In one embodiment, supply chain planner 110 may be coupled with network 170 using communication link 180, which may be any wireline, wireless, or other link suitable to support data communications between supply chain planner 110 and network 170 during operation of supply chain network 100. Inventory system 120 may be coupled with network 170 using communication link 182, which may be any wireline, wireless, or other link suitable to support data communications between inventory system 120 and network 170 during operation of supply chain network 100. Transportation network 130 may be coupled with network 170 using communication link 184, which may be any wireline, wireless, or other link suitable to support data communications between transportation network 130 and network 170 during operation of supply chain network 100. One or more imaging devices 140 are coupled with network 170 using communication link 186, which may be any wireline, wireless, or other link suitable to support data communications between one or more imaging devices 140 and network 170 during operation of distributed supply chain network 100. One or more supply chain entities 150 may be coupled with network 170 using communication link 188, which may be any wireline, wireless, or other link suitable to support data communications between one or more supply chain entities 150 and network 170 during operation of supply chain network 100. One or more computers 160 may be coupled with network 170 using communication link 190, which may be any wireline, wireless, or other link suitable to support data communications between one or more computers 160 and network 170 during operation of supply chain network 100.

Although communication links 180-190 are shown as generally coupling supply chain planner 110, inventory system 120, transportation network 130, one or more imaging devices 140, one or more supply chain entities 150, and one or more computers 160 to network 170, each of supply chain planner 110, inventory system 120, transportation network 130, one or more imaging devices 140, one or more supply chain entities 150, and one or more computers 160 may communicate directly with each other, according to particular needs.

In another embodiment, network 170 includes the Internet and any appropriate local area networks (LANs), metropolitan area networks (MANs), or wide area networks (WANs) coupling supply chain planner 110, inventory system 120, transportation network 130, one or more imaging devices 140, one or more supply chain entities 150, and one or more computers 160. For example, data may be maintained locally or externally of supply chain planner 110, inventory system 120, transportation network 130, one or more imaging devices 140, one or more supply chain entities 150, and one or more computers 160 and made available to one or more associated users of supply chain planner 110, inventory system 120, transportation network 130, one or more imaging devices 140, one or more supply chain entities 150, and one or more computers 160 using network 170 or in any other appropriate manner. For example, data may be maintained in a cloud database at one or more locations external to supply chain planner 110, inventory system 120, transportation network 130, one or more imaging devices 140, one or more supply chain entities 150, and one or more computers 160 and made available to one or more associated users of supply chain planner 110, inventory system 120, transportation network 130, one or more imaging devices 140, one or more supply chain entities 150, and one or more computers 160 using network 170, the cloud, or in any other appropriate matter. Those skilled in the art will recognize that the complete structure and operation of network 170 and other components within supply chain network 100 are not depicted or described. Embodiments may be employed in conjunction with known communications networks and other components.

In accordance with the principles of embodiments described herein, supply chain planner 110 may reallocate inventory of one or more items among demands or orders of one or more supply chain entities 150. In addition, one or more computers 160 associated with supply chain network 100 may instruct automated machinery (i.e., robotic warehouse systems, robotic inventory systems, automated guided vehicles, mobile racking units, automated robotic production machinery, robotic devices and the like) to adjust product mix ratios, inventory levels at various stocking points, production of products of manufacturing equipment, proportional or alternative sourcing of one or more supply chain entities 150, and the configuration and quantity of packaging and shipping of items based on current inventory, production levels, and/or one or more other factors described herein. For example, the methods described herein may include one or more computers 160 receiving product data from automated machinery having at least one sensor and product data 224 corresponding to an item detected by the automated machinery. Received product data may include an image of the item, an identifier, as described above, and/or other data associated with the item, including, for example, dimensions, texture, estimated weight, and the like.

According to embodiments, the methods may further include one or more computers 160 looking up received product data 224 in a database system associated with supply chain planner 110 to identify the item corresponding to product data 224 received from automated machinery. Based on the identification of the item, one or more computers 160 may also identify (or alternatively generate) a first mapping in the database system, where the first mapping is associated with the current location of the identified item. One or more computers 160 may also identify a second mapping in the database system, where the second mapping is associated with a past location of the identified item. One or more computers 160 may also compare the first mapping and the second mapping to determine if the current location of the identified item in the first mapping is different than the past location of the identified item in the second mapping. One or more computers 160 may then send instructions to the automated machinery based, as least in part, on one or more differences between the first mapping and the second mapping such as, for example, to locate items to add to or remove from an inventory of or shipment for one or more supply chain entities 150. In addition, or as an alternative, supply chain planner 110 monitors one or more supply chain constraints of one or more items at one or more supply chain entities 150 and adjusts the orders and/or inventory of one or more supply chain entities 150 at least partially based on one or more supply chain constraints.

FIG. 2 illustrates supply chain planner 110 of FIG. 1 in greater detail, in accordance with an embodiment. As described above, supply chain planner 110 comprises server 112 and database 114. Although supply chain planner 110 is shown as comprising a single server 112 and a single database 114, embodiments contemplate any suitable number of servers 112 or databases 114 internal to or externally coupled with supply chain planner 110.

Server 112 of supply chain planner 110 may comprise modeler 210 and solver 212. Although server 112 is shown and described as comprising a single modeler 210 and a single solver 212, embodiments contemplate any suitable number or combination of these located at one or more locations, local to, or remote from supply chain planner 110, such as on multiple servers or computers at any location in supply chain network 100.

According to embodiments, modeler 210 of server 112 identifies resources, operations, buffers, and pathways, and maps supply chain network 100 using data models 222, as described in more detail below. In one embodiment, modeler 210 maps optional resources and material as primary and alternate pathways. In addition, or in the alternative, modeler 210 generates a supply chain planning problem to represent the flow of materials through supply chain network 100.

According to embodiments, solver 212 of supply chain planner 110 solves a supply chain planning problem as an LPP comprising three components: objectives, constraints, and bounds. According to embodiments, objectives of a multi-objective LPP represent business objectives (such as, for example, minimizing total inventory, maximizing profits, etc.); constraints comprise limitations to capacity, materials, lead times, and the like; and bounds comprise maximum and/or minimum values for decision variables (for example, in an embodiment in which capacity may only be used for ten hours per day, ten hours may be the upper bound on the capacity usage).

Database 114 of supply chain planner 110 may comprise one or more databases or other data storage arrangement at one or more locations, local to, or remote from, server 112. Database 114 comprises, for example, supply chain input data 220, data models 222, product data 224, demand data 226, inventory data 228, supply chain models 230, inventory policies 232, variable lists 234, LPP run results 236, and intermediate objectives data 238. Although database 114 is shown and described as comprising supply chain input data 220, data models 222, product data 224, demand data 226, inventory data 228, supply chain models 230, inventory policies 232, variable lists 234, LPP run results 236, and intermediate objectives data 238, embodiments contemplate any suitable number or combination of these, located at one or more locations, local to, or remote from, supply chain planner 110 according to particular needs.

As an example only and not by way of limitation, database 114 stores supply chain input data 220, including one or more supply chain planning problems of supply chain network 100 that may be used by supply chain planner 110, modeler 210, and/or solver 220. Supply chain input data 220 may comprise, for example, various decision variables, business constraints, goals, and objectives of one or more supply chain entities 150. According to some embodiments, supply chain input data 220 may comprise hierarchical objectives specified by, for example, business rules, master planning requirements, scheduling constraints, and discrete constraints, including, for example, sequence dependent setup times, lot-sizing, storage, shelf life, and the like.

Data models 222 represent the flow of materials through one or more supply chain entities 150 of supply chain network 100. Modeler 210 of supply chain planner 110 may model the flow of materials through one or more supply chain entities 150 of supply chain network 100 as one or more data models comprising, for example, a network of nodes and edges. Material storage and/or transition units may be modeled as nodes, which may be referred to as buffer nodes, buffers, or nodes. Each node may represent a buffer for an item (such as, for example, a raw material, intermediate good, finished good, component, and the like), resource, or operation (including, for example, a production operation, assembly operation, transportation operation, and the like). Various transportation or manufacturing processes are modeled as edges connecting the nodes. Each edge may represent the flow, transportation, or assembly of materials (such as items or resources) between the nodes by, for example, production processing or transportation. A planning horizon for data models 222 may be broken down into elementary time-units, such as, for example, time-buckets, or, simply, buckets. The edge between two buffer nodes denote processing of material and the edge between different buckets for the same buffer indicates inventory carried forward. Flow-balance constraints for most, if not every buffer in every bucket, model the material movement in supply chain network 100.

Product data 224 of database 114 may comprise one or more data structures for identifying, classifying, and storing data associated with products, including, for example, a product identifier (such as a Stock Keeping Unit (SKU), Universal Product Code (UPC), or the like), product attributes and attribute values, sourcing information, and the like. Product data 224 may comprise data about one or more products organized and sortable by, for example, product attributes, attribute values, product identification, sales quantity, demand forecast, or any stored category or dimension. Attributes of one or more products may be, for example, any categorical characteristic or quality of a product, and an attribute value may be a specific value or identity for the one or more products according to the categorical characteristic or quality, including, for example, physical parameters (such as, for example, size, weight, dimensions, fill level, color, and the like).

Demand data 226 of database 114 may comprise, for example, any data relating to past sales, past demand, purchase data, promotions, events, or the like of one or more supply chain entities 150. Demand data 226 may cover a time interval such as, for example, by the minute, hour, daily, weekly, monthly, quarterly, yearly, or any suitable time interval, including substantially in real time. According to embodiments, demand data 226 may include historical demand and sales data or projected demand forecasts for one or more retail locations, customers, regions, or the like of one or more supply chain entities 150 and may include historical or forecast demand and sales segmented according to product attributes, customers, regions, or the like.

Inventory data 228 of database 114 may comprise any data relating to current or projected inventory quantities or states, order rules, or the like. For example, inventory data 228 may comprise the current level of inventory for each item at one or more stocking locations across supply chain network 100. In addition, inventory data 228 may comprise order rules that describe one or more rules or limits on setting an inventory policy, including, but not limited to, a minimum order quantity, a maximum order quantity, a discount, a step-size order quantity, and batch quantity rules. According to some embodiments, supply chain planner 110 accesses and stores inventory data 228 in database 114, which may be used by supply chain planner 110 to place orders, set inventory levels at one or more stocking points, initiate manufacturing of one or more items (or components of one or more items), or the like. In addition, or as an alternative, inventory data 228 may be updated by receiving current item quantities, mappings, or locations from inventory system 120, transportation network 130, one or more imaging devices 140, and/or one or more supply chain entities 150.

Supply chain models 230 of database 114 may comprise characteristics of a supply chain setup to deliver the customer expectations of a particular customer business model. These characteristics may comprise differentiating factors, such as, for example, MTO (Make-to-Order), ETO (Engineer-to-Order) or MTS (Make-to-Stock). Additionally, or in the alternative, supply chain models 230 may comprise characteristics that specify the supply chain structure in even more detail, including, for example, specifying the type of collaboration with the customer (e.g. Vendor-Managed Inventory (VMI)), from which stocking locations or suppliers items may be sourced, customer priorities, demand priorities, how products may be allocated, shipped, or paid for, by particular customers, and the destination stocking locations or one or more supply chain entities 150 where items may be transported. Each of these characteristics may lead to different supply chain models 230.

Inventory policies 232 of database 114 may comprise any suitable inventory policy describing the reorder point and target quantity, or other inventory policy parameters that set rules for supply chain planner 110 to manage and reorder inventory. Inventory policies 232 may be based on target service level, demand, cost, fill rate, or the like. According to embodiments, inventory policies 232 comprise target service levels that ensure that a service level of one or more supply chain entities 150 is met with a certain probability. For example, one or more supply chain entities 150 may set a target service level at 95%, meaning one or more supply chain entities 150 will set the desired inventory stock level at a level that meets demand 95% of the time. Although a particular target service level and percentage is described, embodiments contemplate any target service level, for example, a target service level of approximately 99% through 90%, 75%, or any target service level, according to particular needs. Other types of service levels associated with inventory quantity or order quantity may comprise, but are not limited to, a maximum expected backlog and a fulfillment level. Once the service level is set, supply chain planner 110 may determine a replenishment order according to one or more replenishment rules, which, among other things, indicates to one or more supply chain entities 150 to determine or receive inventory to replace the depleted inventory.

According to embodiments, solver 212 generates variable lists 234 comprising cumulative list of bound changes, a list of common variables, and a list of current run only variables. According to embodiments, solver 212 generates the cumulative list of bound changes while performing variable fixing during the solve of the multi-objective hierarchical LPP for the previous run. In addition, or as an alternative, solver 212 generates the list of common variables and the list of current run only variables after generating the multi-objective hierarchical LPP for the current run by mapping the variables of each multi-objective hierarchical LPP and storing the indication whether the variable is common to both multi-objective LPPs or is present in only the current run. Variable lists 234 are utilized in the process of solving a previous or base run LPP, in order to derive one or more intermediate objectives. Solver 212 may categorize variables according to whether they are used in only a first run (base run or previous run) of solving the LPP problem, used in only a second run (subsequent run or current run) of solving the LPP problem, or are common to both the first and second runs of the LPP problem. According to embodiments, the cumulative list of bound changes comprises a variable name and a status, wherein the status indicates whether the variable is fixed at its upper bound, fixed at its lower bound, or not fixed. According to an embodiment, the status indicates the bound change as per the higher objective which causes the bound change for a variable, if the same variable undergoes bound changes by more than one objective.

Solver 212 generates list of common variables and list of current run only variables. According to an embodiment, solver 212 checks variables in the current run with variables in the previous run and maps those variables common to both the previous run and the current run to the list of common variables and maps those variables present only in the current run to the list of current run only variables.

In an embodiment, solver 212 may store the results and/or solutions of one or more previous (or base run) LPP solves and/or one or more subsequent (or current run) LPP solves in LPP run results data 236 of database 114. As disclosed above, solver 212 calculates one or more intermediate objectives using variable lists 234, comprising the cumulative list of bound changes, list of common variables, and list of current-run only variables, as described in further detail below.

FIG. 3 illustrates base run 300 of a multi-objective hierarchical LPP, in accordance with an embodiment. Base run (Run1) 300 comprises the solutions of the multi-objective hierarchical LPP for each of three objectives: base run solution of the LPP for first objective (Obj1) 302; base run solution of LPP for second objective (Obj2) 304; and base run solution of LPP for third objective (Obj3) 306. In this example, Obj1 comprises improve demand satisfaction, which may be represented by an objective function that minimizes the quantity of unmet demand. Obj2 comprises maximizing usage of primary resources, which may be represented by an objective function that minimizes usage of alternate resources. By way of a further example, Obj3 comprises planning items as just-in-time (JIT) as possible, which may be represented by an objective function that minimizes the quantity of carried-over items. Although particular examples of objectives and objective functions are shown and described, embodiments contemplate any objective represented by minimizing or maximizing any suitable objective function, according to particular needs.

As described in more detail herein, embodiments of solver 212 of supply chain planner 110 may solve a multi-objective hierarchical LPP by iteratively loading and solving the LPP for each objective in accordance with an order described by a hierarchy of the objectives. A hierarchy of the objectives indicates that the hierarchical objectives are solved in the order indicated by the hierarchy, from an objective higher in the hierarchy (higher order or higher priority objective) to an objective lower in the hierarchy (lower order or lower priority objective). The hierarchical order of the objectives may indicate the order of importance of the objectives (i.e. the first objective is more important than the second objective; the second objective is more important than the third objective etc.). When solving the LPP for one or more lower objectives, solver 212 sets decision variables at their upper or lower bounds (which may be referred to as variable fixing) to retain the objective value of one or more higher objectives. In addition, or in the alternative, solver 212 may use, as a starting basis, some LPP solution information from the preceding higher objective when solving for a lower objective. After solving the LPP for a current objective, solver 212 updates the list of the variables to be fixed at their upper or lower bounds based on the solution to the current objective. Solver 212 may then iteratively repeat solving the LPP for each objective following this technique until solver 212 solves all objectives of the multi-objective hierarchical LPP, as described below.

According to embodiments, solver 212 uses a primal simplex method and/or a dual simplex method to solve each objective of an LPP by going from one basis to the next, iteratively, until reaching an optimal basis that is linked to a unique optimal solution of the LPP for the current objective. The optimal basis may be both primal-feasible and dual-feasible. Primal-infeasible and dual-infeasible refer to the performance of a particular starting basis when solving an LPP with a primal simplex method or a dual simplex method, as described below. When using a primal simplex method, solver 212 searches for a primal feasible basis (which may be dual infeasible) and then transforms the found primal feasible basis to another primal feasible basis, iteratively, until solver 212 identifies a primal feasible basis that is also the optimal basis. When using a dual simplex method, solver 212 searches for a dual feasible basis (which may be primal infeasible), and then transforms the found dual feasible basis to another dual feasible basis, iteratively, until solver 212 identifies a dual feasible basis that is also the optimal basis. Solver 212 uses a primal simplex method and a dual simplex method to solve an LPP by going from one basis to the next, iteratively, until reaching an optimal basis that is linked to a unique optimal solution of an LPP, which is both primal-feasible and dual-feasible.

FIG. 4 illustrates method 400 of solving a multi-objective hierarchical LPP incorporating solution information from a base or previous run into a subsequent run, in accordance with an embodiment. Method 400 proceeds by one or more activities, which although described in a particular order may be performed in one or more permutations, according to particular needs.

At activity 402, supply chain planner 110 performs a base run of a multi-objective hierarchical LPP. Modeler 210 may access one or more of supply chain input data 220, data models 222, product data 224, demand data 226, inventory data 228, supply chain models 230, and/or inventory policies 232, and may use data stored therein to generate a supply chain planning problem (including but not limited to a multi-objective hierarchical LPP) to represent the flow of materials through supply chain network 100. Solver 212 of supply chain planner 110 accesses the supply chain planning problem and may solve the supply chain planning problem as a multi-objective hierarchical LPP comprising three components: objectives, constraints, and bounds. Solver 212 may solve the multi-objective hierarchical LPP by iteratively loading and solving the LPP for each objective in accordance with an order described by a hierarchy of the objectives, as described above with reference to FIG. 3. Solver 212 may store the results of solving the multi-objective hierarchical LPP in LPP run results 236 of supply chain planner 110 database. Solver 212 may store, in the cumulative lists of bound changes in supply chain planner 110 database, one or more cumulative lists of all decision variables which solver 212 has set at an upper or lower bound (referred to above as variable fixing) while performing the base run of the multi-objective hierarchical LPP solve. For example, in the process of performing the base run, solver 212 may set all decision variables with negative reduced cost at the upper bound, and all decision variables with positive reduced cost at the lower bound, and may store the cumulative changes made to the decision variables in the cumulative lists of bound changes. Decision variables with zero reduced cost (having neither a good effect nor a bad effect on the objective value) may be free variables and may be set at upper bound, lower bound, or other bounds.

At activity 404, solver 212 accesses cumulative list of bound changes stored in the database. Because it is likely that the decision variables that improved the quality of the LPP base run will have a similar effect on subsequent LPP runs, and that the decision variables that degraded the quality of the LPP base run will have a similar effect on subsequent LPP runs, cumulative list of bound changes provides solution information that solver 212 may use to perform subsequent LPP runs with reduced computational requirements without impairing solution quality.

At activity 406, solver 212 derives one or more intermediate objectives using cumulative list of bound changes. Solver 212 solves the intermediate objective before solving objectives of subsequent LPP runs. For example, in an embodiment in which the base LPP run (Run1) comprises three objectives (Obj1, Run1; Obj2, Run1; and Obj3; Run1), and a subsequent LPP run (Run2) also comprises three objectives (Obj1, Run2; Obj2, Run2; and Obj3, Run2), solver 212 may derive an intermediate objective (Obj0, Run2) after performing Run1, and may solve Obj0, Run2 as the first objective solved in Run2, before solving Obj1, Run2. Solver 212 stores each intermediate objective in one or more intermediate objectives data 238 of supply chain planner database 114.

In an embodiment, solver 212 derives one or more intermediate objectives by accessing, (a) cumulative lists of bound changes from a previous (or base) run; (b) a list of common variables (i.e., variables shared between the previous (or base) run and the subsequent (or current) run; and (c) a list of current run only variables (i.e., variables that are newly introduced in the subsequent (or current) run). Solver 212 categorizes the variables of the list of common variables and the list of current run only variables according to the following four categories: Category a1 are the common variables which were fixed at a lower bound in the previous run; Category a2 are the common variables which were fixed at an upper bound in the previous run; Category a3 are the common variables that were not fixed to an upper bound or a lower bound in the previous run; and Category a4 are the current run only variables. Solver 212 assigns weights and/or coefficients to each of the categories and creates the intermediate objective as a linear minimization objective function comprising the weighted sum of each category of variables. In one embodiment, the intermediate objective is the following minimization problem:

Minimize:

- a1*(sum of common variables fixed at lower bound in previous run)+
- a2*(sum of common variables fixed at upper bound in previous run)+
- a3*(sum of common variables not fixed at upper bound or lower bound in previous run)+
- a4*(sum of current run only variables)

wherein a1, a2, a3, and a4 are the coefficient values assigned to the corresponding category (i.e., Category a1, Category a2, Category a3, and Category a4, respectively). Rules limit the values of the coefficients that solver 212 assigns to each category. According to embodiments, solver 212 assigns values to the coefficients of Category a1-a4 variables subject to the following rules: the coefficient of Category a1 is greater than zero to force these variables to the lower bound; the coefficient of Category a2 is less than zero to force these variables to the upper bound; the coefficient of Category a3 is zero to not influence these variables; and the coefficient of Category a4 is greater than or equal to zero (to have no influence on these variables (a4=0) or to force these variables to the lower bound (a4>0)). According to some embodiments, the value for Category a1 is always greater than the value for Category a4. In addition, or as an alternative, the values for Category a1 and Category a2 are the same magnitude, but opposite sign (e.g., Category a1 is assigned a value of one hundred (100), and Category a2 is assigned a value of negative one hundred (−100)). Although particular values are described for the Categories of variables used to assigned coefficients/weights for the intermediate objective function in the form of a minimization problem comprising the weighted sums of each category of variables, embodiments contemplate other suitable values, according to particular needs.

At activity 408, solver 212 solves the LPP of the subsequent (or current) run for the intermediate objective (Obj0, Run2) and utilizes the solution to generate the starting basis for the first objective of the subsequent LPP run (in the example described above, Obj1, Run2). Because the intermediate objective incorporates information derived from solving the previous run, using the solution of the current run LPP for the intermediate objective as the starting basis for solving the first objective of the current run LPP provides a “warm start” that reduces solve time.

At activity 410, solver 212 performs the solve of the subsequent run of the multi-objective hierarchical LPP. As disclosed above, solver 212 uses the solution of the subsequent run LPP for the intermediate objective (Obj0) as the starting basis for the solve of the first objective of the subsequent LPP run. Solver 212 iteratively solves the subsequent run LPP for each objective and stores the LPP run results and solution information as LPP run results 236 of database 114. After solving the multi-objective hierarchical LPP of the subsequent run, supply chain planner 110 terminates method 400, and method 400 ends. According to embodiments, the multi-objective hierarchical LPP is a master planning problem, wherein the intermediate objective is derived from the solution of the previous master planning problem (such as, for example, the previous day's master planning problem) and used as a warm start that improves the speed of solving the current master planning problem (such as, for example, the current day's master planning problem). By way of a further example and not by way of limitation, the intermediate objective is used to increase the speed of running scenarios by using the solution information from the base run to generate the intermediate objective for improving the speed of solving the different scenarios. Embodiments further contemplate campaign planning to reduce setup time by iteratively solving multi-objective hierarchical linear programming problems representing the campaign planning problem, and deriving the intermediate objective from the prior iteration to improve solve time for the subsequent iteration.

To illustrate supply chain planner 110 solving a multi-objective hierarchical LPP incorporating solution information from a base (or previous) run into a subsequent run, the following example is provided. In this example, supply chain planner 110 implements activities of method 400 to perform a base LPP run (Run1), derive an intermediate objective using cumulative list of bound changes from the base LPP run, solve the intermediate objective, and use the solution of the intermediate objective to reduce solve time of the subsequent LPP run (Run2). Continuing the example, at activity 402, supply chain planner 110 performs a base run of a multi-objective hierarchical LPP. In this example, the base run is Run1, and the subsequent run is Run2, as illustrated by FIG. 5.

FIG. 5 illustrates supply chain planner 110 executing the activities of method 400 of FIG. 4, in accordance with an embodiment. Continuing the example, modeler 210 may access one or more of supply chain input data 220, data models 222, product data 224, demand data 226, inventory data 228, supply chain models 230, and/or inventory policies 232, and uses the accessed data to generate a multi-objective hierarchical LPP (in this example, Run1) to represent the flow of materials through supply chain network 100. Solver 212 of supply chain planner 110 accesses the Run1 LPP 300 and solves the Run1 LPP 300 as a multi-objective hierarchical LPP comprising three components: objectives (in this example, Obj1, Run1 302; Obj2, Run1 304; and Obj3, Run1 306), constraints, and bounds. Solver 212 solves Run1 LPP 300 by iteratively loading and solving the LPP for each objective (Obj1, Run1 302; Obj2, Run1 304; and Obj3, Run1 306), beginning with Obj1, Run1 302 and finishing with Obj3, Run1 306. Solver 212 stores the results of solving Run1 in LPP run results 236 of supply chain planner 110 database. Solver 212 stores, in the cumulative lists of bound changes in supply chain planner 110 database, a cumulative lists of all decision variables which solver 212 has set at an upper or lower bound while solving Run1.

Continuing the example, at activity 404, solver 212 accesses cumulative list of bound changes 510 stored in the database. Because it is likely that the decision variables that improved the quality of Run1 300 will have a similar effect on subsequent Run2 500, and that the decision variables that degraded the quality of Run1 300 will have a similar effect on subsequent Run2 500, cumulative list of bound changes 510 provides solution information that solver 212 uses to perform Run2 500 with reduced computational requirements without impairing solution quality.

Continuing the example, at activity 406, solver 212 derives an intermediate objective 512 (in this example, Obj0) using cumulative list of bound changes 510. Solver 212 may solve the Obj0 intermediate objective 514 before solving any of the three objectives (502-506) of Run 2 500 (in this example, Run2 500 comprises the following three objectives: Obj1, Run2 502; Obj2, Run2 504; and Obj3, Run2 506). Solver 212 stores the Obj0 intermediate objective in intermediate objectives data 238 of supply chain planner 110 database. As disclosed above, solver 212 derives the Obj0 intermediate objective 512 by accessing (a) the cumulative list of bound changes 510, (b) the list of common variables, and (c) the list of current run only variables and categorizing the variables into Category a1, Category a2, Category a3, or Category a4. Solver 212 assigns weights and/or coefficients to each of Categories a1, a2, a3, and a4 to create the linear minimization objective function that is utilized as the intermediate objective. In the embodiment of this example, solver 212 assigns the coefficients to each Category as follows: the coefficient of Category a1 is one hundred, which forces these variables to the lower bound; the coefficient of Category a2 is negative one hundred, which forces these variables to the upper bound; the coefficient of Category a3 is zero which has no influence on these variables; and the coefficient of Category a4 is one, which forces these variables to the lower bound, but with a much lower effect than the variables of Category a1 (which are assigned a higher coefficient and are therefore more affected by the minimization optimization).

Continuing the example, at activity 408, solver 212 solves the Obj0 intermediate objective 514. Solver 212 uses the solution of solving the Obj0 intermediate objective as the starting basis for solving the first objective 502 of Run2 500 (in this example, Obj1, Run2 502). The optimal basis (i.e., solution) of the intermediate objective solve is a feasible solution that has potentially good variables at the upper bound and potentially bad variables at the lower bound, to the extent possible without violating plan feasibility. Using the optimal basis of the intermediate objective solve as a starting basis for the current run is likely to reduce simplex iterations in the current run, which reduces the runtime and without compromising plan quality.