Mahmut Parlar

A survey of maintenance models for multi-unit systems

This paper surveys the literature related to optimal maintenance and replacement models for multi-unit systems. The emphasis is on work appearing since the 1976 survey A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems by W.P. Pierskalla and J.A. Voelker. The literature is divided into five topical categories: machine interference/ repair models, group/ block/ cannibalization/ opportunistic models, inventory/ maintenance models, other maintenance/ replacement models, and inspection/ maintenance models. This paper also provides the reader with a quick guide to a variety of classification schemes. Each of the alternative classification schemes also provides an indication as to the categorization of each of the surveyed articles.

Game theoretic analysis of the substitutable product inventory problem with random demands

This article uses game theoretic concepts to analyze the inventory problem with two substitutable products having random demands. It is assumed that the two decision makers (players) who make ordering decisions know the substitution rates and the demand densities for both products. Since each players decision affects the others single‐period expected profit, game theory is used to find the order quantities when the players use a Nash strategy (i.e., they act rationally). We prove the existence and uniqueness of the Nash solution. It is also shown that when one of the players acts irrationally for the sole purpose of inflicting maximum damage on the other, the maximin strategy for the latter reduces to using the solution for the classical single‐period inventory problem. We also discuss the cooperative game and prove that the players always gain if they cooperate and maximize a joint objective function.

Periodic Review Production Models With Variable Yield And Uncertain Demand

Abstract A periodic-review production model with variable yield (uncertain supply) and uncertain demand is formulated and investigated. First, we provide a complete analysis of the final (single) period problem. The order point turns out to be unaffected by the yield distribution, but the expected yield corresponding to optimal lot size generally does not equal the difference between the order point and initial stock. We then explore properties of the two-period problem, the solution of which is generally non-myopic. Finally, the solution structure of the n-period problem is reported.

Continuous-review inventory problem with random supply interruptions

Abstract This paper considers a continuous-review stochastic inventory problem with random demand and random lead-time where supply may be disrupted due to machine breakdowns, strikes or other randomly occurring events. The supplier availability is modelled as a semi-Markov process (more specifically, as an alternating renewal process). The standard ( q, r ) policy is used when the supplier is available (ON), i.e., when the inventory position reaches the reorder point r, q units are ordered to raise the inventory position to the target level of R = q + r . The form of the policy changes when the supplier becomes unavailable (OFF) in which case orders cannot be placed when the reorder point r is reached. However, as soon as the supplier becomes available again one orders enough to bring the inventory position up to the target level of R . The regenerative cycles are identified by observing the inventory position process. We construct the average cost per time objective function using the renewal reward theorem. It is assumed that the duration of the ON period is E k (i.e., k -stage Erlangian) and the OFF period is general. In analogy with queuing notation we call this an E k /G system. By employing the ‘method of stages’, we obtain a problem with a larger state space for the ON/OFF stochastic process; but the resulting ON process can now be analyzed using Markovian techniques. For asymptotic values of q , the objective function assumes a particularly simple form which is shown to be convex under mild restrictions on the density functions of demand. Numerical examples illustrate the results.

Game theoretic applications in supply chain management : a review

Abstract Recent emphasis on competition and cooperation in supply chains has resulted in the resurgence of game theory as a relevant tool for analyzing such interactions in a supply chain. This paper presents a review of more than 130 papers concerned with game theoretical applications in supply chain management (SCM). We first give a brief summary of the basic solution concepts in non-cooperative and cooperative games such as Nash and Stackelberg equilibria, Nash arbitration scheme and cooperation with sidepayments. the core, the Shapley value and nucleolus. Our review of supply chain-related game theoretical applications is presented in five areas: (i) Inventory games with fixed unit purchase cost, (ii) Inventory games with quantity discounts, (iii) Production and pricing competition, (iv) Games with other attributes, (v) Games with joint decisions on inventory, production/pricing and other attributes. The paper concludes with a summary of our review, suggestions for potential applications of game theory in SCM and an alternative classification of all reviewed papers.

Inventory models with unreliable suppliersin a random environment

We consider infinite‐horizon periodic‐review inventory models with unreliable suppliers where the demand, supply and cost parameters change with respect to a randomly changing environment. Although our analysis will be in the context of an inventory model, it is also appropriate for production systems with unreliable machines where planning is done on a periodic basis. It is assumed that the environmental process follows a Markov chain. The stock‐flow equations of the inventory system subject to environmental fluctuations is represented using a two‐dimensional stochastic process. We show that an environment‐dependentorder‐up‐to level (i.e., base‐stock) policy is optimal when the order cost is linearin order quantity. When there is also a fixed cost of ordering, we show that a two‐parameter environment‐dependent (s, S) policy is optimal under reasonable conditions. We also discuss computational issues and some extensions.

Diversification under yield randomness in inventory models

Abstract In this paper we consider the case of random yield and diversification in two different inventory models. It is assumed that two sources (suppliers) exist who ship an amount which is a random function of the amount requisitioned. Since they may charge different prices and their reliability (in terms of the variance of the yield random variable) may be different, diversification may be more desirable than using a single supplier. We analyze this problem for both the EOQ model and the newsboy model. Analytic results for the optimal order quantities and the minimum cost are obtained for the EOQ model. Convexity of the objective function is also discussed. We develop the necessary conditions for the newsboy model and propose an approximate solution technique. The concavity of the expected profit function is shown. Numerical examples are provided for both models.

An Inventory Problem with Two Randomly Available Suppliers

This paper considers a stochastic inventory model in which supply availability is subject to random fluctuations that may arise due to machine breakdowns, strikes, embargoes, etc. It is assumed that the inventory manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each suppliers availability is modeled as a semi-Markov (alternating renewal) process. We assume that the durations of the ON periods for the two suppliers are distributed as Erlang random variables. The OFF periods for each supplier have a general distribution. In analogy with queuing notation, we call this an Es1[Es2]/G1[G2] system. Since the resulting stochastic process is non-Markovian, we employ the “method of stages” to transform the process into a Markovian one, albeit at the cost of enlarging the state space. We identify the regenerative cycles of the inventory level process and use the renewal reward theorem to form the long-run average cost objective function. Finite time transition fun...

DISCOUNTING DECISIONS IN A SUPPLIER-BUYER RELATIONSHIP WITH A LINEAR BUYER'S DEMAND

In this paper, we analyze discounting decisions for a supplier with a group of homogeneous customers. We focus on two aspects: the gaming nature of the discount problem and the demand consideration in the process. We use a general quantity discount schedule and start with the Stackelberg equilibrium of the problem. It is shown that, for the seller to gain from quantity discount, he has to set up his quantity discount schedule such that the buyer will order more than his EOQ. Both the seller and the buyer can gain significantly from quantity discount. The incentive for discount is twofold: reducing inventory related cost and attracting more demand from the customers. In addition, quantity discount schedule can be very efficient in obtaining the maximum gain the seller and the buyer can possibly obtain together.

Pricing and Lead Time Decisions in Decentralized Supply Chains

This paper studies a decentralized supply chain consisting of a supplier and a retailer facing price-and lead-time-sensitive demands. A Stackelberg game is constructed to analyze the price and lead time decisions by the supplier as the leader and the retailer as the follower. The equilibrium strategies of the two players are obtained. Using the performance of the corresponding centralized system as a benchmark, we show that decentralized decisions in general are inefficient and lead to inferior performance due to the double marginalization effect. However, further analysis shows that the decision inefficiency is strongly influenced by market and operational factors, and if the operational factors are dominating, it may not be significant. This shows that before pursuing a coordination strategy with retailers, a supplier should first improve his or her own internal operations.