A mathematical model for the formation of the pricing policy and the plan of the production and transport system in a timber-processing enterprise

The formation of supply chains for raw materials is closely related to production problems involving the determination of prices for sold goods. The question often arises about the need to study the sources of raw materials and the methodology for pricing the goods produced, taking into account a large number of external aspects of the market. Often, only particular approaches to solving production problems are considered in the literature, and methods for solving the complex problem of forming supply chains for raw materials and pricing are poorly developed. This paper presents a mathematical model that makes it possible to assess the feasibility of interaction between a timber industry enterprise and a commodity exchange, with the daily formation of a price vector over the entire planning horizon. A two-stage algorithm for finding a suboptimal solution is considered, which at the first stage is based on linear optimization, and at the second, on gradient descent with the use of penalty functions. The model was tested on the data of the commodity and raw materials exchange of Russia and one of the enterprises of the Primorsky Territory. The result of testing was the volume of production of each type of product over the entire planning horizon, the volume of delivery of raw materials from regions to enterprises, as well as the methods of delivery of goods to the consumer and the policy of pricing. It is shown that almost all goods should increase in price due to a reduction in the excess volume of applications (demand) over the entire planning horizon, with the exception of two types of products. It is noted that the exchange can provide the necessary volume of raw materials for high-capacity production, which demonstrates the possibility, if necessary, to increase the volume of raw materials purchases. It is shown which goods will be included in the release plan more often than others when optimizing the price vector. The ways of delivery of final types of products are analyzed. The disadvantages and advantages of the mathematical model and algorithm are presented.

Company valuation and the nonlinear state marginal price vector model under agency conflicts

In the present contribution, the innovative nonlinear state marginal price vector model introduced in Toll and Kintzel (CEJOR 27(4):1079–1105, 2019) (plus Errata herein) is enriched to include budgeting problems under agency conflicts. Under asymmetric information, a company owner as principal can only rely on information transmitted to her from her managers as agents. In the related modeling, it is assumed that slack and capital rationing are optimal. The governing budgeting relations are integrated into a nonlinear framework furnished by a multi-period newsvendor approach and are solved numerically by means of a two-step valuation procedure based on two successive nonlinear convex optimizations. The capital market is assumed to be imperfect. As case study, the M&A-valuation case of a merger of two IT-service companies is considered subjected to optimal combined dimensioning of capacities and budgets under stochastic demand. On balance, by addressing agency conflicts within the well-established nonlinear framework, the practical application field of the valuation procedure is widened.

Serial dictatorship mechanisms with reservation prices: heterogeneous objects

We adapt a set of mechanisms introduced by Klaus and Nichifor (Econ Theory 70:665–684, 2020), serial dictatorship mechanisms with (individual) reservation prices, to the allocation of heterogeneous indivisible objects, e.g., specialist clinic appointments. We show how the characterization of serial dictatorship mechanisms with reservation prices for homogeneous indivisible objects (Klaus and Nichifor 2020, Theorem 1) can be adapted to the allocation of heterogeneous indivisible objects by adding neutrality: mechanism $$\varphi $$ φ satisfies minimal tradability, individual rationality, strategy-proofness, consistency, independence of unallocated objects, neutrality, and non wasteful tie-breaking if and only if there exists a reservation price vector r and a priority ordering $$\succ $$ ≻ such that $$\varphi $$ φ is a serial dictatorship mechanism with reservation prices based on r and $$\succ $$ ≻ .

A speedy auction using approximated bidders’ preferences

This paper presents a combinatorial auction, which is of particular interest when short completion times are of importance. It is based on a method for approximating the bidders’ preferences over two types of item when complementarity between the two may exist. The resulting approximated preference relation is shown to be complete and transitive at any given price vector. It is shown that an approximated Walrasian equilibrium always exists if all bidders either view the items as substitutes or complements. If the approximated preferences of the bidders comply with the gross substitutes condition, then the set of approximated Walrasian equilibrium prices forms a complete lattice. A process is proposed that is shown to always reach the smallest approximated Walrasian price vector. Simulation results suggest that the approximation procedure works well as the difference between the approximated and true minimal Walrasian prices is small.

THE ISSUE OF VALUE IN ECONOMICS: PRACTICAL CONSEQUENCES

Value is a standard of the cost, a certain common quality, which makes it possible to compare costs of quite different things. This construct probably cannot be operationalized generically, but in the development of theory operationalization is not imperative. Although neoclassical economics rejects this category ultimately, it is possible to demonstrate that this approach can be well adjusted to it. The issue of value is not merely a theoretical one. The purpose of the work is to show that if a feedback through the market must have an objective basis as an initial standard, that is money must have a benchmark, then the correct choice of a monetary benchmark can result in significant positive macro-economic consequences. Methods of research: scientific and philosophical analysis of texts and theoretical development. Conclusions: The idea that the feedback through the market must have an objective basis as an initial standard - that is money must have a benchmark – is not contradictory theoretically and its realization is desirable in practice. An energy monetary benchmark is probably preferable for a modern economy. The energy monetary benchmark can stabilize currency circulation potentially, optimize the price vector and simplify the valuation of mineral resources.

New conditions for the existence of equilibrium prices

We study the existence of equilibrium price vector in a supply-demand model taking into account the transaction costs associated with the sale of products. In this model, the demand function is the solution to the problem of maximizing the utility function under budget constraints. The supply function is the solution to the problem of maximizing the profit (with given transaction losses) on the technology set. We establish sufficient conditions for the existence of the equilibrium price vector, which are consequences of some theorems in the theory of covering mappings.