Semra Ağralı

Modeling and analysis of an auction-based logistics market

We consider a logistics spot market where the transportation orders from a number of firms are matched with two types of carriers through a reverse auction. In the spot market, local carriers compete with in-transit carriers that have lower costs. In order to analyze the effects of implementing a logistics spot market on these three parties: firms, local carriers, and in-transit carriers and also the effects of various system parameters, we develop a two-stage stochastic model. We first model the auction in a static setting and determine the expected auction price based on the number of carriers engaging in the auction and their cost distributions. We then develop a continuous-time Markov chain model to evaluate the performance of the system in a dynamic setting with random arrivals and possible abandonment of orders and carriers. By combining these two models, we evaluate the performance measures such as the expected auction price, price paid to the carriers, distribution of orders between local and in-transit carriers, and expected number of carriers and orders waiting at the logistics center in the long run. We present analytical and computational results related to the performance of the system and discuss operation of such a logistics spot market in Turkey.

Solving knapsack problems with S-curve return functions

We consider the allocation of a limited budget to a set of activities or investments in order to maximize return from investment. In a number of practical contexts (e.g., advertising), the return from investment in an activity is effectively modeled using an S-curve, where increasing returns to scale exist at small investment levels, and decreasing returns to scale occur at high investment levels. We demonstrate that the resulting knapsack problem with S-curve return functions is NP-hard, provide a pseudo-polynomial time algorithm for the integer variable version of the problem, and develop efficient solution methods for special cases of the problem. We also discuss a fully-polynomial-time approximation algorithm for the integer variable version of the problem.

Joint Spare Parts Inventory and Reliability Decisions Under a Service Constraint

Reliability and inventory levels of spare parts are major factors that determine the service level for the maintenance of machines provided by original equipment manufacturers (OEMs). In general, decisions on reliability and stock levels are made separately in practice, and academic literature offers little guidance on how to jointly make these two decisions. In order to fill in the gap in the literature and provide guidance to OEMs, we jointly model reliability and inventory problems. We consider three different service measures: aggregate fill rate, average downtime per system per year and expected total number of long downs in a year. Our models minimize the sum of holding and emergency shipment costs subject to a limited reliability improvement budget and a target service level. We develop an algorithm that considers reliability and inventory decisions simultaneously, test our solution approach on real-life and randomly generated data sets and compare the results with an approach that considers reliability and inventory decisions sequentially. Numerical results show substantial benefits of integrating reliability and inventory decisions.

Deciding between carbon trading and carbon capture and sequestration: An optimisation-based case study for methanol synthesis from syngas

The economic and technical feasibility of carbon capture and sequestration (CCS) systems are gaining importance as CO2 emission reduction is becoming a more pressing issue for parties from production sectors. Public and private entities have to comply with national schemes imposing tighter limits on their emission allowances. Often these parties face two options as whether to invest in CCS or buy carbon credits for the excess emissions above their limits. CCS is an expensive system to invest in and to operate. Therefore, its feasibility depends on the carbon credit prices prevailing in the markets now and in the future. In this paper we consider the problem of installing a CCS unit in order to ensure that the amount of CO2 emissions is within its allowable limits. We formulate this problem as a non-linear optimisation problem where the objective is to maximise the net returns from pursuing an optimal mix of the two options described above. General Algebraic Modelling Systems (GAMS) software was used to solve the model. The results were found to be sensitive to carbon credit prices and the discount rate, which determines the choices with respect to the future and the present. The model was applied to a methanol synthesis plant as an example. However, the formulation can easily be extended to any production process if the CO2 emissions level per unit of physical production is known. The results showed that for CCS to be feasible, carbon credit prices must be above 15 Euros per ton. This value, naturally, depends on the plant-specific data, and the costs we have employed for CCS. The actual prices (≈5 Euros/ton CO2) at present are far from encouraging the investors into CCS technology.

A single-resource allocation problem with Poisson resource requirements

We consider a stochastic resource allocation problem that generalizes the knapsack problem to account for random item weights that follow a Poisson distribution. When the sum of realized weights exceeds capacity, a penalty cost is incurred. We wish to select the items that maximize expected profit. We provide an effective solution method and illustrate the advantages of this approach via computational experiments.

A facility location model with safety stock costs: analysis of the cost of single-sourcing requirements

We consider a supply chain setting where multiple uncapacitated facilities serve a set of customers with a single product. The majority of literature on such problems requires assigning all of any given customer’s demand to a single facility. While this single-sourcing strategy is optimal under linear (or concave) cost structures, it will often be suboptimal under the nonlinear costs that arise in the presence of safety stock costs. Our primary goal is to characterize the incremental costs that result from a single-sourcing strategy. We propose a general model that uses a cardinality constraint on the number of supply facilities that may serve a customer. The result is a complex mixed-integer nonlinear programming problem. We provide a generalized Benders decomposition algorithm for the case in which a customer’s demand may be split among an arbitrary number of supply facilities. The Benders subproblem takes the form of an uncapacitated, nonlinear transportation problem, a relevant and interesting problem in its own right. We provide analysis and insight on this subproblem, which allows us to devise a hybrid algorithm based on an outer approximation of this subproblem to accelerate the generalized Benders decomposition algorithm. We also provide computational results for the general model that permit characterizing the costs that arise from a single-sourcing strategy.

A dynamic uncapacitated lot-sizing problem with co-production

We consider an extension of the dynamic uncapacitated lot-sizing problem to account for co-production, where multiple products are produced simultaneously in a single production run. We formulate the problem as a mixed-integer linear programming problem. We then show that a variant of the well-known zero-inventory property holds for this problem, and use this property to extend a dynamic program given for the single-item lot-sizing to solve the problem with co-production. Finally, we provide an illustrative example for our approach.

An optimization model for carbon capture & storage/utilization vs. carbon trading: A case study of fossil-fired power plants in Turkey

We consider fossil-fired power plants that operate in an environment where a cap and trade system is in operation. These plants need to choose between carbon capture and storage (CCS), carbon capture and utilization (CCU), or carbon trading in order to obey emissions limits enforced by the government. We develop a mixed-integer programming model that decides on the capacities of carbon capture units, if it is optimal to install them, the transportation network that needs to be built for transporting the carbon captured, and the locations of storage sites, if they are decided to be built. Main restrictions on the system are the minimum and maximum capacities of the different parts of the pipeline network, the amount of carbon that can be sold to companies for utilization, and the capacities on the storage sites. Under these restrictions, the model aims to minimize the net present value of the sum of the costs associated with installation and operation of the carbon capture unit and the transportation of carbon, the storage cost in case of CCS, the cost (or revenue) that results from the emissions trading system, and finally the negative revenue of selling the carbon to other entities for utilization. We implement the model on General Algebraic Modeling System (GAMS) by using data associated with two coal-fired power plants located in different regions of Turkey. We choose enhanced oil recovery (EOR) as the process in which carbon would be utilized. The results show that CCU is preferable to CCS as long as there is sufficient demand in the EOR market. The distance between the location of emission and location of utilization/storage, and the capacity limits on the pipes are an important factor in deciding between carbon capture and carbon trading. At carbon prices over

Mathematical Programming-Based Sales and Operations Planning at Vestel Electronics

15/ton, carbon capture becomes preferable to carbon trading. These results show that as far as Turkey is concerned, CCU should be prioritized as a means of reducing nation-wide carbon emissions in an environmentally and economically rewarding manner. The model developed in this study is generic, and it can be applied to any industry at any location, as long as the required inputs are available.

Modeling of carbon credit prices using regime switching approach

We investigate the sales and operations planning S&OP process at Vestel Electronics, a major television manufacturer located in Turkey. The company has a large product portfolio because its products have many configuration options, and its product portfolio changes rapidly as a result of technological advances. Demand volatility is high, and materials procurement requires long lead times. Hence, the S&OP process is critical for efficient management of company resources and its supply chain and to ensure customer satisfaction. We devise a mathematical programming formulation for Vestels S&OP process and describe our experience in implementing a decision support system DSS based on our optimization model. We fully implemented and deployed our DSS at Vestel, which has used it every day since 2011.