Inventory redistribution for fashion products under demand parameter update

Demand for fashion products is usually highly uncertain. Often, there is only one possibility for procurement before the selling season. In order to improve the traditional newsvendor-type overage-underage trade-off we study a network of two expected profit maximizing retailers selling a fashion product where there is an additional opportunity for redistribution of stock during the selling season. We distinguish between the situation where redistribution is done at the moment when one of the retailers is running out of stock and the situation where the redistribution time is already determined and fixed before the selling season. We model the demand process at a retailer by a Poisson Process with an uncertain mean and use a Bayesian approach to update the distribution parameters before transshipments are done. In a numerical study we compare the different policies and show that timing flexibility and updating are especially beneficial in situations with low profit margins and high parameter uncertainty. Further, we show that depending on the instance, an optimal predetermined transshipment timing depends on the problem parameters and may be between the middle and the end of the selling season

A price-sensitive quantity-flexible supply chain contract model

Tedarik zinciri bir ürünün tasarım aşamasından tüketicinin eline ulaşıncaya kadar geçireceği ve gerekli olan tüm aşamaları kapsar. Bu çalışmamızda tedarik zinciri sözleşmelerinin bir performans geliştiricisi olarak tedarik zinciri katma değerini en üst düzeye çıkartmada nasıl kullanılabileceği araştırılmış ve iki sözleşme modeli incelenmiştir. İlk sözleşme modeli olarak, ürüne olan talebin satış fiyatı ile bağlantılı olduğu bir ortamda, üreticinin satıcıya belli bir miktarda ürün alma garantisi karşılığı önerdiği indirimler ele alınmıştır. İkinci sözleşme modeli olarak ise, üreticinin toplam tedarik zinciri katma değerini arttırmak için satıcıya önerdiği satılamayan ürünü geri alma ve satın almada miktar esnekliği sağlama sözleşmeleri incelenmiştir. Birinci modelde, görüleceği üzere, her ne kadar talep, satış fiyatı ile bağlantılı ise de, sonuç yalnız satıcı açısından değerlendirildiğinden, modelin tedarik zinciri toplam katma değeri üzerindeki etkisi belirsizdir. Diğer yandan, ikinci model tedarik zincirinin toplam katma değerini arttırdığı halde, talebin fiyat duyarlılığı göz önüne alınmamıştır. çalışmamızda geliştirdiğimiz modelin özgün yanı, yukarıdaki iki modelin zayıf noktalarına cevap vermesi ve talebin fiyata duyarlı olduğu bir ortamda üretici satıcı arasında miktar esnekliği sağlayan bir sözleşmenin tedarik zinciri katma değerini en üst düzeye çıkarmasıdır. çalışmamızda ayrıca sözleşmeden kaynaklanan bu ek katma değer artışının her iki tarafın da kazanması için nasıl paylaştırılabileceğini öneren iki yöntem geliştirilmiştir. Anahtar Kelimeler: Tedarik zinciri, esnek miktar sözleşmesi, talep esnekliği.A supply chain consists of all stages involved, directly or indirectly, in fulfilling a customer request. The objective of every supply chain is to maximize the overall value generated. The value a supply chain generates is the difference between what the final product is worth to the customer and the effort the supply chain expends in filling the customer's request. For most commercial supply chains, this value will be strongly correlated with the supply chain profitability, the difference between the revenue generated from the customer and the overall cost across the entire supply chain. The objective of maximizing this supply chain surplus can be achieved by improving the supply chain performance in terms of efficiency and responsiveness using the four supply chain drivers: inventory, transportation, facilities, and information. In this dissertation, we discussed these drivers and introduced supply chain contracts as a new driver to maximize supply chain profitability. Effective use of the contracts can substantially increase the overall supply chain profitability and its competitive advantage by forcing the companies into an intercompany interfunctional scope of strategic fit to evaluate every action in the context of the entire supply chain. This broad scope increases the size of the surplus to be shared among all stages of the supply chain. A contract specifies the parameters within which a buyer places orders and a supplier fulfills them. It may contain specifications regarding quantity, price, time, and quality. As contracts change, the risk different stages of the supply chain bear changes, which affects the buyer's and supplier's decisions and supply chain profitability. By entering into such a contract, the buyer often stands to gain guaranteed delivery of the product, which is very useful in times of scarcity, shorter delivery times, lower purchasing price, and a lower safety stock level. The supplier will also benefit with a better production plan, reduced variance of demand, economies of scale, and less paperwork. Harder to measure, but also important, is the increased level of trust and cooperation which can develop between a buyer and a supplier who decide to engage in such a contract. Of particular interest here are contracts that specify the parameters within which a buyer places orders and a supplier fulfills them in order to maximize the total supply chain surplus. We presented two supply chain contract models.  First, where a retailer facing price sensitive demand may obtain a discount by committing a fixed quantity over a finite horizon, and second where a manufacturer offering buyback or quantity flexibility contracts may increase the total supply chain profit. We concluded that the first model incorporates demand as a function of the selling price but does not address the crucial issue of total supply chain surplus maximization. On the other hand, the second model, although it increases the total supply chain surplus, does not incorporate the demand elasticity. We then developed a model to address the individual weaknesses of the models discussed by incorporating the price sensitive demand into quantity flexibility contracts by determining the optimal level of product availability, as a function of the selling price, which maximizes the total supply chain profit. We also proposed two solutions to the issue of profit sharing related to the distribution of the additional supply chain profit generated by using the contracts. Furthermore, through numerical experiments, we showed that our model maximizes total supply chain surplus by incorporating demand elasticity and profit sharing into quantity flexibility contracts.  We also developed a computer program to help simulate the system to find optimum contract parameters. We then summarized the strength and weaknesses of the models discussed with respect to our model and showed that our model, Maximize Supply Chain Profit with Buyback and Quantity Flexibility Contracts and Profit Sharing with Demand as a Function of the Selling Price Model, combines the strength of the models discussed and addresses their main weaknesses. It is our belief that the supply chain contract model developed in this dissertation can be an integral part of any Advanced Planning and Scheduling (APS) system. Keywords: Supply chain, quantity flexibility contracts, demand elasticity. 

An enhanced approximation mathematical model inventorying items in a multi-echelon system under a continuous review policy with probabilistic demand and lead-time

An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The inventory system is like a hidden entity in a supply chain, where a large complete network synchronizes a series of interrelated processes for a manufacturer, in order to transform raw materials into final products and distribute them to customers. The optimality of inventory and allocation policies in a supply chain for a cement industry is still unknown for many types of multi-echelon inventory systems. In multi-echelon networks, complexity exists when the inventory issues appear in multiple tiers and whose performances are significantly affected by the demand and lead-time. Hence, the objective of this research is to develop an enhanced approximation mathematical model in a multi-echelon inventory system under a continuous review policy subject to probabilistic demand and lead-time. The probability distribution function of demand during lead-time is established by developing a new Simulation Model of Demand During Lead-Time (SMDDL) using simulation procedures. The model is able to forecast future demand and demand during lead-time. The obtained demand during lead-time is used to develop a Serial Multi-echelon Inventory (SMEI) model by deriving the inventory cost function to compute performance measures of the cement inventory system. Based on the performance measures, a modified distribution multi-echelon inventory (DMEI) model with the First Come First Serve (FCFS) rule (DMEI-FCFS) is derived to determine the best expected waiting time and expected number of retailers in the system based on a mean arrival rate and a mean service rate. This research established five new distribution functions for the demand during lead-time. The distribution functions improve the performance measures, which contribute in reducing the expected waiting time in the system. Overall, the approximation model provides accurate time span to overcome shortage of cement inventory, which in turn fulfil customer satisfaction

A methodology for demand learning with an application to the optimal pricing of seasonal products

Cover title.Includes bibliographical references (p. 31-32).by Gabriel R. Bitran, Hitendra K. Wadhwa

Confidence-based Optimization for the Newsvendor Problem

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach can produce an upper and a lower bound for the associated cost. We apply our novel approach to three demand distribution in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist - e.g. based on maximum likelihood estimators - or Bayesian strategies.Comment: Working draf

Dynamic Procurement of New Products with Covariate Information: The Residual Tree Method

Problem definition: We study the practice-motivated problem of dynamically procuring a new, short life-cycle product under demand uncertainty. The firm does not know the demand for the new product but has data on similar products sold in the past, including demand histories and covariate information such as product characteristics. Academic/practical relevance: The dynamic procurement problem has long attracted academic and practitioner interest, and we solve it in an innovative data-driven way with proven theoretical guarantees. This work is also the first to leverage the power of covariate data in solving this problem. Methodology:We propose a new, combined forecasting and optimization algorithm called the Residual Tree method, and analyze its performance via epi-convergence theory and computations. Our method generalizes the classical Scenario Tree method by using covariates to link historical data on similar products to construct demand forecasts for the new product. Results: We prove, under fairly mild conditions, that the Residual Tree method is asymptotically optimal as the size of the data set grows. We also numerically validate the method for problem instances derived using data from the global fashion retailer Zara. We find that ignoring covariate information leads to systematic bias in the optimal solution, translating to a 6–15% increase in the total cost for the problem instances under study. We also find that solutions based on trees using just 2–3 branches per node, which is common in the existing literature, are inadequate, resulting in 30–66% higher total costs compared with our best solution. Managerial implications: The Residual Tree is a new and generalizable approach that uses past data on similar products to manage new product inventories. We also quantify the value of covariate information and of granular demand modeling

Supply Contracts with Financial Hedging

We study the performance of a stylized supply chain where two firms, a retailer and a producer, compete in a Stackelberg game. The retailer purchases a single product from the producer and afterwards sells it in the retail market at a stochastic clearance price. The retailer, however, is budget-constrained and is therefore limited in the number of units that he may purchase from the producer. We also assume that the retailer's profit depends in part on the realized path or terminal value of some observable stochastic process. We interpret this process as a financial process such as a foreign exchange rate or interest rate. More generally the process may be interpreted as any relevant economic index. We consider a variation (the flexible contract) of the traditional wholesale price contract that is offered by the producer to the retailer. Under this flexible contract, at t = 0 the producer offers a menu of wholesale prices to the retailer, one for each realization of the financial process up to a future time . The retailer then commits to purchasing at time a variable number of units, with the specific quantity depending on the realization of the process up to time. Because of the retailer's budget constraint, the supply chain might be more profitable if the retailer was able to shift some of the budget from states where the constraint is not binding to states where it is binding. We therefore consider a variation of the flexible contract where we assume that the retailer is able to trade dynamically between 0 and in the financial market. We refer to this variation as the flexible contract with hedging. We compare the decentralized competitive solution for the two contracts with the solutions obtained by a central planner. We also compare the supply chain's performance across the two contracts. We find, for example, that the producer always prefers the flexible contract with hedging to the flexible contract without hedging. Depending on model parameters, however, the retailer may or may not prefer the flexible contract with hedging. Finally, we study the problem of choosing the optimal timing, of the contract, and formulate this as an optimal stopping problem.Operations Management Working Papers Serie

Optimizing production and inventory decisions at all-you-care-to-eat facilities

Food service, feeding people outside of their home, is one of the largest industries in the world (Hartel and Klawitter, 2008). Restaurants, hospitals, military services, schools and universities are among those organizations providing these services. Management of a food service system requires operations management skill to operate successfully. A key element of food service is food production. Forecasting, demand, managing inventory and preparing menu items are key tasks in the food production process. In this research a series of three studies are presented to improve the food production system policies at an all you care to eat (AYCTE) facility. The first study examines two objectives, limiting its focus to foods for which all overproduction must be discarded (that is, leftovers cannot be saved and used in future periods). The first objective of this research is to present a novel method for estimating shortfall cost in a setting with no marginal revenue per satisfied unit of demand. Our methodology for estimating shortfall cost obtains results that are consistent with CDS management's stated aversion to shortfall, we estimate shortfall values are between 1.6 and 2.7 times larger than the procurement cost and between 30 and over 100 times larger than disposal costs. The second objective is to identify how optimal food production policies at an AYCTE facility would change were life cycle cost estimates of embodied greenhouse gas (GHG) emissions, including carbon dioxide (CO2), methane (CH4) and nitrous oxide (N2O), included in the disposal costs associated with overproduction. We found that optimal production levels are decreased significantly (18-25 percent) for food items with high environmental impacts (such as beef), and reduced less for foods with less embodied CO2. The second study considers a broader set of food types, including both foods that cannot be saved and stored as leftovers (as in the first study), and also foods for which overproduction can potentially be saved and served in the future as leftovers. Food service operations in an AYCTE environment need to consider two conflicting objectives: a desire to reduce overproduction food waste (and its corresponding environmental impacts), and an aversion to shortfalls. Similar to the first study, a challenge in analyzing such buffetstyle operations is the absence of any lost marginal revenue associated with lost sales that can be used to measure the shortfall cost, complicating any attempt to determine a minimum-cost solution. This research presents optimal production adjustments relative to demand forecasts, demand thresholds for utilization of leftovers, and percentages of demand to be satisfied by leftovers, considering two alternative metrics for overproduction waste: mass; and GHG emissions. A statistical analysis of the changes in decision variable values across each of the efficient frontiers can then be performed to identify the key variables that could be modified to reduce the amount of wasted food at minimal increase in shortfalls. The last study's aim is to minimize overproduction and unmet demand under the situation where demand is unknown. It also addresses correlations across demands for certain item (e.g., hamburgers are often demanded with french fries). As in the second study, we again utilize a Hooke-Jeeves optimization method to solve this production planning problem. In order to model a more realistic representation of this problem, demand uncertainty is incorporated in this study's optimization model, using a kernel density estimation approach. We illustrate our approach in all three studies with an application to empirical data from Campus Dining Services operations at the University of Missouri

Stochastic demand forecast and inventory management of a seasonal product a supply chain system

Estimation of seasonal demand prior to an active demand season is essential in supply chain management. The business cycle of the seasonal demand is divided into two stages: stage-1, the slow-demand period, and stage-2, the peak-demand period. The focus here is to determine an appropriate demand forecast for the peak-demand period. In the first set of forecasting model, a standard gamma and an inverse gamma prior distribution are used to forecast demand. The parameters of the prior model are estimated and updated based on current observation using Bayesian technique. The forecasts are derived for both complete and incomplete datasets. The second set of forecast is derived by ARIMA method using Box-Jenkins approaches. A Bayesian ARIMA is proposed to forecast demand from incomplete dataset. A partial dataset of a seasonal product, collected from the US census bureau, is used in the models. Missing values in the dataset often arise in various situations. The models are extended to forecast demand from an incomplete dataset by the assumption that the original dataset contains missing values. The forecast by a multiplicative exponential smoothing model is used to compare all the forecast. The performances are tested by several error measures such as relative errors, mean absolute deviation, and tracking signals. A newsvendor inventory model with emergency procurement options and a periodic review model are studied to determine the procurement quantity and inventory costs. The inventory cost of each demand forecast relative to the cost of actual demand is used as the basis to choose an appropriate forecast for the dataset. This study improves the quality of demand forecasts and determines the best forecast. The result reveals that forecasting models using Bayesian ARIMA model and Bayesian probability models perform better. The flexibility in the Bayesian approaches allows wider variability in the model parameters helps to improve demand forecasts. These models are particularly useful when past demand information is incomplete or limited to few periods. Furthermore, it was found that improvements in demand forecasting can provide better cost reductions than relying on inventory models