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Barter exchange is a system of swapping goods or services for other goods or services in a moneyless and direct manner. Barter has become an effective model of a circular economy because it reduces the consumption impact. Bartering maximizes the utility of assets and existing resources, and can unleash the unspent social, economic, and environmental value of underutilized assets. The present article analyzes the price-setting newsvendor problem with a barter exchange option. The retailer facing a stochastic price-dependent demand sells a product on the market and, additionally, needs another product for its own purposes. Therefore, first, the retailer trades the unsold product for the product it needs by means of barter, and next disposes of the unsold product at a discounted price at the end of the selling season. The retailer’s optimal order quantity and optimal price are derived assuming additive uncertainty in demand. This type of demand function has special characteristics, for example, the actual demand may attain negative values in times of economic uncertainty. The possibility of negative demand realizations is taken into consideration in the study. It proves that, in certain cases, the optimal solution belongs to the set of high barter prices which implies that the actual demand may be negative.
Milena Bieniek. Bartering: Price-Setting Newsvendor Problem with Barter Exchange. Sustainability 2021, 13, 6684 .
AMA StyleMilena Bieniek. Bartering: Price-Setting Newsvendor Problem with Barter Exchange. Sustainability. 2021; 13 (12):6684.
Chicago/Turabian StyleMilena Bieniek. 2021. "Bartering: Price-Setting Newsvendor Problem with Barter Exchange." Sustainability 13, no. 12: 6684.
Inventories are ubiquitous in nature and inventory control is a crucial activity undertaken in the supply chain (SC) by a company’s management. The Vendor Managed Inventory (VMI) contract has become a common technique for supply chain management (SCM) since the 1980’s. In this technique, the decision about how much inventory to hold is made by the vendor. In the paper, we consider VMI with consignment (VMCI). Consignment is a frequently used form of business arrangement, in which the vendor retains the ownership of the inventory and gets paid by the retailer on actual units sold. Under VMCI, decisions are made in two steps. In the first step, the vendor specifies a consignment price and an order quantity with the objective to maximize the vendor’s expected profit. In the second step, the retailer chooses a retail price which maximizes the retailer’s expected profit. The customer demand is assumed to be stochastic, additive and price–sensitive. Additive uncertainty can produce negative demand realizations, which may occur in adverse market conditions. We prove that in this case an optimal and possibly non–unique solution to VMCI exists. We calculate closed–form formulas for optimal quantities for uniformly distributed demand. Finally, we demonstrate our approach through a numerical example and we show that the imposition of a non–negativity constraint can cause a higher vendor’s expected profit.
Milena Bieniek. The ubiquitous nature of inventory: Vendor Managed Consignment Inventory in adverse market conditions. European Journal of Operational Research 2021, 291, 411 -420.
AMA StyleMilena Bieniek. The ubiquitous nature of inventory: Vendor Managed Consignment Inventory in adverse market conditions. European Journal of Operational Research. 2021; 291 (2):411-420.
Chicago/Turabian StyleMilena Bieniek. 2021. "The ubiquitous nature of inventory: Vendor Managed Consignment Inventory in adverse market conditions." European Journal of Operational Research 291, no. 2: 411-420.
Consignment is a form of business arrangement, in which a vendor places goods at a retailer’s location without receiving payment until the products are sold. This paper examines consignment with consumer non-defective returns behaviour, where the upstream vendor makes a contract with the downstream retailer. The vendor decides what the consignment and refund prices are, and the retailer chooses the retail price. The vendor gets paid based on the sold units, salvages and returns. We analyze two contracts, called retailer and vendor managed consignment inventory (RMCI and VMCI, respectively), the only difference being that under RMCI, the retailer chooses the service level, and under VMCI, the vendor specifies it. We present precise solutions to VMCI for additive uncertainty and compare them to the multiplicative case. We prove that the vendor’s optimal return policy depends on a salvage value since if it is equal to zero, the vendor should not offer the return policy. We show that the channel may gain profit from the return policy for the positive salvage value. We demonstrate that the form of uncertainty and the presence of consumer returns considerably affect the solutions to the problems. As an extension, we give the results obtained under RMCI.
Milena Bieniek. Consumer returns in consignment contracts with inventory control and additive uncertainty. INFOR: Information Systems and Operational Research 2020, 59, 169 -189.
AMA StyleMilena Bieniek. Consumer returns in consignment contracts with inventory control and additive uncertainty. INFOR: Information Systems and Operational Research. 2020; 59 (1):169-189.
Chicago/Turabian StyleMilena Bieniek. 2020. "Consumer returns in consignment contracts with inventory control and additive uncertainty." INFOR: Information Systems and Operational Research 59, no. 1: 169-189.
In this research note the satisficing newsvendor problem is considered which is defined as the maximization of the probability of exceeding the expected profit multiplied by a positive constant. This constant called optimism coefficient can be chosen by the firm’s management either based on their preference or the market conditions. The coefficient indicates whether there is a low or high optimistic decision maker. For the general demand distribution the results are significantly dependent on this coefficient.
Milena Bieniek. Satisficing Newsvendor Problem with the Optimism Coefficient. Foundations of Computing and Decision Sciences 2019, 44, 261 -271.
AMA StyleMilena Bieniek. Satisficing Newsvendor Problem with the Optimism Coefficient. Foundations of Computing and Decision Sciences. 2019; 44 (3):261-271.
Chicago/Turabian StyleMilena Bieniek. 2019. "Satisficing Newsvendor Problem with the Optimism Coefficient." Foundations of Computing and Decision Sciences 44, no. 3: 261-271.
Consignment is the shifting of the inventory ownership to the supplier. In this form of business arrangement the supplier places goods at a customer’s location without receiving payment, until the goods are sold. We consider a single period supply chain model, where the supplier contracts with the retailer. Market demand for the product is price–dependent and uncertain. The supplier decides the consignment price and the retailer chooses the retail price for each unit sold. Two arrangements called retailer managed consignment inventory (RMCI), and vendor managed consignment inventory (VMCI) are studied. The only difference between these arrangements is that under RMCI contract the retailer is allowed to choose the service level, and under VMCI contract the supplier decides about this service level. In our paper we give the optimal solutions for the retail price, the service level and the consignment price in closed–form, which maximize the expected profit of the retailer or the supplier under both consignment regimes. We consider the additive demand linearly dependent on price. We also illustrate the solutions by a numerical example, which explains the general results well.
Milena Bieniek. Vendor and retailer managed consignment inventory with additive price–dependent demand. Optimization Letters 2018, 13, 1757 -1771.
AMA StyleMilena Bieniek. Vendor and retailer managed consignment inventory with additive price–dependent demand. Optimization Letters. 2018; 13 (8):1757-1771.
Chicago/Turabian StyleMilena Bieniek. 2018. "Vendor and retailer managed consignment inventory with additive price–dependent demand." Optimization Letters 13, no. 8: 1757-1771.
Milena Bieniek. Goal setting in the newsvendor problem with uniformly distributed demand. Multiple Criteria Decision Making 2018, 13, 91 -102.
AMA StyleMilena Bieniek. Goal setting in the newsvendor problem with uniformly distributed demand. Multiple Criteria Decision Making. 2018; 13 ():91-102.
Chicago/Turabian StyleMilena Bieniek. 2018. "Goal setting in the newsvendor problem with uniformly distributed demand." Multiple Criteria Decision Making 13, no. : 91-102.
Milena Bieniek. Bicriteria optimization in the risk-adjusted newsvendor problem. Multiple Criteria Decision Making 2017, 12, 9 -21.
AMA StyleMilena Bieniek. Bicriteria optimization in the risk-adjusted newsvendor problem. Multiple Criteria Decision Making. 2017; 12 ():9-21.
Chicago/Turabian StyleMilena Bieniek. 2017. "Bicriteria optimization in the risk-adjusted newsvendor problem." Multiple Criteria Decision Making 12, no. : 9-21.
Milena Bieniek. Bicriteria Optimization In the Newsvendor Problem with Exponentially Distributed Demand. Multiple Criteria Decision Making 2016, 11, 20 -35.
AMA StyleMilena Bieniek. Bicriteria Optimization In the Newsvendor Problem with Exponentially Distributed Demand. Multiple Criteria Decision Making. 2016; 11 ():20-35.
Chicago/Turabian StyleMilena Bieniek. 2016. "Bicriteria Optimization In the Newsvendor Problem with Exponentially Distributed Demand." Multiple Criteria Decision Making 11, no. : 20-35.
Milena Bieniek. A note on the facility location problem with stochastic demands. Omega 2015, 55, 53 -60.
AMA StyleMilena Bieniek. A note on the facility location problem with stochastic demands. Omega. 2015; 55 ():53-60.
Chicago/Turabian StyleMilena Bieniek. 2015. "A note on the facility location problem with stochastic demands." Omega 55, no. : 53-60.
In this paper we consider the influence of the safety factor on the decision of the inventory location. This decision is done based on the model which centralizes or decentralizes the safety stock. In this model we have to choose between the location of the inventory in the regional warehouses or the location in the central warehouse. The decision is made due to the minimizing the holding costs and the supply costs of the safety stock from the central warehouse to the customer. The main assumption is that the customers have the stochastic demands on the inventory items. Moreover, the customers’ demands have the known distribution with the known parameters. The complex analysis of the influences of possible probabilistic demands' distributions on the safety factors is conducted. The numerical computations for the safety factors used in the facility location model are also presented. In numerical examples we take into considerations the demands’ distributions the most often used in practice like the normal, the Poisson, the Gamma and the exponential distribution. Some graphs for the safety factors of these distributions are also drawn. Moreover for the mentioned demands’ distributions the model of the safety stock location depends on the specific factors. Among other things these factors are the mean and the variance of the demand, the number of the regional warehouses, the assumed service level, and some cost factors like the holding costs and the transportation costs. Some graphs which illustrated the dependence of the model elements on some listed before parameters are presented and their influence on the location decision is studied also.
Milena Bieniek. SERVICE LEVEL IN MODEL OF INVENTORY LOCATION WITH STOCHASTIC DEMAND. Archives of Transport 2014, 31, 7 -21.
AMA StyleMilena Bieniek. SERVICE LEVEL IN MODEL OF INVENTORY LOCATION WITH STOCHASTIC DEMAND. Archives of Transport. 2014; 31 (3):7-21.
Chicago/Turabian StyleMilena Bieniek. 2014. "SERVICE LEVEL IN MODEL OF INVENTORY LOCATION WITH STOCHASTIC DEMAND." Archives of Transport 31, no. 3: 7-21.
Explicit formulae for single, central, and product moments of k-th upper and lower record values from the linear exponential distribution are given. The limited moments and the mean residual life function are also investigated. Moreover, recurrence relations for moments of k-th upper and lower record values from this distribution are derived.
Milena Bieniek; D. Szynal. On moments of k-th record values from the linear exponential distribution. Journal of Mathematical Sciences 2013, 191, 526 -537.
AMA StyleMilena Bieniek, D. Szynal. On moments of k-th record values from the linear exponential distribution. Journal of Mathematical Sciences. 2013; 191 (4):526-537.
Chicago/Turabian StyleMilena Bieniek; D. Szynal. 2013. "On moments of k-th record values from the linear exponential distribution." Journal of Mathematical Sciences 191, no. 4: 526-537.
We present sharp mean–variance bounds for expectations of kth record values based on distributions coming from restricted families of distributions. These families are defined in terms of convex or star ordering with respect to generalized Pareto distribution. The bounds for expectations of kth record values from DD, DFR, DDA, and DFRA families are special cases of our results. The bounds are derived by application of the projection method.
Milena Bieniek. Projection Mean–Variance Bounds on Expectations ofkth Record Values from Restricted Families. Communications in Statistics - Theory and Methods 2007, 36, 679 -692.
AMA StyleMilena Bieniek. Projection Mean–Variance Bounds on Expectations ofkth Record Values from Restricted Families. Communications in Statistics - Theory and Methods. 2007; 36 (4):679-692.
Chicago/Turabian StyleMilena Bieniek. 2007. "Projection Mean–Variance Bounds on Expectations ofkth Record Values from Restricted Families." Communications in Statistics - Theory and Methods 36, no. 4: 679-692.
We give new formula for moments of k-th record values in terms of Stirling numbers of the first kind. In particular, the formulae allow to derive the explicit formulae for moments of k-th lower record values from exponential distribution which have not been known yet. Moreover, some interesting identities involving harmonic numbers are also obtained as corollaries to presented results.
Milena Bieniek; Dominik Szynal. On k-th record times, record values and their moments. Journal of Statistical Planning and Inference 2007, 137, 12 -22.
AMA StyleMilena Bieniek, Dominik Szynal. On k-th record times, record values and their moments. Journal of Statistical Planning and Inference. 2007; 137 (1):12-22.
Chicago/Turabian StyleMilena Bieniek; Dominik Szynal. 2007. "On k-th record times, record values and their moments." Journal of Statistical Planning and Inference 137, no. 1: 12-22.
Milena Bieniek; Dominik Szynal. On random split of the segment. Applicationes Mathematicae 2005, 32, 243 -261.
AMA StyleMilena Bieniek, Dominik Szynal. On random split of the segment. Applicationes Mathematicae. 2005; 32 (3):243-261.
Chicago/Turabian StyleMilena Bieniek; Dominik Szynal. 2005. "On random split of the segment." Applicationes Mathematicae 32, no. 3: 243-261.