Pegging Resources to Shipments in a Pre-Existing Production Plan

Abstract

In software systems for resource-constrained production planning (RCPP), it is often beneficial to determine a detailed association, or “pegging”, between the resources and the shipments that are enabled by those resources. The method implemented in the software systems is called “Pegging By Explosion” (PBE), for constructing a pegging of a production plan for an RCPP problem. The Pegging By Explosion technique takes a feasible production plan and reconstructs it, using its own specialized incremental allocation technique. A Pegging By Monitoring technique is applied to this reconstruction in order to produce the pegging. The reconstruction is accomplished by a specialized “explosion” technique related to the explosion technique of Material Requirements Planning (MRP).

1 - 15 . (canceled) 
     
     
         16 . A non-transitory computer readable medium containing code implementing a method for constructing a pegging of a pre-existing production plan for a resource-constrained production planning (RCPP) problem, said method comprising the step of constructing the pegging after the production plan already had been generated,
 wherein the plan includes individual resources and individual shipments, and the pegging associates the individual resources in the plan and the individual shipments in the plan and reflects for a given shipment in the plan which resources were used specifically to enable that shipment.   
     
     
         17 . The computer readable medium recited in  claim 16 , wherein the step of constructing the pegging comprises the steps of:
 reconstructing a modified version of the production plan by an incremental allocation technique, and   then applying a Pegging By Monitoring technique to the reconstructed production plan in order to produce the pegging.   
     
     
         18 . The computer readable medium recited in  claim 17 , wherein the step of reconstructing a modified version of the production plan is accomplished by a series of “explosion” steps similar to an explosion technique of Material Requirements Planning (MRP). 
     
     
         19 - 20 . (canceled) 
     
     
         21 . The computer readable medium recited in claim  16 , further comprising the steps of:
 setting ConsSupVol I  (r, tr)←Min ((ConsSupVol (r, tr)−ConsSupVol R  (r, tr)), ReqVol (r, tr)), and   setting ReqVol (r, tr)←+−ConsSupVol I  (r, tr),   
       and wherein the step exploding the requirement to production by operation j comprises the steps of:
 setting ProdVol I  (j, tr)−Min ((ProdVol (j, tr)−ProdVol R  (j, tr)), ReqVol (r, tr)), 
 ∀r′εBOR (j), where BOR is Bill-of-Resources, performing the following three steps:
 ∀tr′εAllPer, performing the following step:
 setting ReqVol (r′, tr′)+UsageRate (j, tr, r′, tr′)*ProdVol I  (j, tr), 
 
 setting ReqVol (r, tr)←+−ProdVol I  (j, tr), and 
 
 
       wherein the step exploding the requirement to stock in period tr−1 comprises the steps of
 if tr=1, doing nothing, but otherwise performing the following three steps:
 setting StockVol I  (r, tr−1)←Min ((StockVol (r, tr−1)−StockVol R  (r, tr−1)), ReqVol (r, tr)), 
 setting ReqVol (r, tr−1)←+StockVol I  (r, tr−1), and 
 setting ReqVol (r, tr)←+−StockVol I  (r, tr−1). 
 
 
     
     
         22 . The computer readable medium recited in  claim 16 , further comprising steps of netting the requirement against supply, exploding the requirement to production by operation j, and exploding the requirement to stock in period tr−1 performed in any order, where this method is called Pegging By Explosion Technique for Positive Consumption RCPP Problems, or PC-PBE technique. 
     
     
         23 - 26 . (canceled) 
     
     
         27 . The computer readable medium recited in  claim 16 , specifically applied to construct a pegging of the solution of a Material Requirements Planning problem. 
     
     
         28 . The computer readable medium recited in  claim 22 , wherein the method is restricted to be used only on problems in which Nperiods=1, where the method is made simpler to implement in the following ways:
 by eliminating the concept of a period from all of the data and notation;   by eliminating the distinction between material resources and capacity resources;   by deleting all references to stock volume (StockVol ( )) and its pegging; and   by removing the exploding the requirement to stock step from the method.   
     
     
         29 . The computer readable medium recited in  claim 22 , wherein the method is restricted to be used only on problems in which each resource can only be produced by at most one operation, where the method is made simpler to implement in the following ways:
 by eliminating the concept of an operation from all of the data and notation, eliminating all data associated with an operation and replacing it by corresponding data associated with a product, so that, e.g., ProdVol (j, tj) for operation j is replaced by ProdVol (r, tr) for product resource r;   by eliminating the following two steps from method:
 ∀jεProdOpns (r), performing the following step:
 exploding the requirement to production by operation j; 
 
   by replacing the above two steps with the following step:
 exploding the requirement to production, if the resource is a product. 
   
     
     
         30 . The computer readable medium recited in  claim 22 , wherein the method is restricted to be used only on problems in which Nperiods=1 and in which each resource can only be produced by at most one operation, where the method is made simpler to implement in the following ways:
 by eliminating the concept of a period from all of the data and notation;   by eliminating the distinction between material resources and capacity resources;   by deleting all references to stock volume (StockVol ( )) and its pegging;   by removing the exploding the requirement to stock step from the method.   by eliminating the concept of an operation from all of the data and notation, eliminating all data associated with an operation and replacing it by corresponding data associated with a product, so that, e.g., ProdVol (j, tj) for operation j is replaced by ProdVol (r, tr) for product resource r;   by eliminating the following two steps from method:
 ∀jεProdOpns (r), performing the following step:
 exploding the requirement to production by operation j; 
 
   by replacing the above two steps with the following step:
 exploding the requirement to production, if the resource is a product. 
   
     
     
         31 . A computer implemented method for constructing a pegging of a production plan for a resource-constrained production planning (RCPP) problem, comprising:
 constructing, performed by an RCPP system, the pegging after the production plan has already been generated;   netting, performed by the RCPP system, a requirement against supply, wherein the netting comprises:
 setting ConsSupVol I  (r, tr)←Min ((ConsSupVol (r, tr)−ConsSupVol R  (r, tr)), ReqVol (r, tr)), and 
 setting ReqVol (r, tr)←+−ConsSupVol I  (r, tr), 
   exploding, performed by the RCPP system, the requirement to production by operation j, wherein the exploding the requirements to production comprises:
 setting ProdVol I  (j, tr)←Min ((ProdVol (j, tr)−ProdVol R  (j, tr)), ReqVol (r, tr)), 
   ∀r′εBOR (j), where BOR is Bill-of-Resources, performing the following three steps:
 ∀tr′εAllPer, performing the following step:
 setting ReqVol (r′, tr′)+UsageRate (j, tr, r′, tr′)*ProdVol I  (j, tr), 
 
 setting ReqVol (r, tr)←+−ProdVol I  (j, tr); 
   exploding the requirement to stock in period tr−1, wherein the exploding the requirement to stock comprises:   doing nothing when tr=1, but otherwise performing the following three steps:
 setting StockVol I  (r, tr−1)←Min ((StockVol (r, tr−1)−StockVol R  (r, tr−1)), ReqVol (r, tr)), 
 setting ReqVol (r, tr−1)←+StockVol I  (r, tr−1), and 
 setting ReqVol (r, tr)←+−StockVol I  (r, tr−1). 
   
     
     
         32 . A computer implemented method for constructing a pegging of a production plan for a resource-constrained production planning (RCPP) problem which is a Positive Consumption RCPP problem, comprising:
 receiving into an RCPP system as input the Positive Consumption RCPP problem;   receiving into the RCPP system as input a feasible production plan for the problem;   either receiving as input into the RCPP system a shipment sequence corresponding to shipments in the production plan, or computing by the RCPP system a default shipment sequence;   constructing by the RCPP system the pegging after the production plan has already been generated; wherein the constructing the pegging comprises:
 (1) reconstructing a modified version of the production plan by an incremental allocation technique, wherein the reconstructing is accomplished by performing a series of “explosion” steps to produce a reconstructed production plan; followed by 
 (2) applying a Pegging By Monitoring technique to the reconstructed production plan in order to produce the pegging; 
   initializing the reconstructed production plan to zero, initializing the pegging to zero,   proceeding through the triples (d*, td*, IncShipVol) in the shipment sequence, with each demand d* in period td*;   constructing, by performing a set of specialized explosion steps, an incremental production plan denoted by ProdVol I  ( ), StockVol I  ( ), ConsSupVol I  ( ), and ShipVol I  ( ) that specifies a feasible means of enabling a shipment of IncShipVol units to demand d* in period td* without using any resources that have already been pegged,
 wherein the specialized explosion steps comprise: 
   initializing the incremental production plan to zero,   associating a quantity, ReqVol (r, tr), with each resource r in each period tr,   initializing all values of ReqVol (r, tr) to zero,   setting ShipVol I  (d*, td*) to IncShipVol,   setting ReqVol (DemRes (d*), td*) to IncShipVol,   proceeding through each resource rεAllRes in order of decreasing ResIdx (r):   proceeding through each period trεAllPer in decreasing order:   netting the requirement against supply, ∀jεProdOpns (r):   
       wherein the netting the requirement against supply comprises:
 setting ConsSupVol I  (r, tr)←Min ((ConsSupVol (r, tr)−ConsSupVol R  (r, tr)), ReqVol (r, tr)), and 
 setting ReqVol (r, tr)←+−ConsSupVol I  (r, tr), 
 exploding the requirement to production by operation j, wherein the exploding the requirement to production by operation j comprises: 
 setting ProdVol I  (j, tr)←Min ((ProdVol (j, tr)−ProdVol R  (j, tr)), ReqVol (r, tr)), 
 ∀r′εBOR (j), where BOR is Bill-of-Resources, performing the following three steps:
 ∀tr′εAllPer, performing the following step:
 setting ReqVol (r′, tr′)+UsageRate (j, tr, r′, tr′)*ProdVol I  (j, tr), 
 
 setting ReqVol (r, tr)←+−ProdVol I  (j, tr), and 
 
 exploding the requirement to stock in period tr−1, wherein the exploding the requirement to stock in period tr−1 comprises: 
 doing nothing when tr=1, but otherwise performing the following three steps:
 setting StockVol I  (r, tr−1)←Min ((StockVol (r, tr−1)−StockVol R  (r, tr−1)), ReqVol (r, tr)), 
 setting ReqVol (r, tr−1)←+StockVol I  (r, tr−1), and 
 setting ReqVol (r, tr)←+−StockVol I  (r, tr−1) 
 
 adding the incremental production plan to the reconstructed production plan; 
 pegging the incremental production plan to the current shipment (d*, td*); and 
 reporting the pegging. 
 
     
     
         33 . The computer readable medium recited in  claim 18 , wherein the method is restricted to be used only on Positive Consumption resource-constrained production planning (RCPP) problems and comprises of the steps of:
 reading in a Positive Consumption RCPP problem,   reading in a feasible pre-existing production plan for the problem,   either reading in a shipment sequence corresponding to the shipments in the pre-existing production plan, or computing a default shipment sequence,   initializing the reconstructed production plan to zero,   initializing the pegging to zero,   proceeding through the triples (d*, td*, IncShipVol) in the shipment sequence, with each demand d* in period td*, and performing the following three steps:
 employing a specialized explosion technique to construct an incremental production plan (denoted by ProdVol I  ( ), StockVol I  ( ), ConsSupVol I  ( ), and ShipVol I  ( )) that specifies a feasible means of enabling a shipment of IncShipVol units to demand d* in period td* without using any resources that have already been pegged, 
 adding the incremental production plan to the reconstructed production plan, and 
 pegging the incremental production plan to the current shipment (d*, td*), and 
   reporting the pegging.   
     
     
         34 . The computer implemented method recited in claim  7 , wherein the method comprises constructing a pegging of a production plan for any RCPP problem, and
 explicitly constructing an auxiliary problem and production plan identical to the original problem and production plan, except that
 for each resource, an “auxiliary” operation is added that produces that resource and consumes no resources, 
 the negative consumption of each resource is replaced with production by the auxiliary operation for that resource, and 
 all negative usage rates are set to zero, and 
   applying the PC-PBE technique to the auxiliary problem and production plan, and   transferring the resulting pegging back into the original problem and production plan.   
     
     
         35 . The computer implemented method recited in claim  7 , comprising constructing a pegging of a production plan for any RCPP problem, and
 conceptually defining the auxiliary problem and production plan identical to the original problem and production plan, except for steps comprising:
 for each resource, adding an “auxiliary” operation that produces that resource and consumes no resources, 
 replacing the negative consumption of each resource with production by the auxiliary operation for that resource, and 
 setting all negative usage rates to zero. 
   
     
     
         36 . The computer implemented method recited in  claim 35  comprising constructing a pegging of a production plan for a variant of an RCPP problem that has been generalized and into which has been substituted therein a Bill-of-Resources (BOR) structure, the method comprising:
 conceptually defining a transformed RCPP problem and production plan that is equivalent to the original problem and production plan, but has no substitution. 
 
     
     
         37 . The computer implemented method recited in  claim 35 , comprising constructing a pegging of a production plan for a variant of an RCPP problem that has been generalized and into which has been substituted therein a Bill-of-Resources (BOR) structure and in which violations of the resource constraints are permitted, the method comprising:
 conceptually defining a transformed RCPP problem and production plan that is equivalent to the original problem and production plan, but has no substitution and does not violate any of the resource constraints.   
     
     
         38 . The computer readable medium recited in  claim 22 , wherein the method comprises construction of a pegging of a production plan for any RCPP problem, and
 explicitly constructing an auxiliary problem and production plan identical to the original problem and production plan, except that
 for each resource, an “auxiliary” operation is added that produces that resource and consumes no resources, 
 the negative consumption of each resource is replaced with production by the auxiliary operation for that resource, and 
 all negative usage rates are set to zero, and 
   applying the PC-PBE technique to the auxiliary problem and production plan, and   transferring the resulting pegging back into the original problem and production plan.   
     
     
         39 . The computer readable medium recited in  claim 22 , wherein the method comprises construction of a pegging of a production plan for any RCPP problem, and
 conceptually defining the auxiliary problem and production plan identical to the original problem and production plan, except that
 for each resource, an “auxiliary” operation is added that produces that resource and consumes no resources, 
 the negative consumption of each resource is replaced with production by the auxiliary operation for that resource, and 
 all negative usage rates are set to zero, 
   working with the original problem and production plan, and   performing a sequence of steps that are mathematically equivalent to those that the PC-PBE technique would be performing, if it were being applied to the auxiliary problem and production plan, whereby the method is called Pegging By Explosion Technique for RCPP Problems, or the PBE technique.   
     
     
         40 . The computer readable medium recited in  claim 39 , wherein the method comprises construction of a pegging of a production plan for a variant of an RCPP problem that has been generalized so as to allow substitution in a Bill-of-Resources (BOR) structure, and
 conceptually defining a transformed RCPP problem and production plan that is equivalent to the original problem and production plan, but has no substitution,   working with the original problem and production plan, and   performing a sequence of steps that are mathematically equivalent to those that the PBE technique would be performing, if it were being applied to the transformed problem and production plan.   
     
     
         41 . The computer readable medium recited in  claim 39 , wherein the method comprises construction of a pegging of a production plan for a variant of an RCPP problem that has been generalized so as to allow substitution in a Bill-of-Resources (BOR) structure and to permit violations of the resource constraints, and
 conceptually defining a transformed RCPP problem and production plan that is equivalent to the original problem and production plan, but has no substitution and does not violate any of the resource constraints,   working with the original problem and production plan, and   performing a sequence of steps that are mathematically equivalent to those that the PBE technique would be performing, if it were being applied to the transformed problem and production plan.