A production planning model for an unreliable production facility: Case of finite horizon and single demand

We study a two-level inventory system that is subject to failures and repairs. The objective is to minimize the expected total cost so as to determine the production plan for a single quantity demand. The expected total cost consists of the inventory carrying costs for finished and unfinished items, the backlog cost for not meeting the demand due-date, and the planning costs associated with the ordering schedule of unfinished items. The production plan consists of the optimal number of lot sizes, the optimal size for each lot, the optimal ordering schedule for unfinished items, and the optimal due-date to be assigned to the demand. To gain insight, we solve special cases and use their results to device an efficient solution approach for the main model. The models are solved to optimality and the solution is either obtained in closed form or through very efficient algorithms.     

Joint production and preventive maintenance scheduling for a single degraded machine by considering machine failures

Production scheduling and maintenance planning are two interdependent issues that most often have been investigated independently. Although both preventive maintenance (PM) and minimal repair affect availability and failure rate of a machine, only a few researchers have considered this interdependency in the literature. Furthermore, most of the existing joint production and preventive maintenance scheduling methods assume that machine is available during the planning horizon and consider only a possible level for PM. In this research, an integrated model is proposed that coordinates preventive maintenance planning with single-machine scheduling to minimize the weighted completion time of jobs and maintenance cost, simultaneously. This paper not only considers multiple PM levels with different costs, times and reductions in the hazard rate of the machine, but also assumes that a machine failure may occur at any time. To illustrate the effectiveness of the suggested method, it is compared to two situations of no PM and a single PM level. Eventually, to tackle the suggested problem, multi-objective particle swarm optimization and non-dominated sorting genetic algorithm (NSGA-II) are employed and their parameters are tuned Furthermore, their performances are compared in terms of three metrics criteria.     

Integrated production and maintenance planning for parallel machine system considering cost of rejection

Production scheduling and maintenance planning have interdependencies but been often considered and optimized independently in practice and in the literature. Furthermore, product quality has direct relationship with maintenance planning. This paper proposes an integrated approach for production scheduling and maintenance planning for parallel machine system considering the effect of cost of rejection. The approach aims to determine optimal production schedule and maintenance plan such that overall operations cost is minimized. A simulation-based optimization approach is used to solve the problem. A numerical investigation is performed to illustrate the approach. The integrated approach shows between 0.6 and 35.8% improvement in term of overall operations cost over independent approach for various scenarios. The results indicate that simultaneous consideration of production scheduling and maintenance planning results into better system performance.     

Two-warehouse production model for deteriorating inventory items with stock-dependent demand under inflation over a random planning horizon

This paper develops a production-inventory model for a deteriorating item with stock-dependent demand under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. The effects of learning in set-up, production, selling and reduced selling is incorporated. Different inflation rates for various inventory costs and time value of money are also considered. A hybrid genetic algorithm is designed to solve the optimization problem which is hard to solve with existing algorithms due to the complexity of the decision variable. To illustrate the model and to show the effectiveness of the proposed approach a numerical example is provided. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.     

Time-dependent and independent control rules for coordinated production and pricing under demand uncertainty and finite planning horizons

We address the effect of uncertainty on a manufacturer’s dynamic production and pricing decisions over a finite planning horizon. The demand for products, which depends on their price, is characterized by two stochastic processes: potential demand and customer price sensitivity. An optimal policy for coordinating production and pricing is a time-dependent feedback rule with respect to the state of the manufacturer’s inventories. We show that when the volatility of customer sensitivity to the product price is negligible, the optimal policy can be obtained analytically. Moreover, our simulations demonstrate that the volatility of stochastic customer price sensitivity does not have a strong effect on the manufacturer’s expected profit. Therefore, the solution derived for the case of customer price sensitivity with zero volatility can serve as a good approximation heuristic for the optimal policy if the true volatility of customer price sensitivity is within 40 % of its mean and the volatility of potential demand is within 25 % of its mean. Moreover, under these conditions, a simplified, time-independent control rule deteriorates expected profits by only 1.5 %.     

A dynamic production planning and scheduling algorithm for two products processed on one line

This paper presents a dynamic production planning and scheduling algorithm for two products processed on one line over a fixed time horizon. Production rates are assumed fixed, and restrictions are placed or inventory levels and production run lengths. The resulting problem is a nonlinear binary program, which is solved using an implicit enumeration strategy. The algorithm focuses on the run changeover period while developing tighter bounds on the length of the upcoming run to improve computational efficiency. About 99% pf 297 randomly generated problems with varying demand patterns are solved in less than 15 seconds of CPU time on a CDC Cyber 172 Computer. A mixed integer programming formulation of the generalized multi-product case under no-backlogging of demand is also given.     

Supply chain model for a deteriorating product with time-varying demand and production rate

The paper develops a two-echelon supply chain model with a single-buyer and a single-vendor. The buyer sells a seasonal product over a short selling period and its inventory is subject to deterioration at a constant rate over time. The vendor's production rate is dependent on the buyer's demand rate, which is a linear function of time. Also, the vendor's production process is not perfectly reliable; it may shift from an in-control state to an out-of-control state at any time during a production run and produce some defective (non-conforming) items. Assuming that the vendor follows a lot-for-lot policy for replenishment made to the buyer, the average total cost of the supply chain is derived and an algorithm for finding the optimal solution is developed. The numerical study shows that the supply chain coordination policy is more beneficial than those policies obtained separately from the buyer's and the vendor's perspectives.     

Optimum policy for a production system with major repair and preventive maintenance

This study applies periodic preventive maintenance (PM) to a repairable production system with major repairs conducted after a failure. This study considers failed PM due to maintenance workers incorrectly performing PM and damages occurring after PM. Therefore, three PM types are considered: imperfect PM, perfect PM and failed PM. Imperfect PM has the same failure rate as that before PM, whereas perfect PM makes restores the system perfectly. Failed PM results in system deterioration and major repairs are required. The probability that PM is perfect or failed depends on the number of imperfect maintenance operations conducted since the previous renewal cycle. Mathematical formulas for expected total production cost per unit time are generated. Optimum PM time that minimizes cost is derived. Various special cases are considered, including the maintenance learning effect. A numerical example is given.     

A new heuristic and an exact approach for a production planning problem

Central European Journal of Operations Research - We deal with a very complex and hard scheduling problem. Two types of products are processed by a heterogeneous resource set, where resources have...     

A multiperiod model for production planning and design in a multiproduct batch environment

A general multiperiod model to optimize simultaneously production planning and design decisions applied to multiproduct batch plants is proposed. This model includes deterministic seasonal variations of costs, prices, demands and supplies. The overall problem is formulated as a mixed-integer linear programming model by applying appropriate linearizations of non-linear terms. The performance criterion is to maximize the net present value of the profit, which comprises sales, investment, inventories, waste disposal and resources costs, and a penalty term accounting for late deliveries. A noteworthy feature of this approach is the selection of unit dimensions from the available discrete sizes, following the usual procurement policy in this area. The model simultaneously calculates the plant structure (parallel units in every stage, and allocation of intermediate storage tanks), and unit sizes, as well as the production planning decisions in each period (stocks of both product and raw materials, production plans, policies of sales and procurement, etc.).     

Strong planning and forecast horizons for a model with simultaneous price and production decisions

In this paper, we have solved a general inventory model with simultaneous price and production decisions. Both linear and non-linear (strictly convex) production cost cases are treated. Upper and lower bounds are imposed on state as well as control variables. The problem is solved by using the Lagrangian form of the maximum principle. Strong planning and strong forecast horizons are obtained. These arise when the state variable reaches its upper or lower bound. The existence of these horizons permits the decomposition of the whole problem into a set of smaller problems, which can be solved separately, and their solutions put together to form a complete solution to the problem. Finally, we derive a forward branch and bound algorithm to solve the problem. The algorithm is illustrated with a simple example.     

On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.     

An optimization model for the aggregate production planning of a Brazilian sugar and ethanol milling company

This work presents an optimization model to support decisions in the aggregate production planning of sugar and ethanol milling companies. The mixed integer programming formulation proposed is based on industrial process selection and production lot-sizing models. The aim is to help the decision makers in selecting the industrial processes used to produce sugar, ethanol and molasses, as well as in determining the quantities of sugarcane crushed, the selection of sugarcane suppliers and sugarcane transport suppliers, and the final product inventory strategy. The planning horizon is the whole sugarcane harvesting season and decisions are taken on a discrete fraction of time. A case study was developed in a Brazilian mill and the results highlight the applicability of the proposed approach.     

Integrated production planning and scheduling for a mixed batch job-shop based on alternant iterative genetic algorithm

An integrated optimization production planning and scheduling based on alternant iterative genetic algorithm is proposed here. The operation constraints to ensure batch production successively are determined in the first place. Then an integrated production planning and scheduling model is formulated based on non-linear mixed integer programming. An alternant iterative method by hybrid genetic algorithm (AIHGA) is employed to solve it, which operates by the following steps: a plan is given to find a schedule by hybrid genetic algorithm; in turn, a schedule is given to find a new plan using another hybrid genetic algorithm. Two hybrid genetic algorithms are alternately run to optimize the plan and schedule simultaneously. Finally a comparison is made between AIHGA and a monolithic optimization method based on hybrid genetic algorithm (MOHGA). Computational results show that AIHGA is of higher convergence speed and better performance than MOHGA. And the objective values of the former are an average of 12.2% less than those of the latter in the same running time.     

An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon

An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

Priority planning of a dynamic complex product mix: Elements for a computerized interface between delivery times and plant utilization

The priority planning process is both the management of ensuring reliability in confirming delivery times and maximizing plant capacity utilization.A framework is presented for the decision process of order planning in a business environment with a dynamic product mix consisting of both standard and non-standard products and with a limited machine capacity.The concept of a computerized interface between the priority planning process and the confirmed order file is presented.A simulation study is done to determine the relationship between different manufacturing strategies, delivery time policies and plant efficiency. The method is applied to the production of engineering plastic materials.     

Effect of declining selling price: profit analysis for a single period inventory model with stochastic demand and lead time

In this paper, considering the empirical trend for sales and price of fashion apparels as prototype, optimal ordering policy for a single period stochastic inventory model is investigated. The impact of the presence of random lead time and declining selling price on the profitability of the retailer is explored. Existence of unique optimal solutions for net profit functions is proved. Numerical examples are presented to illustrate the method of identifying profitable levels of inventory holding and penalty costs. Percentage profit per unit investment in inventory is obtained in order to assist managers in taking business decisions, specifically to the extent of whether or not to take up a particular business under known constraints. It is demonstrated that the optimal inventory policy in the absence of price decline and lead time differs considerably from that when lead time and price decline are simultaneously considered.     

Optimal production and distribution policies for a two-stage supply chain with imperfect items and price- and advertisement-sensitive demand: A note

This paper develops inventory models of a vendor–buyer supply chain with imperfect products and shortages based on Rad et al. (2014) and assumes that both the selling price and advertisements influence market demand. For this reason, the buyer mandates an advertising company for promoting the product. The objective of the paper is to determine pricing, advertising, lot-sizing, backordering, and shipment policies under independent and joint optimization. Numerical examples and a sensitivity analysis illustrate the proposed models. The results indicate that coordination becomes more and more advantageous for the supply chain as the sensitivity of demand to price or advertisements increases. Furthermore, as the uncertainty in item quality increases, the buyer reduces its demand to better match demand and supply.