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Technological advance and changing customer preferences lead to falling demand with the passage of time for some products, often referred to as short life cycle. In this paper, we examine the inventory management of a short life cycle product that also deteriorates as time elapses. We consider a finite horizon multi-period setting where demand is deterministic, stock-level-dependent, time varying, and price-dependent. We seek to maximize the average profit per period by choosing an appropriate replenishment and pricing policy. Leveraging properties of the objective function, we develop an algorithm that determines the optimal value of several system decision variables that maximize profitability. We provide a numerical example that illustrates our solution approach after which we perform a sensitivity analysis.

In this paper, the dotted inner-fit raster (DIFR) is used to build an improved dotted board model, denoted as (IDBM). The DIFR is a new concept can be utilized to define the feasible solution matrix of each item and to define the dotted no-fit raster in the two dimensional cutting and packing problems. It is found that using DIFR to build the IDBM instead of using regular dotted board model (DBM) has many benefits, such as that IDBM can be used for any shape, not only polygon, it reduces the number of constraints in the optimization model, and it makes the number of decision variable depends on the number of piece types not on the total number of pieces. Consequently, seven instance groups; 6 from literature and one from real work, with maximum piece types of 8 and with number of pieces ranging from 24 to 60 were optimally solved in acceptable computational time by IDBM, which was impossible by older concepts.

We point out that all models in a previous paper are incorrect.Four improved mathematical programming models are presented.Relationship among scheduling problems are analyzed. The aim of this paper is to point out that all mathematical programming models proposed by Ying et al. (2016) are incorrect. We present four revised mathematical programming models and four improved mathematical programming models by adding and revising some constraints and decision variables. Moreover, we show that the first three scheduling problems considered in their paper are equivalent to the problems with the objective of minimizing the sum of completion times or minimizing the maximum lateness, which can be solved by algorithms proposed by Luo et al. (2015) in O(n2) time.

This paper examines the optimal decisions for e-tailer issuing diamond card considering shipping policy. We propose a strong revenue-sharing contract when the order quantity is below Free Shipping Quantity (FSQ); and a weak revenue-sharing contract when the quantity is up to FSQ. We find that the diamond card and shipping policy can entice the e-tailer to order more quantities. In the strong revenue-sharing contract, when the e-tailer shares more revenues, the optimal order quantity increases or decreases depending on price. However, the optimal order quantity always decreases when the weak share rate increases. In addition, we find that the e-retailer also can obtain the optimal decisions when the discount is decision variable. In the strong revenue-sharing contract, both the optimal order quantity and discount decrease when the share rate increases; and when price increases, both the optimal order quantity and discount increase.

In this paper, we study an extended warranty model under which the customer is offered an additional warranty period after the original two-phase warranty expires. Under the original two-phase warranty, the warranty period is divided into two non-overlapping subintervals, one of which is for replacement warranty, and the other is for minimal repair warranty. If the system failure occurs during the original warranty period, the failed system is either replaced or minimally repaired by the manufacturer, and if the failure occurs during the extended warranty period, only the minimal repair is conducted. For the system failure during the replacement warranty period, the failed system is replaced by a new one, and the warranty term is renewed anew. Following the expiration of extended warranty, the customer is solely responsible for maintaining the system for a fixed length of time period and replaces the system at the end of such a maintenance period. During the maintenance period, only the minimal repair is given for each system failure. Such a maintenance model can be considered as a generalization of several existing maintenance models which can be obtained as special cases. The main purpose of this article is to determine, from the customer’s perspective, the optimal length of maintenance period after the extended warranty expires. As the criterion to determine the optimal replacement strategy, we adopt the expected cost rate per unit time during the life cycle of the system. Given the cost structures incurred during the life cycle of the system, we formulate the expected cost and the expected length of life cycle to obtain the expected cost rate. The uniqueness of optimal solution for the decision variable is verified when the life distribution of the system shows an increasing failure rate. Numerical examples are provided to illustrate the proposed optimal replacement strategy.

We address two scheduling problems arising when two agents (agents A and B ), each with a set of jobs, compete to perform their respective jobs on a common machine, where the due dates of agent A ’s jobs are decision variables to be determined by the scheduler. Specifically, the objective is to determine the optimal due dates for agent A ’s jobs and the job sequence for both agents’ jobs simultaneously to minimize the total cost associated with the due date assignment and weighted number of tardy jobs of agent A , while keeping the maximum of regular functions (associated with each B -job) or the number of tardy jobs of agent B below or at a fixed threshold. We prove that both problems are NP -hard in the strong sense and develop polynomial or pseudo-polynomial solutions for some important special cases.

Solid waste produced as a by-product of our daily activities poses a major threat to societies as populations grow and economic development advances. Consequently, the effective management of solid waste has become a matter of critical importance for communities. However, solid waste management systems are inherently large-scale, diverse, and subject to many uncertainties, and must serve numerous stakeholders with divergent objectives. In this study, we propose a simulation-based decision-making and optimization framework for the analysis and development of effective solid waste management and recycling programs. The proposed solution includes a database and two main modules: an assessment module and a resource allocation optimization module. The assessment module identifies the sources of uncertainties in the system, which are then parameterized and incorporated into the resource allocation optimization module. The resource allocation optimization module involves a novel discrete-continuous model of the system under consideration, in which the continuous nature of decision variables is maintained while inherently discrete processing and transfer operations are accurately captured. The model operates with respect to the waste types and characteristics, costs, environmental impacts, types, location and capacities of processing facilities, and their technological capabilities. Then, an optimization mechanism embedded in the resource allocation optimization module solves the multi-criteria problem of the allocation of limited resources by simultaneously optimizing all relevant decision variables, evaluating performance in real-time via the model. Here, the optimum solution is considered as the combination of parameters that will lead to the highest recycling rate with minimum cost. The proposed framework has been successfully demonstrated for the Miami-Dade County Solid Waste Management System in the State of Florida.

A finite-horizon, periodic-review inventory model with inflow forecasting updates following the Martingale Model of Forecast Evolution (MMFE) in multiresevoirs is considered. This model introduces a new method of determining an operating policy in which the policy is based on the Dynamic Programming (DP) model with a physical equation and a recursive equation. Some important constraints are described for the multireservoirs operation. We propose two methods to adjust the decision variable during the optimization. The adjustment policy is essential to improve the profit and decrease the shortage in multireservoirs management. Finally, to assess the effectiveness of the policies, the model is compared with other models and is applied to the Chinese South-North Water Diversion project.

In this paper, we formulate a deteriorating inventory model with stock-dependent demand by allowing preservation technology cost as a decision variable in conjunction with replacement policy. Moreover, it is assumed that the shortages are allowed and partially backlogged, depending on the length of the waiting time for the next replenishment. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total profit per unit time is a concave function of preservation technology cost when the replenishment schedule is given. We then provide a simple algorithm to find the optimal preservation technology cost and replenishment schedule for the proposed model. Finally, we use some numerical examples to illustrate the model.

Reliability problems are an important type of optimization problems that are motivated by different needs of real-world applications such as telecommunication systems, transformation systems, and electrical systems, so on. This paper studies a special type of these problems which is called redundancy allocation problem (RAP) and develops a bi-objective RAP (BORAP). The model includes non-repairable series-parallel systems in which the redundancy strategy is considered as a decision variable for individual subsystems. The objective functions of the model are (1) maximizing system reliability and (2) minimizing the system cost. Meanwhile, subject to system-level constraint, the best redundancy strategy among active or cold-standby, component type, and the redundancy level for each subsystem should be determined. To have a more practical model, we have also considered non-constant component hazard functions and imperfect switching of cold-standby redundant component. To solve the model, since RAP belong to the NP-hard class of the optimization problems, two effective multi-objective metaheuristic algorithms named non-dominated sorting genetic algorithms (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are proposed. Finally, the performance of the algorithms is analyzed on a typical case and conclusions are demonstrated.

This paper is to deal with a mixed policy between precise inspection and CSP-1 with inspection errors (Types I and II) and return cost. First, the concept of a renewal reward process is employed to obtain the long-term net profit of the mixed inspection policy. Then, with respect to non-repairable and repairable products, we determine the following four decision variables such that the unit net profit is maximal: (1) the optimal clearance number, (2) the optimal sampling frequency, and (3) the proportions which should be taken precise inspection for the non-inspected items in the procedure of CSP-1 and the non-defectives identified by CSP-1. Overall, the analytical results indicate that depending on seven parameters (Type I error, Type II error, the selling price of an item, the unit repair cost, the unit return cost, the unit cost of precise inspection, and the process defective fraction), there are three possible optimal inspection policies for CSP-1: ''Do not inspect'', ''Do 100% inspection'', or any setting for (i,s); for both of the non-defectives identified in CSP-1 and the non-inspected items, there are three possible proportions which should be performed a precise inspection: all, none, or any proportion.

This study analyses a production-management model that considers the possibility of implementing a reverse-logistics system for remanufacturing end-of-life products in a lean production environment (as opposed to models that use EOQ approaches). Decision variables are identified (including manufacturing and remanufacturing capacities and return rates and use rates for end-of-life products) and optimal policies are determined. Moreover, the structure of these optimal policies is analysed. The conclusion drawn is that, in many realistic scenarios, mixed policies (that is, with return rates and use rates strictly between 0 and 1) can be optimal. This conclusion is contrary to results published in earlier studies, which are based on more restrictive assumptions.

In service organizations, customer demand varies over the course of an operating day and across the days of an operating week. These organizations must assign employees to weekly tour schedules in an attempt to satisfy the fluctuating customer demand. The tour-scheduling problem has been traditionally formulated by the set-covering approach. However, this approach requires a separate integer variable for each variation in the tour schedule due to different work days and different shift and break start times on these days, and this explicit representation results in an enormously large number of decision variables. In this paper, an implicit integer-programming model is presented, which combines daily shift assignments and alternate day-on patterns and also schedules break periods for shifts within the specified break windows. The implicit form of the model requires very few integer variables compared to the set-covering approach. (C) 2002 Elsevier Science Ltd. All rights reserved.

This paper presents a combined statistical model for probationer risk classification and nonlinear multi-criteria programming resource allocation model for workload balancing. A statistical model of individual probationer failure was used to classify individuals as high, medium or low risk for probation purposes. The proportion of probationers in each risk category was used as an input into the integer, nonlinear resource allocation model where the decision variables were the number of visits to probationers by type of visit and risk classification.

The research objective is to develop models and algorithms to provide quality solutions for large-scale service design problems. Service design problems arising at railroads, airlines, trucking firms, intermodal partnerships, etc. require the determination of the cost minimizing or profit maximizing set of services and their schedules, given limited resources and service requirements. The model is applied to a large express shipment transportation problem involving over 1.3 billion decision variables and 200,000 constraints. We develop a new model and solution approach — branch-and-price-and-cut. Computational results show that near optimal solution is achieved within a reasonable run time using novel problem reduction methods involving node consolidation, link consolidation, derived schedules and a branch-and-price-and-cut solution procedure.

The rehandling work influences the performance of transfer cranes significantly in a container terminal. The height and the width of a bay in the container stack are important decision variables in designing the storage configuration. And they are key factors which determine the average number of rehandles to pick up a container. In this paper, we propose a methodology to estimate the expected number of rehandles to pick up an arbitrary container and the total number of rehandles to pick up all the containers in a bay for a given initial stacking configuration. Simple tables and equations are provided to help the estimation of the number of rehandles.

We consider the problem of determining the optimal integer start time and end time of each inter-tank move for a given cyclic schedule of a material handling hoist in a circuit board production line. This problem frequently arises in automated electroplating lines for manufacturing of printed circuit boards where each board must flow through a sequence of tanks and the processing time at each tank must fall inside a given time interval. The existing model for the problem assumes that the times required to perform inter-tank moves are given constants. However, as shown in a simple example, under this restrictive assumption a feasible cyclic schedule may be identified as infeasible. In this paper, the times for inter-tank moves are considered as decision variables of the problem. An algorithm is proposed to solve the problem optimally. A numerical example is used to illustrate the algorithm. The proposed model generalizes the existing model as the assumption of constant inter-tank move times is relaxed. © 1997 Elsevier Science Ltd

An optimal design problem is considered for man-machine systems, where a group of numerically controlled (NC) machines is operated by a single worker. The processing time at each machine and the service time by the worker are assumed to be random variables. The decision variable is the number of machines in the group and the optimal criterion is to minimize the cost for producing a product. It is found that the minimum-cost number of machines, N c , is the lower bound on the optimal numbers of machines under other important criteria. We present the upper and lower bounds on N c s for the systems where the coefficients of variations of the service- and processing-time distributions are less than 1. Moreover, it is shown that the bounds are tight for such systems.