Studies On The Decision Of Dynamic Lot Sizing And Forecast Horizon Under Demand Substitution And Production Changeovers

The dynamic lot sizing model is widely applicable in production planning and inventory management,especially in the context of material requirement planning.Because of the wide applications,the dynamic lot sizing problem has received a significant amount of academic attention since it was first introduced six decades ago.To obtain the forecast horizon is as important as the optimal lot sizing decision in the dynamic lot sizing problem.A forecast horizon is a period with the property that data for periods beyond it are not required in order to determine the optimal decisions for the first few periods.The important of the determination for the forecast horizon is immediate: the forecasts become less reliable and the forecasting costs become more expensive for the reason that the forecasts further into the future are needed.In addition,there is the increased calculating burden related with solving problems with long horizon.The shorter the problem horizon,the more ineffective the first few periods decision is in reducing the total cost.With the increasingly fierce market competition,the enterprises always expand the production lines,and then can produce series products with nuance.This way can extend the volume growth by subdividing market demands,further,enhance competitiveness and increase profit.While the production of multiple products can improve the clients' satisfaction,it brings a huge challenge for the production decision-making of the enterprise at the same time.There exists the substitution effect among the products and alternate production on the same production line.There are very few literature on dynamic lot sizing model and forecast horizon under demand substitution and production changeovers.Furthermore,these studies ignore a great many realistic factors that may influence the optimal decision-makings of the firms.These realistic factors include setup costs,time-invariant costs,the limited lifetime of the products,batch production and others.The studies of forecast horizon base on the approximate solution of the dynamic lot sizing model.Based on the importances of product substitution and production changeovers and the shortcomings of the existing studies,we study the optimal decision and forecast horizon in the dynamic lot sizing problem with demand substitution and production changeover.The main contents are as follows:(1)The two-product dynamic lot sizing model with no setup costs undertime-invariant costs.Firstly,we review the classical two-item dynamic lot sizing model with demand downward substitution and production changeovers,and the properties of the optimal solution.Based on the properties of the optimal solution,we devise the forward dynamic programming algorithm to solve the problem.We give the lower bound of the number of switching point in the optimal solution and prove the monotonicity of production points for two products.According to the relationship between the production point and regeneration point,we establish the monotonicity of regeneration point for two products.By establishing the regeneration set for two products,we give the sufficient condition to obtain the forecast horizon.Finally,we extend the model by considering two-way substitution.By comparing the one-way substitution model with two-way substitution model,we find that the properties and forward dynamic programming algorithms have symmetries.Based on the symmetries,it is not intricate to solve the model with two-way substitution.Therefore,we focus on the one-way model in this thesis and do not investigate the two-way model.(2)The two-product dynamic lot sizing model with setup costs under time-invariant costs.In the production of the firm,a kind of fixed costs such as the wage and rental fee are very common.This kind of fixed costs are referred to as the setup costs.We generalize the classical model by considering the setup costs and construct the cost minimization model including the changeover costs,setup costs,substitution costs and holding costs.Next,it is similar to the study of the classical model.Based on the properties of the optimal solution,we devise the forward dynamic programming algorithm to solve the problem.Furthermore,We consider two variants of the model with the setup costs,backloggings and lost sales(stockouts)are permitted.For the dynamic lot sizing model with backlogging,we also consider two sub-cases: one is no backlogging at the end of period T,in the other sub-case,backlogging is permitted at the end of period T.Compared with the forward dynamic programming algorithm in the dynamic lot sizing models with no backlogging at the end of period T and stockouts,we find that the dynamic lot sizing model with stockouts can be regarded as a special case of the dynamic lot sizing model with backlogging.(3)The two-product dynamic lot sizing model under time-variant costs.The costs of raw materials are not always stationary.It is very common that the costs of raw materials are time-variant.Thus,the unit production costs are time-invariant because of the non-stationary costs of raw materials.We generalize the classical model byconsidering the time-variant unit production costs and construct the cost minimization model including the changeover costs,variable production costs,substitution costs and holding costs.Based on the properties of the optimal solution,we devise the forward dynamic programming algorithm to solve the problem.By the marginal cost analysis method,we give the sufficient condition to establish the monotonicity of production points for two products,then we establish the regeneration set for two products and give the sufficient condition to obtain the forecast horizon.If there is no speculative motive in holding inventory,then the methods of obtaining the forecast horizon is same to as the case of time-invariant unit production costs.(4)The two-product dynamic lot sizing model under the short lifetime.We study the two-product dynamic lot sizing problem with the short lifetime under demand substitution and production changeovers.The famous Zero-Inventory-Property does not hold under the no unlimited time-varying unit production costs.We prove the first-in-first-out property.This property shows that The practitioner will adopt the rule of first-in-first-out to manage the inventories of the products with the short lifetime.By the marginal cost analysis method,we give the forecast horizon results.There also exists an interesting phenomenon: if there is no speculative motive in holding inventory,the Zero-Inventory-Property still holds even in the dynamic lot sizing problem under the products with the short lifetime.This means that we can solve the problem under the products with the short lifetime as the the products with the long lifetime.(5)The two-product dynamic lot sizing model under batch production.We first consider two dynamic lot sizing models with batch production under demand substitution and production changeover.In the first model,we consider the setup costs and redefine the regeneration point.In the second model,we consider the penalty cost for changing the production rate from lower level to higher level,and define the production block.Based on the production block,we define the production point.We also consider a special case for the penalty cost.The penalty costs are charged for changing the production rate from zero to nonzero level.We also give an important property in the optimal solution,that is the period before the production point is the regeneration point.Similarly,the forward dynamic programming algorithm is developed to solve the problem.For the two kind of models,the properties in the optimal solution are different under time-invariant and time-variant costs.We can not obtain the forecast horizon results under batch production and demand substitution.We will solve thischallenging problem in the future.The optimal lot sizing decision and forecast horizon under demand substitution and production changeover have the practical significance in the field of production operation management,the two issues are also important parts in the theoretical research of operation management.However,there are no effective ways to solve the two issues.Therefore,we devise the forward dynamic programming algorithm to obtain the optimal production decision under different production situation in the enterprise.Moreover,we study the forecast horizon under different cost structures systematically.The studies of the optimal production decision by devising the forward dynamic programming algorithm and forecast horizon by establishing the regeneration set of two product are the main innovation points of the research.The in-depth research for the optimal decision and forecast horizon of two-product dynamic lot sizing problem can not only promote the study of the existence of forecast horizon for multi-product,and enrich the methods and techniques of obtaining the forecast horizon results,but also has momentous instructional significance on the practice of production management in the enterprise.