system. This decomposition result reduces complex multi-dimensional control problems to 'simple' one-dimensional problems, which closely resemble the classical newsboy problem achieving a proper trade-off between the consequences of too much stock and too little inventory. Keywords: multi-echelon, optimal control, inventory, allocation, rationing, divergent