Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.     

Optimal ordering policies for continuous review perishable inventory models

This paper extends the notions of perishable inventory models to the realm of continuous review inventory systems. The traditional perishable inventory costs of ordering, holding, shortage or penalty, disposal and revenue are incorporated into the continuous review framework. The type of policy that is optimal with respect to long run average expected cost is presented for both the backlogging and lost-sales models. In addition, for the lost-sales model the cost function is presented and analyzed.     

A discrete time markovian inventory model for perishable commodities

In this paper, we analyze a Markovian inventory model for perishable commodities, in which the arrivals of items into the system as well as the demands for these items are assumed to be discrete r.v.'s having a common support {0, 1,…}. Each item in the system is classified into one of N age categories. New items arriving in the system are placed into the first age category. Items of age category j, j = 1,…, N-l, which have not been removed by demand during a day, are placed into age category j+1 at the beginning of the next day. Items of age N, which have not been removed by demand, are registered as outdates. Results concerning the characteristics of such a model are derived for the case of two and three age categories.     

Weak aggregating algorithm for the distribution-free perishable inventory problem

We formulate the multiperiod, distribution-free perishable inventory problem as a problem of prediction with expert advice and apply an online learning method (the Weak Aggregating Algorithm) to solve it. We show that the asymptotic average performance of this method is as good as that of any time-dependent stocking rule in a given parametric class.     

A controlled M / G / 1 workload process with an application to perishable inventory systems

We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload . The result is used to obtain the overflow distribution of this controlled workload process; we derive and , where T is the duration of the first cycle. W(t) can be linked to a certain perishable inventory model, and we use our results to determine the distribution of the duration of an empty period.D. Perry was supported by a Mercator Fellowship of the Deutsche Forschungsgemeinschaft.     

A perishable inventory system with service facility and finite source

In this article, we consider a continuous review (s,S)$(s\text{,}S)$ perishable inventory system with a service facility, wherein the demand of a customer is satisfied only after performing some service on the item which is assumed to be of random duration. We also assume that the demands are generated by a finite homogeneous population. The service time, the lead time are assumed to have Phase type distribution. The life time of the item is assumed to have exponential distributions. The joint distribution of the number of customers in the system and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. The results are illustrated numerically.     

Continuous review inventory models for perishable items ordered in batches

This paper is an in-depth treatment of an inventory control problem with perishable items. We focus on two prototypes of perishability for items that have a common shelflife and that arrive in batches with zero lead time: (i) sudden deaths due to disasters (e.g., spoilage because of extreme weather conditions or a malfunction of the storage place) and (ii) outdating due to expirations (e.g., medicine or food items that have an expiry date). By using known mathematical tools we generalize the stochastic analysis of continuous review (s, S) policies to our problems. This is achieved by integrating with each inventory cycle stopping times that are independent of the inventory level. We introduce special cases of compound Poisson demand processes with negative jumps and consider demands (jumps) that are exponentially distributed or of a unit (i.e., Poisson) demand. For these special cases we derive a closed form expression of the total cost, including that of perishable items, given any order up to level. Since the stochastic analysis leads to tractable expressions only under specific assumptions, as an added benefit we use a fluid approximation of the inventory level to develop efficient heuristics that can be used in general settings. Numerical results comparing the solution of the heuristics with exact or simulated optimal solutions show that the approximation is accurate.     

Risk-sensitive dynamic pricing for a single perishable product

We show that the monotone structures of dynamic pricing for a single perishable product under risk-neutrality are preserved under risk-sensitivity with the additive general utility and atemporal exponential utility functions. We also show that the optimal price is decreasing over the degree of risk-sensitivity under the exponential class of both additive and atemporal utility functions.     

Inventory models for perishable items with inventory level dependent demand rate

This paper presents inventory models for perishable items with inventory level dependent demand rate. The models with and without backlogging are studied. In the backlogging model, it is assumed that the backlogging rate is dependent on the waiting time and the amount of products already backlogged simultaneously. Two cases that holding inventory is profitable or not are studied, respectively. The smallest shelf space to ensure shortage not occur when holding inventory is not profitable is obtained. In the model without backlogging, it is assumed that the remaining stock at the end of the inventory cycle is disposed of with salvage value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution of these models are investigated. At last, some numerical examples are presented to illustrate the effectiveness of the proposed model. The model in this paper is generalization of present ones. In particularly, the model is reduced to Padmanabhan and Vrat’s when δ₁ = 0, and Dye and Ouyang’s when δ₂ = 0. If S = s and δ₂ = 0, it is Chang, Goyal and Teng’s model.     

Dynamic economic lot size model with perishable inventory and capacity constraints

In this study, we consider a dynamic economic lot sizing problem for a single perishable item under production capacities. We aim to identify the production, inventory and backlogging decisions over the planning horizon, where (i) the parameters of the problem are deterministic but changing over time, and (ii) producer has a constant production capacity that limits the production amount at each period and is allowed to backorder the unmet demand later on. All cost functions are assumed to be concave. A similar problem without production capacities was studied in the literature and a polynomial time algorithm was suggested (Hsu, 2003 [1]). We assume age-dependent holding cost functions and the deterioration rates, which are more realistic for perishable items. Backordering cost functions are period-pair dependent. We prove the NP-hardness of the problem even with zero inventory holding and backlogging costs under our assumptions. We show the structural properties of the optimal solution and suggest a heuristic that finds a good production and distribution plan when the production periods are given. We discuss the performance of the heuristic. We also give a Dynamic Programing-based heuristic for the solution of the overall problem.     

Location of a distribution center for a perishable product

A model that combines an inventory and location decision is presented, analyzed and solved. In particular, we consider a single distribution center location that serves a finite number of sales outlets for a perishable product. The total cost to be minimized, consists of the transportation costs from the distribution center to the sales outlets as well as the inventory related costs at the sales outlets. The location of the distribution center affects the inventory policy. Very efficient solution approaches for the location problem in a planar environment are developed. Computational experiments demonstrate the efficiency of the proposed solution approaches.     

Analysis of inventory policies for perishable items with fixed leadtimes and lifetimes

This paper deals with a continuous review inventory system with perishable items and Poisson demand. Lifetimes and leadtimes are assumed to be fixed. First, a quite general base-stock model is developed where a number of combinations between backorder- and lost sales policies are evaluated and optimized. The solution technique for all these combinations is exact. Secondly, we consider the case with non-negligible ordering costs and assume that the inventory policy employed is the commonly used ( \(R,Q\) ) policy. We develop a new heuristic approach for evaluating and analyzing the proposed \((R,Q)\) model and compare our results with those obtained by related papers. This heuristic approach uses the base-stock model developed as a building block. The results reveal that our approach works reasonably well in all cases considered.     

A column generation-based heuristic algorithm for an inventory routing problem with perishable goods

An inventory routing problem is a variation of the vehicle routing problem in which inventory and routing decisions are determined simultaneously over a given time horizon. The objective is to minimize the sum of transportation and inventory costs. In this paper, we study a specific inventory routing problem in which goods are perishable (PIRP). We develop a mathematical model for PIRP and exploit its structure to develop a column generation-based solution approach. Cutting planes are added to improve the formulation. We present computational experiments to demonstrate that our methodology is effective, and that the integration of routing and inventory can yield significant cost savings.     

RFID-generated traceability for contaminated product recall in perishable food supply networks

As perishable food supply networks become more complex, incidents of contamination in these supply networks have become fairly common. Added to this complexity is the fact that there have been long delays in identifying the contamination source in several such incidents. Even when the contamination source was identified, there have been cases where the ultimate destination of all contaminated products were not known with complete certainty due, in part, to dispersion in these supply networks. We study the recall dynamics in a three-stage perishable food supply network through three different visibility levels in the presence of contamination. Specifically, we consider allocation of liability among the different players in the perishable supply network based on the accuracy with which the contamination source is identified. We illustrate the significance of finer levels of granularity both upstream and downstream as well as determine appropriate visibility levels and recall policies.     

A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods

Most of the research on integrated inventory and routing problems ignores the case when products are perishable. However, considering the integrated problem with perishable goods is crucial since any discrepancy between the routing and inventory cost can double down the risk of higher obsolescence costs due to the limited shelf-life of the products. In this paper, we consider a distribution problem involving a depot, a set of customers and a homogeneous fleet of capacitated vehicles. Perishable goods are transported from the depot to customers in such a way that out-of-stock situations never occur. The objective is to simultaneously determine the inventory and routing decisions over a given time horizon such that total transportation cost is minimized. We present a new “arc-based formulation” for the problem which is deemed more suitable for our new tabu search based approach for solving the problem. We perform a thorough sensitivity analysis for each of the tabu search parameters individually and use the obtained gaps to fine-tune the parameter values that are used in solving larger sized instances of the problem. We solve different sizes of randomly generated instances and compare the results obtained using the tabu search algorithm to those obtained by solving the problem using CPLEX and a recently published column generation algorithm. Our computational experiments demonstrate that the tabu search algorithm is capable of obtaining a near-optimal solution in less computational time than the time required to solve the problem to optimality using CPLEX, and outperforms the column generation algorithm for solving the “path flow formulation” of the problem in terms of solution quality in almost all of the considered instances.