Emre Berk

Age-based vs. stock level control policies for a perishable inventory system

Abstract In this study, we investigate the impact of modified lotsize-reorder control policy for perishables which bases replenishment decisions on both the inventory level and the remaining lifetimes of items in stock. We derive the expressions for the key operating characteristics of a lost sales perishable inventory model, operating under the proposed age-based policy, and examine the sensitivity of the optimal policy parameters with respect to various system parameters. We compare the performance of the suggested policy to that of the classical ( Q , r ) type policy through a numerical study over a wide range of system parameters. Our findings indicate that the age-based policy is superior to the stock level policy for slow moving perishable inventory systems with high service levels.

Note on future supply uncertainty in EOQ models

We present an inventory model where the supply becomes randomly unavailable for random periods of time. We investigate the operating characteristics of the model, and we study the robustness of the optimal order quantity. Our work builds on Parlar and Berkin [2].

Analysis of the (Q, r) Inventory Model for Perishables with Positive Lead Times and Lost Sales

We consider a perishable inventory system with Poisson demands, fixed shelf lives, constant lead times, and lost sales in the presence of nonnegligible fixed ordering costs. The inventory control policy employed is the continuous-review (Q,r) policy, where r<Q. The system is modeled using an embedded Markov process approach by introducing the concept of the effective shelf life of a batch in use. Using the stationary distribution of the effective shelf life, we obtain the expressions for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determination of the policy parameters exactly as modeled herein results in significant improvements in cost rates with respect to a previously proposed heuristic. We also compare the (Q,r) policy with respect to a time-based benchmark policy and find that the (Q,r) policy might be impractical for rare events, but overall appears to be a good heuristic policy.

Bayesian demand updating in the lost sales newsvendor problem: A two-moment approximation

We consider Bayesian updating of demand in a lost sales newsvendor model with censored observations. In a lost sales environment, where the arrival process is not recorded, the exact demand is not observed if it exceeds the beginning stock level, resulting in censored observations. Adopting a Bayesian approach for updating the demand distribution, we develop expressions for the exact posteriors starting with conjugate priors, for negative binomial, gamma, Poisson and normal distributions. Having shown that non-informative priors result in degenerate predictive densities except for negative binomial demand, we propose an approximation within the conjugate family by matching the first two moments of the posterior distribution. The conjugacy property of the priors also ensure analytical tractability and ease of computation in successive updates. In our numerical study, we show that the posteriors and the predictive demand distributions obtained exactly and with the approximation are very close to each other, and that the approximation works very well from both probabilistic and operational perspectives in a sequential updating setting as well.

Supplier diversification under binomial yield

We consider supplier diversification in an EOQ type inventory setting with multiple suppliers and binomial yields. We characterize the optimal policy for the model and show that, in this case, it does not pay to diversify, in contrast to previous results in the random yield literature.

Analysis of maintenance policies for M machines with deteriorating performance

In this paper, we consider the maintenance scheduling of a group of M identical machines, the performance of which deteriorates with usage. Examples of such situations are frequently found in the heavy machine tooling, petro-chemical and semi-conductor industries among others. Assuming a limited maintenance resource and that the maintenance times are i.i.d., we propose a dynamic maintenance policy which utilities the information about the number of operating machines and their ages. We analyze the system for the special cases of constant and exponentially distributed maintenance times. We investigate the impact of maintenance time variability on system performance and evaluate the performance of various maintenance policies within the proposed policy class when the expected profit rate is maximized

The impact of small lot ordering on traffic congestion in a physical distribution system

In recent years, some managers and researchers have advocated reducing lot sizes by decreasing setup costs, arguing that smaller lot sizes improve quality while reducing inventory levels and associated holding costs. However, smaller lot sizes result in an increased number of shipments which, in turn, exacerbates traffic congestion. This results in longer delivery times and, thereby, higher inventory levels. In this paper we study the relation between lot sizes and traffic congestion by constructing a model with numerous retailers who share a common congested delivery road. Using a numerical example, we illustrate the models managerial implications with respect to several factors, including lot sizes, traffic congestion, and inventory levels. Our findings suggest that in a physical distribution system, if there are a relatively large number of retailers, no single retailer has an incentive to increase batch sizes because one retailers effect on reducing traffic congestion will be negligible. If all retailers increase their lotsizes, however, traffic congestion will be reduced and all retailers will experience lower costs.

Dynamic lot sizing problem for a warm/cold process

We consider a dynamic lot sizing problem with finite capacity for a process that can be kept warm until the next production period at a unit variable cost ω t only if more than a threshold value has been produced and is cold, otherwise. That is, the setup cost in period t is K t if x t−1 < Q t−1 and k t , otherwise (0 ≤ k t ≤ K t ). We develop a dynamic programming formulation of the problem, establish theoretical results on the structure of the optimal production plan and discuss its computational complexity in the presence of Wagner-Whitin-type cost structures. Based on our stuctural results, we present an optimal polynomial-time solution algorithm for k t = 0, and also show that an optimal linear-time solution algorithm exists for a special case. Our numerical study indicates that utilizing the undertime option (i.e., keeping the process warm via reduced production rates) results in significant cost savings, which has managerial implications for capacity planning and selection.

A Continuous Review Replenishment-Disposal Policy for an Inventory System with autonomous supply and fixed disposal costs

In this study, we analyze an inventory system facing stochastic external demands and an autonomous supply (independent return flow) in the presence of fixed disposal costs and positive lead times under a continuous review replenishment-disposal policy. We derive the analytical expressions of the operating characteristics of the system; and, construct the objective function to minimize the total expected costs of ordering, holding, purchasing and disposal per unit time subject to a fill rate constraint. An extensive numerical analysis is conducted to study the sensitivity of the policy parameters and the benefit of employing a policy which allows for disposal of excess stock in this setting. We model the net demand process as the superposition of normally distributed external demand and inflows, which is expressed as a Brownian motion process. Our findings indicate that the disposal option results in considerable savings even (i) in the presence of non-zero fixed disposal costs, (ii) large actual demand rates with high return ratios (resulting in small net demands) and (iii) for moderate return ratios with high demand variability.

Optimal Spacing of “Covered” and “Exposed” Time Intervals in a Stochastic Process with High Penalty Costs: Applications to Parking and Insurance

This paper studies a class of policies for a stochastic process that is constituted of several time intervals of total time T. The intervals can be covered (or insured) at a pay-per-use rate or exposed (uninsured) with the risk of a large penalty. A decision maker has the three options: (i) Pay the user fee for the full period, (ii) not pay at all, and (iii) sporadically pay a user fee leaving an uncovered period at the end of each covered one. The penalty risk is assumed to occur during an uncovered interval according to a Poisson process. We present the expected cost model and find the optimal coverage policy. We present conditions under which it is always optimal to pay in full or not pay at all to minimize the expected total cost. Finally, we relax two assumptions and allow for the consideration of setup costs for every time the decision maker pays the coverage fees as well as a random duration T and derive new conditions for optimal strategies. Possible application of our model is paying parking meter fees and deciding between self-insuring one’s property and buying full (or partial) insurance coverage.