## Contributed Session Tue.3.H 3027

#### Tuesday, 15:15 - 16:45 h, Room: H 3027

**Cluster 7: Finance & economics** [...]

### Applications and algorithms

**Chair: Galina Vakulina**

**Tuesday, 15:15 - 15:40 h, Room: H 3027, Talk 1**

**Emilie Joannopoulos**

Feeding cost optimization of several diet formulations and environmental impact in the swine industry

**Coauthors: François Dubeau, Jean-Pierre Dussault, Candido Pomar**

**Abstract:**

The diet formulation is a classic example of mathematical programming. We present several new models applied to the swine industry, where feed represent more than 70% of the total production cost, and compare the cost and environmental impact with the traditional feeding solution. Modern producers feed pigs with a 3 phases system with fixed energy rate. First, we will explain the classic and multiphase feeding models. This last one is unrealistic in practice so we introduce two formulation, one so called fixed and the other so called free. The so called free premix model departs from the traditional linear programming formulation in tackling simultaneously the diet's premix contents and the daily proportions, resulting in a bi-linear formulation. Just by using a daily phase feeding system and two premixes, producers already save. Deeper analysis of the problem revealed that the cost of a premix increases with its energy rate. So we finally present the unfixed energy rate model and show how it is related to the previously presented models. The free energy rate free premix bi-linear model appears to give substantial improvements over more traditional solutions.

**Tuesday, 15:45 - 16:10 h, Room: H 3027, Talk 2**

**Takahashi Satoshi**

2-approximation algorithms for the winner determination problem in VCG based single-item multi-unit auctions

**Coauthors: Yoichi Izunaga, Maiko Shigeno, Satoshi Takahashi, Naoki Watanabe**

**Abstract:**

This paper studies the winner determination problem in Vickrey-Clarke-Groves (VCG) based single-item multi-unit auctions: given a set of bids in such an auction, find an allocation of units of an item to bidders that maximizes the seller's revenue. (The seller can keep some units of the item.) This problem is known to be NP-hard. We thus propose two simple 2-approximation algorithms for the problem. One is a linear time algorithm and the other is a greedy algorithm.

Numerical experiments and human subject experiments were conducted to evaluate the computational efficiency and economic efficiency of these approximation algorithms.

Our results are as follows. (1) Approximate ratios of the algorithms are at least 95% in numerical experiments. (2) Under-bidding was observed in human subject experiments although the VCG mechanism theoretically induces bidders to tell their valuation truthfully.

**Tuesday, 16:15 - 16:40 h, Room: H 3027, Talk 3**

**Galina Vakulina**

Project risks analysis using approach of fuzzy sets theory

**Abstract:**

The report presents a method of analysis of the riskiness of the project

using fuzzy sets. The net present value or NPV used as the main

indicator of the effectiveness of the project. If the NPV takes value

less than zero, the project is considered to be ineffective. The main

objective of the work is describing a method to calculate the

probability that the project will be ineffective. The method is to

consider all the variables of the system as fuzzy numbers with certain

characteristics. Function NPV can be represented as a combination of

fuzzy parameters and is is also a fuzzy number. Different versions of

membership functions that can describe the parameters of the project and

the number of NPV can be considered. The

method is used in practice for the proposed business plan of the project.