A discrete approach to designing optimal hedging-point control policies for production-inventory systems with general stochastic behavior

The hedging-point policy for a production-inventory system is investigated under the effect of probabilistic machine breakdowns and repairs assuming general discrete distributions for the repair time and the time to failure. Using a methodology whereby inventory levels can assume only discrete values, an optimal safety stock size that minimizes the total expected cost per unit time is determined.     

Inventory systems with stochastic demand and supply: Properties and approximations

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.     

Numerical simulation based on fuzzy stochastic analysis

In this paper mathematical methods for fuzzy stochastic analysis in engineering applications are presented. Fuzzy stochastic analysis maps uncertain input data in the form of fuzzy random variables onto fuzzy random result variables. The operator of the mapping can be any desired deterministic algorithm, e.g. the dynamic analysis of structures. Two different approaches for processing the fuzzy random input data are discussed. For these purposes two types of fuzzy probability distribution functions for describing fuzzy random variables are introduced. On the basis of these two types of fuzzy probability distribution functions two appropriate algorithms for fuzzy stochastic analysis are developed. Both algorithms are demonstrated and compared by way of an example.     

The stochastic economic lot scheduling problem: A survey

The present literature survey focuses on the stochastic economic lot scheduling problem (SELSP). The SELSP deals with the make-to-stock production of multiple standardized products on a single machine with limited capacity under random demands, possibly random setup times and possibly random production times. The main task of a production manager in this setting is the construction of a production plan for the machine. Based on the critical elements of such a production plan, we present a classification and extensive overview of the research on the SELSP together with an indication of open research areas. By doing so, we intend to stimulate the discussion on the important problems concerning the SELSP both from a theoretical and a practical point of view.     

A stochastic program based lower bound for assemble-to-order inventory systems

In this paper we introduce a multi-stage stochastic program that provides a lower bound on the long-run average inventory cost of a general class of assemble-to-order (ATO) inventory systems. The stochastic program also motivates a replenishment policy for these systems. Our lower bound generalizes a previous result of Do?ru et al. (2010) [3] for systems with identical component replenishment lead times to those with general deterministic lead times. We provide a set of sufficient conditions under which our replenishment policy, coupled with an allocation policy, attains the lower bound (and is hence optimal). We show that these sufficient conditions hold for two examples, a single product system and a special case of the generalized W model.     

Central versus local multiple stage inventory planning: An analysis of solutions

Supply chain management refers to the integration of all activities associated with moving goods from raw material stages through to end users. Yet this system-wide vision of inventory planning often requires the coordination of several commercially independent entities, such as suppliers, manufacturers and distributors. This study explores the issue of friction between replenishment policies, defined as the disparity between centrally and locally planned solutions to 98,820 deterministic, multiple stage inventory planning problems modeling systems of varying levels of complexity. Friction is found to be strongly related to certain cost factors, suggesting that certain supply chains could be more vulnerable to tension and inefficiencies when replenishment policies are derived without cooperation between commercially independent yet logistically interdependent stages. These results can also be applied to identify relationships between the findings of otherwise seemingly disparate previous studies of coordination schemes for supply chain partners.     

Structured construction and simulation of nondeterministic stochastic activity networks

In this work we deal with nondeterministic stochastic activity networks (NDSANs). Their stochastic character results from activity durations, which are given by nonnegative continuous random variables. The nondeterministic behavior of an NDSAN is a consequence of its variable topology, based on two additional features. First, by associating choice probabilities with the immediate successors of an activity, some branches of execution are not always taken. Second, by allowing iterated executions of a group of activities according to predetermined probabilities, the number of times an activity is to be executed is not determined a priori. These properties lead to a wide variety of activity networks, capable of modelling many real situations in process engineering and project management. We describe a simple, recursively structured construction of NDSANs, which both provides a coherent syntactic mechanism to incorporate the two abovementioned nondeterminism features and allows the analytic formulation of completion time. This construction also directly gives rise to a recursive simulation algorithm for NDSANs, whose repeated execution produces an estimate of the probability distribution of the completion time of the network. We also report on real-world case studies, using the Komolgorov–Smirnov statistic for validation.     

An index heuristic for transshipment decisions in multi-location inventory systems based on a pairwise decomposition

In multi-location inventory systems, transshipments are often used to improve customer service and reduce cost. Determining optimal transshipment policies for such systems involves a complex optimisation problem that is only tractable for systems with few locations. Consequently simple heuristic transshipment policies are often applied in practice. This paper develops an approximate solution method which applies decomposition to reduce a Markov decision process model of a multi-location inventory system into a number of models involving only two locations. The value functions from the subproblems are used to estimate the fair charge for the inventory provided in a transshipment. This estimate of the fair charge is used as the decision criterion in a heuristic transshipment policy for the multi-location system. A numerical study shows that the proposed heuristic can deliver considerable cost savings compared to the simple heuristics often used in practice.     

Environmental safety stock: The impacts of regulatory and voluntary control policies on production planning,inventory control,and environmental performance

This paper analyzes the impacts of different pollution control policies on a firm’s decisions of production planning and inventory control. Based on a stochastic model with both demand and environmental uncertainties, we derive the optimal policies of production planning and inventory control under both regulatory and voluntary pollution control approaches, and investigate their operational and environmental effects. We establish that the conventional wisdom which suggests that reduction of environmental waste at the end of a production process also decreases the stock and throughput levels of a production system is not necessarily true. Rather, a regulatory environmental standard that limits the total amount of waste may induce the firm to raise its planned stock level, which would lead to a higher expected amount of environmental wastes before the standard is enforced as well as environmental risks at other stages of the production process. The additional planned stock level, which is termed “environmental safety stock,” can be reversed by using the voluntary control approach that provides the firm with the flexibility to occasionally exceed the environmental standard. We also conduct numerical experiments to analyze the effects of different values of model parameters under different control approaches. The analytical results provide new insights to the impacts of a firm’s production and inventory decisions on the natural environment as well as to the choices of pollution control approaches by decision makers in both the private and public sectors.     

Supply chain cooperation in industrial districts: A simulation analysis

In the past few years the literature on supply chain management has widely emphasized that cooperation among supply chain (SC) firms is a key source of competitive advantage. This paper explores the topic in a particular context, i.e. the industrial district (ID), which constitutes a specific production model where complex SC networks can be identified. SC cooperation may take on several forms in IDs and may produce several benefits (e.g. upgrading quality and reducing costs) so this paper also analyzes the benefits of a specific form of SC cooperation in different competitive scenarios and for diverse ID organizational structures. An agent-based model of SC cooperation in IDs has been developed and a simulation analysis carried out.     

Online retailers’ promotional pricing,free-shipping threshold,and inventory decisions: A simulation-based analysis

We consider a two-stage decision problem, in which an online retailer first makes optimal decisions on his profit margin and free-shipping threshold, and then determines his inventory level. We start by developing the retailer’s expected profit function. Then, we use publicly-available statistics to find the best-fitting distribution for consumers’ purchase amounts and the best-fitting function for conversion rate (i.e., probability that an arriving visitor places an online order with the retailer). We show that: (i) a reduction of the profit margin does not significantly affect the standard deviation of consumers’ order sizes (purchase amounts) but increases the average order size; whereas, (ii) variations in a positive finite free-shipping threshold affect both the average value and the standard deviation of the order sizes. We then use Arena to simulate the online retailing system and OptQuest to find the retailer’s optimal decisions and maximum profit. Next, we perform a sensitivity analysis to examine the impact of the ratio of the unit holding and salvage cost to the unit shipping cost on the retailer’s optimal decisions. We also draw some important managerial insights.     

A tabu search heuristic for the split delivery vehicle routing problem with production and demand calendars

The purpose of this article is to propose a tabu search heuristic for the split delivery Vehicle Routing Problem with Production and Demand Calendars (VRPPDC). This new problem consists of determining which customers will be served by a common carrier, as well as the delivery routes for those served by the private fleet, in order to minimize the overall transportation and inventory costs. We first model this problem and then propose a simple decomposition procedure that can be used to provide a starting solution. Next, we introduce a new tabu search heuristic and we describe two new neighbor reduction strategies. Finally, we present the results of our extensive computational tests. According to these tests, our reduction strategies are efficient not only at reducing computing time but also at improving the overall solution quality.     

Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping

This paper proposes a novel method to select an experimental design for interpolation in random simulation, especially discrete event simulation. (Though the paper focuses on Kriging, this design approach may also apply to other types of metamodels such as non-linear regression models and splines.) Assuming that simulation requires much computer time, it is important to select a design with a small number of observations (or simulation runs). The proposed method is therefore sequential. Its novelty is that it accounts for the specific input/output behavior (or response function) of the particular simulation at hand; i.e., the method is customized or application-driven. A tool for this customization is bootstrapping, which enables the estimation of the variances of predictions for inputs not yet simulated. The method is tested through two classic simulation models, namely the expected steady-state waiting time of the M/M/1 queuing model, and the mean costs of a terminating (s, S) inventory simulation. For these two simulation models the novel design indeed gives better results than a popular alternative design, namely Latin Hypercube Sampling (LHS) with a prefixed sample.     

A stochastic multi-period industrial hazardous waste location-routing problem: Integrating NSGA-II and Monte Carlo simulation

The present study extends a multi-objective mathematical model in the context of industrial hazardous waste management, which covers the integrated decisions of three levels with locating, vehicle routing, and inventory control. Analyzing these decisions simultaneously not only may lead to the most effective structure in the waste management network, but also may reduce the potential risk of managing the hazardous waste. Furthermore, because of the inherent complexity of the waste management system, uncertainty is inevitable and should be acknowledged to guarantee reliability in the decision-making process. From this perspective, the proposed model is novel in the following three aspects: (1) shifting from a deterministic to stochastic environment; (2) considering a multi-period planning horizon; and (3) incorporating the inventory decisions into the problem. The problem is formulated as a multi-objective stochastic Mixed-Integer Nonlinear Programming (MINLP) model, which can be easily converted into a MILP one. In terms of methodological contribution, a new simheuristic approach that is an integration of Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) and Monte Carlo simulation is developed to overcome the stochastic combinatorial optimization problem of this study. Our findings verify the efficiency of the proposed approach as it is able to find a high-quality solution within a relatively reasonable computational time.     

A stochastic programming and simulation based analysis of the structure of production on the arable land

This paper is devoted to the analysis of the effectiveness of the use of arable land. This is an issue, which is important for national-level decision makers. The particular calculations are carried out for Hungary, but similar analysis can be made for each country having several parts with different geographical conditions.     

Model for cost estimation in a finite-capacity stochastic environment based on shop floor optimization combined with simulation

In recent years several researchers suggested cost estimation models that consider limited capacity. These researchers ignored the stochastic nature of the shop floor. This paper presents a cost estimation model that takes into account the stochastic environment. It is based on marginal analysis – the difference between the total cost without the new order and the total cost with the new order. The proposed model is based on the integration of simulation and optimization. Data generated by the simulation is inserted into the optimization procedure that finds good feasible solutions quickly. A significant advantage of the proposed stochastic cost estimation over an existing deterministic approach is shown. A computational study is performed to test different factors affecting the proposed model.     

Balancing stocks, flexible recipe costs and high service level requirements in a batch process industry: A study of a small scale model

Process industries often obtain their raw materials from mining or agricultural industries. These raw materials usually have variations in quality which often lead to variations in the recipes used for manufacturing a product. Another reason for varying the recipe is to minimize production costs by using the cheapest materials that still lead to a satisfactory quality in the product. A third reason for using recipe flexibility is that it may occur that not all materials for the standard recipe are available. If variations in supply and demand are large, keeping sufficient safety stock to cope with these variations may incur prohibitive high costs. This means that the costs of keeping safety stock should be balanced with the costs of sometimes using more expensive recipes. The question now is for what situations and to what extent the use of recipe flexibility is justified. In this paper we study this question by means of a small scale model. For this simple situation we derive a decision procedure to balance safety stock costs and flexibility costs. This procedure is applied to a range of different situations, that are characterized by a set of parameter values, in order to determine for which situations recipe flexibility should be used.     

Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes

It is still a challenge to study the degradation mechanisms of complex systems with multiple performance characteristics. This paper develops a two-stage stochastic degradation model. The degeneration processes of two correlated performance characteristics are described by a correlated bivariate Wiener process in the first stage, in which neither of the degradation levels of performance characteristics reaches their thresholds. When one of the degradation levels of performance characteristics reaches its threshold, the system operates defectively in the second stage, and the system degradation process is described by the other performance characteristic which is modeled by a univariate Wiener process. The system fails completely when both the degradation levels of performance characteristics reach their thresholds. Explicit expressions of the system reliability and availabilities are given based on different inspection and maintenance policies. Simulation is also presented, and it shows that the analytical results and the simulation results are in good agreement. Finally, a detailed case study of the rail track geometry degradation is given to demonstrate the results obtained in the paper.