Inventory model for an inventory system with time-varying demand rate

The standard inventory problems of the multi-period have been modeled under different situations. Specifically we have considered the demand subjects of a continuous distribution and a discrete distribution, and whether the demand of each period is unchanged or not. A method to get an economic order quantity in inventory systems with discrete and unchanged demand was presented in a previous paper, and this method has been generalized to an inventory model with varying continuous demand. However, it was not achieved due to there being many classified cases in the general situations. In this article the above method is discussed in the case discrete demand to determine whether it increases or decreases from period to period. A theoretical method is presented by using previous results and some examples are given which suggest how the concept can handle on inventory system. In order to make the decision, an algorithm is also presented under some conditions, and examples are shown by using the computer software program, Mathematica, which helps to explain the findings. In general cases, we view the optimal policy in the inventory problems in only a few periods.     

Omitted budget constraint bias in discrete-choice demand models

A large body of discrete-choice demand studies estimate a demand model in which the consumer’s budget constraint is not taken into account. We illustrate how incorrectly specifying the consideration set, when in fact the budget constraint binds for some products, may bias the demand estimates. We illustrate and quantify the nature of the bias in three ways: (i) in analytical examples; (ii) in field data commonly used in the literature and (iii) in a Monte Carlo study. We find that the price sensitivity can be substantially lower when correctly imposing the budget constraint, and own-price elasticities are typically overestimated although the direction of the own-price elasticity bias is in general ambiguous and depends on the income distribution.     

Multi-product newsvendor problem with value-at-risk considerations

We consider the single period stochastic inventory (newsvendor) problem with downside risk constraints. The aim in the classical newsvendor problem is maximizing the expected profit. This formulation does not take into account the risk of earning less than a desired target profit or losing more than an acceptable level due to the randomness of demand. We utilize Value at Risk (VaR) as the risk measure in a newsvendor framework and investigate the multi-product newsvendor problem under a VaR constraint. To this end, we first derive the exact distribution function for the two-product newsvendor problem and develop an approximation method for the profit distribution of the N-product case (N>2). A mathematical programming approach is used to determine the solution of the newsvendor problem with a VaR constraint. This approach allows us to handle a wide range of cases including the correlated demand case that yields new results and insights. The accuracy of the approximation method and the effects of the system parameters on the solution are investigated numerically.     

A serial mixed produce-to-order and produce-in-advance inventory model with multiple retailers

We formulate a general mixed produce-to-order and produce-in-advance inventory model having multiple stocking echelons and multiple retailers. We show that the problem to find an optimal inventory policy for such a model with a uniform or a normal demand distribution can be reduced to a general constrained optimization problem.     

Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications

We present a general solution framework for the price-setting newsvendor problem with a multiplicative stochastic demand. Under mild assumptions, such as increasing price elasticity on the mean demand function and increasing generalized failure rate on the distribution of the random factor, we first prove that both the profit function with respect to price and its derived function with respect to order quantity are quasi-concave. Three applications are then studied under our solution framework: (1) We consider a wholesale price only contract by which a manufacturer sets a wholesale price and a newsvendor determines an order quantity and the retail price, and show that the manufacturer's profit function is unimodal with respect to retailing price or stocking factor under certain conditions. (2) We consider a newsvendor problem in which the demand depends on both the retail price and the level of sales effort, and the cost exerting the sales effort is proportional to the order quantity; we prove that there exists a unique pair of price and sales-effort levels that maximize the total profit. This result is established under a set of mild assumptions on the demand and cost functions. (3) We identify a property in the single-period profit function that satisfies Condition 1 of Huh and Janakiraman (2008), which in turn guarantees the optimality of (s, S) policy for an infinite stationary dynamic inventory-price control system with lost sales and fixed order costs. Finally, the unimodality of the newsvendor problem with a general stochastic and price-sensitive demand is studied.     

Stock rationing under service level constraints in a vertically integrated distribution system

This paper addresses a rationing problem in a two-level, vertically integrated distribution system composed of one manufacturer and several retail points. The motivating case, developed in the vending machine sector and modeled as a newsvendor-like problem, is representative of many real settings where short-term changes in demand can be substantial while capacity modification is not a viable option. The paper provides an analytical discussion of the problem from two different standpoints: a pure profit-maximization perspective and a minimum service-level perspective, both subject to a product availability constraint that affects the service level the company can provide, and the related expected profit. By analyzing the Lagrangean formulation of the problem, we devise efficient computational procedures based on dichotomy search to find the optimal allotments to retailers, maximizing the expected profit and ensuring a minimum service level. Then, we extend the analysis to the evaluation of the highest service level that can be provided, under a product availability constraint. We identify conditions such that the proposed search procedures succeed in finding the optimal solutions, as well as bounds for the search domains. The proposed approach is legitimated under several demand distribution functions subject to a few commonly adopted restrictions that encompass many of the usually adopted continuous distributions. Finally, the paper presents a three-step decision-making framework using the proposed procedures, summarizing the decision paths the manufacturer might follow in order to optimize the allocation decision.     

Hybrid particle swarm optimization with mutation for optimizing industrial product lines: An application to a mixed solution space considering both discrete and continuous design variables

This article presents an artificial intelligence-based solution to the problem of product line optimization. More specifically, we apply a new hybrid particle swarm optimization (PSO) approach to design an optimal industrial product line. PSO is a biologically-inspired optimization framework derived from natural intelligence that exploits simple analogues of collective behavior found in nature, such as bird flocking and fish schooling. All existing product line optimization algorithms in the literature have been so far applied to consumer markets and product attributes that range across some discrete values. Our hybrid PSO algorithm searches for an optimal product line in a large design space which consists of both discrete and continuous design variables. The incorporation of a mutation operator to the standard PSO algorithm significantly improves its performance and enables our mechanism to outperform the state of the art Genetic Algorithm in a simulated study with artificial datasets pertaining to industrial cranes. The proposed approach deals with the problem of handling variables that can take any value from a continuous range and utilizes design variables associated with both product attributes and value-added services. The application of the proposed artificial intelligence framework yields important implications for strategic customer relationship and production management in business-to-business markets.     

Algorithm portfolios for logistics optimization considering stochastic demands and mobility allowance

The vehicle routing problem with stochastic demand (VRPSD) is a well known NP-hard problem. The uncharacteristic behaviour associated with the problem enhances the computational efforts required to obtain a feasible and near-optimal solution. This paper proposes an algorithm portfolio methodology based on evolutionary algorithms, which takes into account the stochastic nature of customer demand to solve this computationally complex problem. These problems are well known to have computationally complex objective functions, which make their solutions hard to find, particularly when problem instances of large dimensions are considered. Of particular importance in such situations is the timeliness of the solution. For example, Apple was forced to delay their shipments of iPads internationally due to unprecedented demand and issues with their delivery systems in Samsung Electronics and Seiko Epson. Such examples illustrate the importance of stochastic customer demands and the timing of delivery. Moreover, most of the evolutionary algorithms, known for providing computationally efficient solutions, are unable to always provide optimal or near optimal solutions to all the VRPSD instances within allocated time interval. This is due to the characteristic variations in the computational time taken by evolutionary algorithms for same or varying size of the VRPSD instances. Therefore, this paper presents portfolios of different evolutionary algorithms to reduce the computational time taken to resolve the VRPSD. Moreover, an innovative concept of the mobility allowance (MA) in landmoves based on the levy’s distribution function has been introduced to cope with real situations existing in vehicle routing problems. The proposed portfolio approach has been evaluated for the varying instances of the VRPSD. Four of the existing metaheuristics including Genetic Algorithm (GA), Simulated Annealing (SA), Artificial Immune System (AIS), TABU Search (TS) along with new neighbourhood search, are incorporated in the portfolios. Experiments have been performed on varying dimensions of the VRPSD instances to validate the different properties of the algorithm portfolio. An illustrative example is presented to show that the set of metaheuristics allocated to certain number of processors (i.e. algorithm portfolio) performed better than their individual metaheuristics.     

Minimizing mean absolute deviation of completion time about a common due window subject to maximum tardiness for a single machine

This study deals with the problem of scheduling jobs on a single machine to minimize the mean absolute deviation of the job completion time about a large common due window subject to the maximum tardiness constraint. Using the well-known three-field notation, the problem is identified as MAD/large DueWindow/T_max. The common due window is set to be large enough to allow idle time prior to the beginning of a schedule to investigate the effect of the T_max constraint. Penalties arise if a job is completed outside the due window. A branch and bound algorithm and a heuristic are proposed. Many properties of the solutions and precedence relationships are identified. Our computational results reveal that the branch and bound algorithm is capable of solving problems of up to 50 jobs and the heuristic algorithm yields approximate solutions that are very close to the exact solution.     

流水工序调度与生产效率的关系模型分析

提出一种基于粒子群算法的流水工序调度任务优化模型。利用流水工序调度任务的特点得到流水工序时间约束条件,利用粒子群算法的原理建立流水工序调度任务优化模型,利用粒子群算法对模型进行求解。仿真实验表明,利用该算法能够得到流水工序调度问题的最优解,提高生产效率。     

An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain

Ben-Daya et al. (2010) established a joint economic lot-sizing problem (JELP) for a three-layer supply chain with one supplier, one manufacturer, and multiple retailers, and then proposed a heuristic algorithm to obtain the integral values of four discrete variables in the JELP. In this paper, we first complement some shortcomings in Ben-Daya et al. (2010), and then propose a simpler improved alternative algorithm to obtain the four integral decision variables. The proposed algorithm provides not only less CPU time but also less total cost to operate than the algorithm by Ben-Daya et al. (2010). Furthermore, our proposed algorithm can solve certain problems, which cannot be solved by theirs. Finally, the solution obtained by the proposed algorithm is indeed a global optimal solution in each of all instances tested.     

A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system

We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize the weighted number of just-in-time jobs and the second criterion is to minimize the total resource consumption cost. We prove that although the problem is known to be NP-hard even for constant processing times, a pseudo-polynomial time algorithm for its solution exists. In addition, we show how the pseudo-polynomial time algorithm can be converted into a two-dimensional fully polynomial approximation scheme for finding an approximate Pareto solution.     

The linear dynamic lot size problem with minimum order quantity

This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allow us to develop a solution algorithm based on the concept of atomic sub-problems. We present an optimal solution to an atomic sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the original problem. Computational tests and a comparison with a published algorithm confirm the efficiency of the solution algorithm developed here.     

Exact and approximated calculation of the cycle service level in a continuous review policy

The paper proposes a method to compute the exact cycle service level for (s, Q) continuous review policy in the presence of undershoots and discrete demand in the discrete time domain. Prior to this, it is necessary to review the definition of the cycle service level in order to avoid the problems that can be found when applied it to the periodic review policy. Therefore, the aim of this paper is: (a) to review the definitions of the cycle service level when applied to continuous review policies; (b) to develop an exact calculation method of the CSL for a continuous review policy when undershoots are allowed and demand is discrete; and (c) to examine some common believes about the cycle service properties. Finally, the bias obtained when the service cycle level is estimated applying the common assumption of neglecting undershoots at the order point is illustrated with some numerical examples which show that it may lead to significant deviations to be ignored.     

Budget allocation for permanent and contingent capacity under stochastic demand

We develop a model of budget allocation for permanent and contingent workforce under stochastic demand. The level of permanent capacity is determined at the beginning of the horizon and is kept constant throughout, whereas the number of temporary workers to be hired must be decided in each period. Compared to existing budgeting models, this paper explicitly considers a budget constraint. Under the assumption of a restricted budget, the objective is to minimize capacity shortages. When over-expenditures are allowed, both budget deviations and shortage costs are to be minimized. The capacity shortage cost function is assumed to be either linear or quadratic with the amount of shortage, which corresponds to different market structures or different types of services. We thus examine four variants of the problem that we model and solve either approximately or to optimality when possible. A comprehensive experimental design is designed to analyze the behavior of our models when several levels of demand variability and parameter values are considered. The parameters consist of the initial budget level, the unit cost of temporary workers and the budget deviation penalty/reward rates. Varying these parameters produce several trade-offs between permanent and temporary workforce levels, and between capacity shortages and budget deviations. Numerical results also show that the quadratic cost function leads to smooth and moderate capacity shortages over the time periods, whereas all shortages are either avoided or accepted when the cost function is linear.     

Optimizing the capital rationing decision with uncertain returns

In this article, we develop a new optimization model for capital rationing with uncertain project returns. Our model maximizes the probability of meeting a predefined target return by selecting a feasible set of projects subject to budget constraints in multiple time periods. We employ a mixed-integer nonlinear algorithm recently developed in the optimization field to solve the resulting nonconvex optimization problem to optimality. Our model and solution methods are tested and validated through a comprehensive computational experiment. Several managerial insights are obtained about the impact of available budget and target return on the optimal solutions. Notably, we have found that increasing target return may not necessarily result in an increase in optimal total expected return of the selected projects. Our model and solution method offer a unified and computationally tractable approach to precisely quantify the tradeoff between project returned and risk.     

Partial monitoring,adverse selection,and the internal efficiency of the firm

The paper investigates an adverse selection model with monitoring of managerial effort. In contrast to the literature, we assume that the manager can be punished only if his effort is below a certain level that is monitored by the principal. Surprisingly, the optimal labor contract may induce an equilibrium effort which is lower than in the standard model without monitoring. This result holds for any discrete distribution of managerial types. In the continuous type case, the optimal contracts for high-quality (low-quality) managers are purely output-dependent (effort-dependent).     

The selective pickup and delivery problem: Formulation and a memetic algorithm

The pickup and delivery problem addresses the real-world issues in logistic industry and establishes an important category of vehicle routing problems. The problem is to find the shortest route to collect and distribute commodities under the assumption that the total supply and the total demand are in equilibrium. This study presents a novel problem formulation, called the selective pickup and delivery problem (SPDP), by relaxing the constraint that all pickup nodes must be visited. Specifically, the SPDP aims to find the shortest route that can supply delivery nodes with required commodities from some pickup nodes. This problem can substantially reduce the transportation cost and fits real-world logistic scenarios. Furthermore, this study proves that the SPDP is NP-hard and proposes a memetic algorithm (MA) based on genetic algorithm and local search to resolve the problem. A novel representation of candidate solutions is designed for the selection of pickup nodes. The related operators are also devised for the MA; in particular, it adapts the 2-opt operator to the sub-routes of the SPDP for enhancement of visiting order. The experimental results on several SPDP instances validate that the proposed MA can significantly outperform genetic algorithm and tabu search in terms of solution quality and convergence speed. In addition, the reduced route lengths on the test instances and the real-world application to rental bikes distribution demonstrate the benefit of the SPDP in logistics.     

A class of chance constrained multiobjective linear programming with birandom coefficients and its application to vendors selection

In this paper, a class of chance constrained multiobjective linear programming model with birandom coefficients is considered for vendor selection problem. Firstly we present a crisp equivalent model for a special case and give a traditional method for crisp model. Then, the technique of birandom simulation is applied to deal with general birandom objective functions and birandom constraints which are usually difficult to be converted into their crisp equivalents. Furthermore, a genetic algorithm based on birandom simulation is designed for solving a birandom multiobjective vendor selection problem. Finally, a real numbers example is given. The paper makes certain contribution in both theoretical and application research related to multiobjective chance constrained programming, as well as in the study of vendor selection problem under uncertain environment.     

Heuristics for operational fixed job scheduling problems with working and spread time constraints

Operational fixed job scheduling problems select a set of jobs having fixed ready and processing times and schedule the selected jobs on parallel machines so as to maximize the total weight. In this study, we consider working time and spread time constrained versions of the operational fixed job scheduling problems. The working time constraints limit the total processing load on each machine. The spread time constraints limit the time between the start of the first job and the finish of the last job on each machine. For the working time constrained problem, we present a filtered beam search algorithm that evaluates the promising nodes of the branch and bound tree. For the spread time constrained problem we propose a two phase algorithm that defines the promising sets for the first jobs and finds a solution for each promising set. The results of our computational tests reveal that our heuristic algorithms perform very well in terms of both solution quality and time.