Browsing by Subject "Inventory control--Mathematical models."

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Open Access
Analyzing the effect of consumer returns in a multi-period inventory system
(2012) Erikçi, İsmail
Return of a sold item by a customer becomes tremendously common situation in many industries. Increase in the amount of returned items promotes return information to be a critical factor for inventory control. Undoubtedly another critical parameter for an inventory system is the length of the review period. Effect of the review period or length of the time-bucket is amplified with returned items, because available return information at a decision point is related to the frequency of the review. In this study, we analyze the effects of these two parameters over a multiperiod inventory system where the length of a time horizon is fixed. Dynamic programming approach is used to calculate the optimal inventory positions. In dynamic programming, it is assumed that a fixed proportion of sold items are returned. Computational results are obtained to compare the effects of return information under different return proportions and period lengths. These results are used to conduct various analyses to explore the level of the advantage gained by using return information.
Open Access
An application of Silver Meal Heuristic to MRP lot sizing decisions at Turk Traktor Fabrikasi
(1995) Esmer, Berkhan N.
MRP does not consider setup and inventory holding costs for lot sizing but very quick algorithms like Silver-Meal can be used for lot sizing decisions. A module to apply Silver-Meal Heuristic to manufacturing work order releases at Türk Traktör Fabrikasy, Ankara, Turkey is designed and tested for 3 months. The module processes demand for finished goods, determines lot sizes, checks capacities by loading machines according to the schedule and reports the setup, inventory holding and overtime costs. These cost figures are compared with the MRP lot sizes. It is observed that, the planning time decreased by 90% by designing module in PCs connected to the main databases, and the total costs decreased by 50%.
Open Access
Carbon restricted newsvendor problem under CVAR objective and resource constraints
(2014) Korkmaz, Özüm
Newsboy problem has been studied in the literature extensively. The classical newsvendor, representing the risk neutral decision maker, determines the optimal order/production quantity by maximizing the expected profit or minimizing the expected total cost of a single period with stochastic demand. This approach is not suitable if one also aims to reduce the chances of facing unexpected losses due to demand uncertainty. In this thesis, two problems are investigated with a single product newsvendor under CVaR maximization objective. The first problem addresses the newsvendor model with two different carbon emission reduction policies, namely, mandatory emission allowance and carbon emission trading mechanism. In the second problem, as an extension of the first one, a newsvendor with multiple resource constraints is considered for the cases where the resources have quotas with trade options. Analytical expressions for optimal order/production quantities are determined together with the optimal trading policy and numerical examples are provided.
Open Access
Continuous time control of make-to-stock production systems
(2010) Bulut, Önder
We consider the problem of production control and stock rationing in a make-tostock production system with multiple servers –parallel production channels--, and several customer classes that generate independent Poisson demands. At decision epochs, in conjunction with the stock allocation decision, the control specifies whether to increase the number of operational servers or not. Previously placed production orders cannot be cancelled. We both study the cases of exponential and Erlangian processing times and model the respective systems as M /M /s and M /Ek /s make-to-stock queues. We characterize properties of the optimal cost function, and of the optimal production and rationing policies. We show that the optimal production policy is a state-dependent base-stock policy, and the optimal rationing policy is of state-dependent threshold type. For the M /M /s model, we also prove that the optimal ordering policy transforms into a bang-bang type policy when we relax the model by allowing order cancellations. Another model with partial ordercancellation flexibility is provided to fill the gap between the no-flexibility and the full-flexibility models. Furthermore, we propose a dynamic rationing policy for the systems with uncapacitated replenishment channels, i.e., exogenous supply systems. Such systems can be modeled by letting s --the number of replenishment channels-- go to infinity. The proposed policy utilizes the information on the status of the outstanding replenishment orders. This work constitutes a significant extension of the literature in the area of control of make-to-stock queues, which considers only a single server. We consider an arbitrary number of servers that makes it possible to cover the spectrum of the cases from the single server to the infinite servers. Hence, our work achieves to analyze both the exogenous and endogenous supply leadtimes.
Open Access
A dynamic pricing policy for perishables with stochastic demand
(2001) Yıldırım, Gonca
III this study, we consider the pricing of perishables in an inventory system where items have a fixi'd lifetime. Unit demands come from a Poisson Process with a price-dependent rate. The instances at which an item is withdrawn from inventory due to demand constitute decision epochs for setting the sales price; the time elapsed between two such consecutive instances is called a period. The sales price at each decision epoch is taken to be a lunction of Tj denoting the remaining lifetime when tin' inventory level drops to z, i = 1,...,Q. The objective is to determine the optimal pricing policy (under the proposed class) and the optimal initial stocking level to maximize the discounted expected profit. A Dynamic Programming approach is used the solve the problem numerically. Using the backward recursion, the optimal price paths are determined for the discounted expected profit for various combinations of remaining lifetimes. Our numerical studies indicate that a single price policy results in significantly lower profits when compared with our formulation.
Open Access
Essays on non-cooperative inventory games
(2012) Körpeoğlu, Evren
In this thesis we study different non–cooperative inventory games. In particular, we focus on joint replenishment games and newsvendor duopoly under asymmetric information. Chapter 1 contains introduction and motivation behind the research. Chapter 2 is a preliminary chapter which introduce basic concepts used in the thesis such as Nash equilibrium, Bayesian Nash equilibrium and mechanism design. In Chapter 3, we study a non-cooperative game for joint replenishment of multiple firms that operate under an EOQ–like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We consider two variants of the participation-contribution game: in the single–stage variant, participation and contribution decisions are made simultaneously, and, in the two-stage variant, participating firms become common knowledge at the contribution stage. We characterize the behavior and outcomes under undominated Nash equilibria for the one-stage game and subgame-perfect equilibrium for the two-stage game. In Chapter 4, we extend the private contributions game to an asymmetric information counterpart. We assume each firm only knows the probability distribution of the other firms’ adjusted demand rates (demand rate multiplied by inventory holding cost rate). We show the existence of a pure strategy Bayesian Nash equilibrium for the asymmetric information game and provide its characterization. Finally, we conduct some numerical study to examine the impact of information asymmetry on expected and interim values of total contributions, cycle times and total costs. quantities for all firm types except the type that has the highest possible unit cost, who orders the same quantity as he would as a monopolist newsboy. Consequently, competition leads to higher total inventory in the industry. A firm’s equilibrium order quantity increases with a stochastic increase in the total industry demand or with an increase in his initial allocation of the total industry demand. Finally, we provide full characterization of the equilibrium, corresponding payoffs and comparative statics for a parametric special case with uniform demand and linear market shares.
Open Access
Final phase inventory management of spare parts under nonhomogeneous poisson demand rate
(2013) Çay, Sertalp Bilal
In product lifecycle, there are three phases, initial phase, normal phase and final phase. Final phase begins when the product is out of production, and ends when the last contract expires. It is generally the longest period in the lifecycle. Although the product is not manufactured any more, spare parts of the product need to be supplied to the market. Firms need to provide these parts at the retailer level until the end of the phase due to legal responsibilities. Because of lack of historical data and unavailability of forecasting, retailers need a systematic policy to decide replenishment quantity and time to prevent excessive holding, backordering, unit and setup costs. In our problem, we assume that demand of the spare part is a non-homogeneous Poisson process where the rate parameter is a non-increasing function of time. We consider all costs and lead time are fixed and known. Due to characteristics of the final phase, the planning horizon is taken as finite and known. In this study, we developed two alternative heuristics for retailer’s problem to minimize total cost during the final phase. First heuristic is a continuous-review policy based on estimation of future replenishments by solving series of deterministic demand subproblems. Second heuristic is a periodic-review policy with variable period lengths, which solves myopic problems, by selecting subsequent time points to check inventory position. We also developed a simulation model to evaluate performances of the heuristics. This study provides an efficient way to decide on replenishment quantity and time. Limited numerical results show that heuristics provide near-optimal results for homogeneous cases studied in the literature. Moreover, this is one of the initial studies that considers final phase with non-homogeneous demand rate. In that sense, it makes a contribution to the literature of final phase problems and provides a systematic way of replenishment decisions for the retailers.
Open Access
Financial valuation of flexible supply chain contracts
(2008) Erön, Ali Gökay
We consider a single buyer - single supplier multiple period quantity flexibility contract in which the buyer has options to buy in case of a higher than expected demand in addition to the committed purchases at the beginning of each period of the contract. We take the buyer’s point of view and find the maximum value of the contract for the buyer by analyzing the financial and real markets simultaneously. We assume both markets evolve as discrete scenario trees. Furthermore, under the assumption that the demand of the item correlates perfectly with the price of the risky security we present a model to find the buyer’s maximum acceptable price of the contract. Applying duality, we develop sufficient conditions on some parameters to decrease the value of the contract. Then, an experimental study is presented to illustrate the impacts of all the parameters on the value of the contract and the option. We show that the model can also be extended to the case of partially correlated demand and the risky asset price under the assumption that the markets evolve as binomial trees. Finally, we apply duality and perform numerical analysis for the latter assumption.
Open Access
Finite perturbation analysis methods for optimization of periodic (s, S) inventory control systems
(2008) Mert, Erdinç
We are dealing with single item inventory systems where the period time is constant and the unsatisfied demands are backordered. The demands are independent and identically distributed random variables, but the distribution of those variables are not known. The total cost of a period consists of; ordering cost "K" which is independent of the ordering quantity, holding cost "h" for each item that remains in stock, and penalty cost "p" for the each backordered item. In the considered system, it is known that when the parameters of an (s,S) inventory policy are chosen appropriate, then the expected period cost can be minimized. There are some exact methods or heuristics for finding the optimal s and S parameters in the literature for the case where the demand distribution is known. In our study, we introduce a perturbation analysis based method for finding the optimal s and S parameters where the demand distribution is not known. Our method anticipates the sensitivity of (s,S) parameters to the period cost for the observed demand quantities. This method's performance is compared with a method that uses Integer Programming with the past data and with a method that calculates the mean and standard variation values with the past data and feeds them to the Ehrhardt's Heuristic.
Open Access
Impact of product variety on inventory performance : an empirical analysis of pharmaceutical and medical device industries
(2012) Aydınlı, Ali Yağmur
In this thesis, we construct empirical models to analyze the effect of various financial measures and product variety on inventory performance. We apply multiple regression models and simultaneous equations models using 2010 financial data for 128 U.S. firms in pharmaceutical and medical device industries. Using multiple regression models, we investigate the correlation of inventory turnover with product variety, gross margin, capital intensity and type of the firm. Product variety data are obtained from U.S. Food and Drug Administration. The best multiple regression model explains 38.50% of the total variation in inventory turnover and we observe that inventory turnover is negatively correlated with product variety. Since inventory turnover is the ratio of cost of goods sold (sales) to inventory level, a change in product variety might have an effect both on inventory level and cost of goods sold. In order to investigate the effects of product variety on cost of goods sold and inventory level separately, we employ simultaneous equation models. The best simultaneous equation model explains 96.22% of the variation in inventory level and shows that inventory level is positively associated with product variety.
Open Access
Integrated machine-scheduling and inventory planning of door manufacturing operations at OYAK Renault factory
(2012) Bozkaya, Nurcan
A car passes through press, body shell, painting and assembly stages during its manufacturing process. Due to the increased competition among car manufacturers, they aim to continuously advance and improve their processes. In this study, we analyze planning operations for the production of front/back and left/right doors in body shell department of Bursa Oyak-Renault factory and propose heuristic algorithms to improve their planning processes. In this study, we present four different mathematical models and two heuristics approaches which decrease the current costs of the company particularly with respect to inventory carrying and setup perspectives. In the body shell department of the company, there are two parallel manufacturing cells which produces doors to be assembled on the consumption line. The effective planning and scheduling of the jobs on these lines requires solving the problem of integrated machine-scheduling and inventory planning subject to inclusive eligibility constraints and sequence independent setup times with job availability in flexible manufacturing cells of the body shell department. The novelty in the models lie in the integration of inventory planning and production scheduling decisions with the aim of streamlining operations of the door manufacturing cells with the consumption line. One of the proposed heuristic approaches is Rolling Horizon Algorithm (RHA) which divides the planning horizon into sub-intervals and solves the problem by rolling the solutions through sub-intervals. The other proposed algorithm is Two-Pass Algorithm which divides the planning horizon into sub-intervals and solves each sub-problem in each sub-interval to optimality for two times by maintaining the starting and ending inventory levels feasible. These approaches are implemented with Gurobi optimization software and Java programming language and applied within a decision support system that supports daily planning activities.
Open Access
Integration of production, transportation and inventory decisions in supply chains
(2012) Koç, Utku
This dissertation studies the integration of production, transportation and inventory decisions in supply chains, while utilizing the same vehicles in the inbound and outbound. The details of integration is studied in two levels: operational and tactical. In the first part of the thesis, we provide an operational level model for coordination of production and shipment schedules in a single stage supply chain. The production scheduling problem at the facility is modelled as belonging to a single process. Jobs that are located at a distant origin are carried to this facility making use of a finite number of capacitated vehicles. These vehicles, which are initially stationed close to the origin, are also used for the return of the jobs upon completion of their processing. In the first part, a model is developed to find the schedules of the facility and the vehicles jointly, allowing effective utilization of the vehicles for both in the inbound and outbound transportation. In the second part of the dissertation, we provide a tactical level model and study a manufacturer’s production planning and outbound transportation problem with production capacities to minimize transportation and inventory holding costs. The manufacturer in this setting can use two vehicle types for outbound shipments. The first type of vehicle is available in unlimited number. The availability of the second type, which is less expensive, changes over time. For each possible combination of operating policies affecting the problem structure, we either provide a pseudo-polynomial algorithm for general cost structure or prove that no such algorithm exists even for linear cost structure. We develop general optimality properties, propose a generic model formulation that is valid for all problems and evaluate the effects of the operating policies on the system performance. The third part of the dissertation considers one of the problems defined in the second part in detail. Motivated by some industry practices, we present formulations for three different solution approaches, which we refer to as the uncoordinated solution, the hierarchically-coordinated solution and the centrallycoordinated solution. These approaches vary in how the underlying production and transportation subproblems are solved, i.e., sequentially versus jointly, or, heuristically versus optimally. We provide intractability proofs or polynomialtime exact solution procedures for the subproblems and their special cases. We also compare the three solution approaches to quantify the savings due to integration and explicit consideration of transportation availabilities.
Open Access
Inventory control system: a case study
(1992) Kocaoğlu, Neriman
There are two objectives of inventory control system. The first one is to maximize the level of the costumer service by having the right goods in sufficient quantities, in the right place, and at the right time. The other is to minimise the cost of providing the right level of customer service. The inventory problem is to determine an ordering policy, determinig when to order and how much to order. In this study,an ordering policy is attempted to be determined for a small merchandise company. The A B C approach is one method to classify inventory items according to their importance. Different ordering policies could be used according to the result of A-B-C classification. The required data are collected and processed in order to determine the ordering polic for each item.
Open Access
An inventory model for randomly perishing goods
(2000) Yüksel, Banu
In this study, we consider an (s, S) ordering policy with backordering for a continuous review inventory system, where the items have a random shelflife. Assuming zero lead time and no decay until the shelflife, we derive the exact expressions for both unit and random batch demand cases with renewal demand arrivals. We present some analytical results on the cost rate function for unit demand case. A detailed numerical analysis is also provided to investigate the performance of the model which incorporates the random shelflife and comparisons with flxed shelflife are given.
Open Access
A joint pricing and replenishment policy for perishable products with fixed shelf life and positive lead times
(2009) Bayramoğlu, Könül
Most of the existing inventory models in the literature are based on the assumption that the items have infinite shelf life and do not deteriorate no matter how long they stay on the shelf. However this assumption may not be applicable in many situations since there are also many types of products with limited shelf lives. In the inventory literature stored items with fixed finite lifetimes are usually referred to as perishable items. Examples of perishable products include fresh foods, medical products, whole-blood units, packaged chemical products and photographic films. In this study, we consider the joint pricing and ordering policy, (Q, r, P1, P2), for an inventory model with perishable items, with constant shelf lives and positive lead times. The demand process is assumed to be Poisson. If there is a single batch on hand, the items in a batch are sold at price P1. If there are two batches in stock, the items in the older batch are sold at price P2, where P1 > P2. The younger batch is not sold until the older one is totally depleted. Although the shelf lives are constant, the sequence of remaining shelf lives of the items at the instances where stock level hits Q, is a random sequence. The limiting distribution of this sequence is obtained and the analytical derivations of the operating characteristics of the model is based on this limiting distribution. Numerical results are also presented.
Open Access
Multicriteria ABC classification with AHP method: an application
(1996) Erdinç, Emrah
The traditional ABC classification is an inventory management technique that is applied by many companies in different industries. The method classifies the items in the inventory as class A. B. and C. The classification enables the managers to exert different levels of control on each class according to their importance for the company. Class A is constituted of the most important items and class C is constituted of the least important ones. Class B items have intermediate importance for the company. The Traditional ABC Classification method uses only one criterion in order to classify the items, however management may need to consider multiple criteria. The Multicriteria ABC Classification method provides a solution to this problem. This method also enables the managers to incorporate their judgments into the analysis. In this thesis both the traditional and the multicriteria ABC classification methods are applied to the inventory of a Turkish pharmaceutical company and the results are compared. The Analytic Hierarchy Process (AHP) technique is utilized in order to conduct the multicriteria inventory classification.
Open Access
On the newsvendor problem with multiple inputs under a carbon emission constraint
(2012) Sözüer, Sibel
In this thesis, we consider two problems in the newsvendor setting with multiple inputs, under a carbon emission constraint and non-linear production functions. In the first problem, we assume a strict carbon cap and find the optimal production quantity and input allocation that will maximize the expected profit under this constraint. In the second problem, we consider an emission trading scheme where an advance purchase of carbon emission permits is made at an initial price before the random demand is realized. When the demand is realized and new carbon trade prices are revealed, it is possible to buy additional permits or to sell an excess amount. The aim is to decide on the optimal allocation of the inputs as well as the carbon trading policy so as to maximize the expected profit. In both problems, the production quantity is linked to multiple inputs via the Cobb-Douglas and Leontief production functions. Optimal policy structures are derived and numerical examples are provided.
Open Access
Order quantity and pricing decisions in linear cost inventory systems
(1992) Polatoglu, Lutfi Hakan
The primary concern of this study is to reveal the fundamental characteristics of the linear cost inventory model where price is a decision variable in addition to procurement quantity. In this context, the optimal solution must not only strike a balance between leftovers and shortages, but also simultaneously search for the best pricing alternative within the low price high demand and high price low demand tradeoff. To some extent, this problem has been studied in the literature. However, it seems that, there is a need to improve the model in order to understand the decision process better. To this end, optimal decisions must be characterised under a more general problem setting than it has been assumed in the existing models. In this study, we employ such a general model. The overall decision problem can be formulated under a dynamic programming structure. It follows that, the single period model is the basis of this periodic decision model. For this reason, we concentrate first on this problem. Having characterised the optimal solution to this basic model we extend the decision model to account for the multi-period setting. It is established with the results of this study that the decision problem in question is understood better. It is found that the characteristics of the optimal decision under the proposed model can be substantially different from the properties of the optimal solution of the corresponding classical model where there is no pricing decision. The primary reason for this is the fact that when there is a shortage in any period, the price that is set in this period could affect the future revenue which must be accounted in the overall decision problem. That is in a general model, price is an information which has an economic value that is transferred from one period to another just like transfering inventories or backlogs to future periods.
Open Access
Sales forecast inaccuracy and inventory turnover performance : an empirical analysis of US retail sector
(2010) Hançerlioğulları, Gülşah
We develop an empirical model to investigate the impact of various financial measures on inventory turnover performance. In particular, we used inaccuracy of quarterly sales forecasts as a proxy for demand uncertainty and study its impact on firm level inventory turnover ratios. The model is implemented on a sample financial data for 304 publicly listed U.S. retail firms for the 25-year period 1985-2009. Controlling for the effects of retail sub-segments and year, it is found that inventory turnover is negatively correlated with mean absolute percentage error in sales forecast and gross margin, and positively correlated with capital intensity and sales surprise. In addition to providing managerial insights regarding the determinants of a major operational performance metric, our results can also be used to benchmark a retailer’s inventory performance against its competitors.