Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q10/00—Administration; Management
  • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling

Definitions

• the present invention is related to determining an at least near optimal schedule for utilizing resources, and, in particular, to a method and system for determining an at least near optimal schedule of resources that increases customer satisfaction and resource satisfaction, and that lowers operational costs.
• customer satisfaction is achieved by supplying an appropriate number of resources that satisfy expected customer needs during a given time interval.
• the number of resources needed to satisfy customer needs during a given time interval is referred to as "demand.”
• demand For example, during the checkout phase of a typical retail store transaction, customer satisfaction may be achieved by staffing an appropriate number of qualified cashiers to lessen customer-checkout-wait-time and address customer needs.
• payroll costs typically contribute significantly to the operating costs of a retail store.
• Staffing a large number of cashiers may significantly increase customer satisfaction, but at the expense of reducing profits.
• managers need to ensure that resource satisfaction is also achieved.
• a manager may wish to retain valued employees because of their experience, expertise, and loyalty to the organization over a long period of time.
• managers may take into consideration seniority, job, and shift preferences, scheduling paid and unpaid breaks, consecutive days off, decreasing boredom and frustration by assigning the right mixture of work activities, and assigning overtime, when appropriate, in an effort to achieve employee satisfaction.
• Equipment satisfaction may be achieved by taking into consideration deterioration, depreciation, and maintenance. In general, managers use a fixed schedule of shifts to assign resources.
• Figures 1-4 illustrate an example of assigning cashiers to fixed shifts in order to satisfy customer checkout demand on a typical shopping day at a hypothetical retail store.
• horizontal axes such as axis 101 in Figure 1 corresponds to the time, in hours, the retail store is open on a typical shopping day.
• Figure 1 is a plot of a hypothetical demand curve for cashier services during operating hours of the hypothetical retail store.
• vertical axis 102 corresponds to the demand for cashiers.
• Demand curve 105 represents the demand for cashier services between opening time 103 and closing time 104. For example, between 12pm 106 and 3pm 107, the demand for cashier services is 4 cashiers, as indicated by edge 108 of curve 105.
• Figure 2 illustrates three of many possible fixed overlapping shifts employed to satisfy the demand curve shown in Figure 1.
• three 9-hour shifts referred to as "morning,” “afternoon,” and “evening,” are represented by lines 201-203, respectively.
• line 201 represents a 9-hour morning shift beginning at 8am 204 and ending at 5pm 205.
• the shifts are staggered in time by 2 hours so that the maximum number of cashiers present during the day coincides as close as possible to periods of highest customer demand.
• a retail store manager having only 5 cashiers available to work on a given day may use the fixed shifts described in Figure 2 to assign 2 cashiers to the morning shift 201, 2 cashiers to the mid-day shift 202, and 1 cashier to the evening shift 203.
• Figure 3 is a plot of the number of cashiers scheduled during open hours of the hypothetical retail store described above with reference to Figures 1 and 2.
• vertical axis 301 corresponds to the number of working cashiers.
• Curve 302 represents the number of cashiers working per hour in an effort to satisfy customer demand represented by demand curve 105 ( Figure 1) and is one example of a "supply curve.”
• Supply curve 302 is constructed by summing the number of employees assigned to work per hour. For example, edge 303 of supply curve 302 indicates that 5 cashiers are assigned to satisfy customer demand between the times 12pm 304 and 5pm 305 and is determined by summing the number of employees assigned to shifts 201-203 between times 12pm 206 and 5pm 205 in Figure 2.
• Subtracting supply curve 303 from demand curve 105 ( Figure 1) identifies the time periods of possible overstaffing and understaffing. Overstaffing is the condition of having more resources scheduled than are needed to satisfy expected demand.
• FIG 4 is a plot identifying overstaffing and understaffing for the demand and supply curves shown in Figures 1 and 3, respectively.
• vertical axis 401 corresponds to the demand curve (105 Figure 1) minus supply curve (302 Figure 3).
• Hash-marked region 402 identifies a period of overstaffing, and shaded regions 403 and 404 identify periods of understaffing.
• the information provided in Figure 4 can be used by a retail store manager to assign cashiers the additional task of straightening counters or handling customer returns during the overstaffing period identified by region 402.
• the retail store manager may assign other employees assigned to complete tasks elsewhere in the store, such as stocking, to double as cashiers during the understaffing period identified by regions 403 and 404.
• the example provided above with reference to Figures 1-4 represents a simplified model of customer demand and resource supply for a hypothetical retail store.
• employers and managers responsible for scheduling a large number of employees, such 20, 50, 500, 1,000 or more employees are faced with the difficult task of achieving customer satisfaction and employee satisfaction while, at the same time, lowering operating costs.
• Employers and managers may also need to consider each employee's skills, experience, seniority, pay-rate, and availability to determine a schedule of employees. Moreover, managers may need to schedule equipment, such as vehicles and tools, used to perform specific tasks. Employers and managers continue to seek better, generally applicable methods and systems for scheduling resources that increase customer satisfaction and resource satisfaction while, at the same time, decreasing operational costs.
• One embodiment of the present invention provides a method for determining an at least near optimal schedule of resources in linear time by providing an optimal resource ordering scheme.
• the method receives a set of resources and associated resource data.
• the method determines a resource-rank-function value for each resource, based on the associated resource data.
• Based on the resource-rank- function value associated with each resource each resource is rank ordered.
• the method determines a set of candidate shifts, based on the associated resource data.
• the method determines a weight value for the candidate shifts associated with each resource. Based on the weight values associated with each candidate shift, the method determines a schedule of shifts for each resource in rank order.
• Figure 1 is a plot of a hypothetical demand curve for cashier services during operating hours of a hypothetical retail store.
• Figure 2 illustrates three of many possible fixed overlapping shifts employed to satisfy the demand curve shown in Figure 1.
• Figure 3 is a plot of the number of cashiers scheduled during open hours of a hypothetical retail store.
• Figure 4 is a plot identifying overstaffing and understaffing.
• Figure 5 illustrates eligibility of hypothetical resources for hypothetical workloads.
• Figure 6A shows plots of availabilities for three hypothetical resources.
• Figure 6B is a plot of the total availability of the three hypothetical resources shown in Figure 6A.
• Figures 7A-D are plots of hypothetical demand curves.
• Figure 8 is table of assignment costs for resources and workloads shown in Figure 5.
• Figure 9 is a table of hypothetical workload costs for the workloads shown in Figure 5.
• Figure 10 is a table of hypothetical minimum average qualifications for the workloads shown in Figure 5.
• Figure 11 is table of hypothetical qualification levels for the resources and workloads shown in Figure 5.
• Figure 12 is a table displaying variables and rank values determined for three hypothetical resources.
• Figure 13 is a table of the average qualifications needed for each workload of a hypothetical resource.
• Figure 14 is a table of the qualification costs for each workload of a hypothetical resource.
• Figure 15 is a plot of the total availability of remaining hypothetical resources.
• Figures 16A-C are plots of raw-demand curves.
• Figures 17A-C are plots of adjusted-raw-demand curves.
• Figures 18A-C are plots of weight lists.
• Figure 19 illustrates a set of candidate-shift assignments for a hypothetical resource.
• Figures 20A-C illustrate determining weight values for a hypothetical candidate shifts based on the weight lists shown in Figures 18A-C.
• Figure 21 shows weight values associated with each candidate shift shown in Figure 19.
• Figures 22-23 illustrate shift assignments for a hypothetical resource.
• Figures 24A-B illustrates the concept of a minimum gap between shifts within a single period.
• Figure 25 illustrates shortening the availability time interval for a last shift in a first period in order to increase the length of the availability time interval for a first shift in a second period.
• Figures 30A-C are plots of demand curves for workloads after assignment of a hypothetical resource.
• Figure 27 is a control-flow diagram that represents one of many possible embodiments of the present invention.
• Figure 28 is a control-flow diagram for a routine "Scheduler” that represents one of many possible embodiments of the present invention.
• Figure 29 is a control-flow diagram for a routine "Determine Weight List” that represents one of many possible embodiments of the present invention.
• Figure 30 is a control-flow diagram for a routine "Shift Scheduling” that represents one of many possible embodiments of the present invention.
• Embodiments of the present invention are directed to a method for determining an at least near-optimal schedule of available resources that increases customer satisfaction and resource satisfaction and that decreases operational costs.
• One embodiment of the present invention provides a method for determining an at least near optimal schedule of resources in linear time by providing an optimal resource ordering scheme.
• the present invention is described, in part below, with reference to a hypothetical set of resources and associated resource data, and with reference to graphical illustrations, control-flow diagrams, and mathematical equations, and includes the following four subsections: (1) Brief Overview; (2) Input; (3) Scheduling Resources; and (4) Implementation.
• the resources may include employees and/or equipment and each task may include one or more work activity.
• An at least near optimal schedule of the resources is accomplished by first setting up a resource ranking objective function and then ranking each resource from lowest value of the objective function to highest value of the objective function. For each resource, beginning with the resource having the lowest objective function value and ending with the resource having the highest objective function value, the method of the present invention determines a resource schedule. Determination of the resource schedule may be based on the demand and importance associated with each activity, the qualifications needed to perform each activity, and the cost and qualifications associated with scheduling each resource. After each resource is scheduled, the demand for each activity the resource is scheduled to perform is adjusted and any workloads completely satisfied are removed from further consideration in scheduling the remaining higher ranked resources.
• Resource data refers to resource supply, such as a list of employees or equipment, and includes information about resource eligibility, availability, and priority.
• Tasks may include one or more pieces or elements of work where each piece of work is related to a specific activity. These one or more activities are referred to as workloads.
• a call center task called “technical support”
• Two workloads of the task can include answering questions in English and answering questions in Spanish.
• Resource eligibility refers to whether a particular resource is qualified or capable of performing a particular activity or workload of a task.
• Figure 5 illustrates eligibility of a set of hypothetical resources that are capable of performing certain hypothetical workloads.
• three different resources 501-503 are represented by Rj, R 2 , and R 3 , respectively, and three different tasks 504- 506 are represented by Tj, T2, and T 3 , respectively.
• Tasks 7/ 504 and 2 505 are each composed of a single workload represented by 508, respectively.
• Task T 3 506 is composed of two workloads represented by W 509 and W 510. Note that, for each workload, superscripts refer to the associated task index and subscripts are workload indices.
• each resource is connected to three different workloads via lines, such as line 511, that represent resource eligibility.
• task T 3 506 may represent the call center "technical support" described above, and resources Rj 501, R 2 502, and R 3 503 may represent employees.
• the two workloads W? and w of the task "technical support" include answering questions about the product in English 509, and answering questions about the product in Spanish 510, respectively.
• resource R] 501 is fluent in English and Spanish
• resource Rj is eligible to perform workloads w 509 and Wl , as indicated by lines 511 and 512, respectively.
• line 513 indicates that resource R 2 502 is eligible to perform workload W ⁇ .
• resource R 3 is fluent in Spanish
• line 514 indicates that resource R 3 503 is eligible to perform workload W 2 3 .
• Resource availability refers to time intervals during a scheduling period when a resource is able or willing to work. For example, availability of an employee refers to the time intervals during the week when the employee can and cannot work.
• Figure 6A illustrates separate resource availabilities for each of the resources described above with reference to Figure 5.
• horizontal axes such as axis 601 correspond to a time period of length T composed of 26 time units, denoted by t, such as time unit 602.
• the period is the total number of time units to be scheduled, and each time unit represents the smallest amount of time a resource can be scheduled to work.
• a time unit may be 0.25 hours (15 minutes), with a scheduled period of one week containing 672 time units (4 units/hour X 24 hours/day X 7 days/week).
• vertical axes 603-605 correspond to the resources Rj, R 2 , and R 3 , respectively.
• Curves 606-611 are each one unit in height, and identify the availability time intervals 713-718 when resources Rj, R 2 , and R 3 can be scheduled to work during the period T. For example, curves 610 and 611 indicate that resource R 3 is available to work during first and second availability time intervals 617 and 618, respectively. Curves 610 and 611 indicate that, during time intervals 617 and 618, resource R 3 is available to execute any of workloads , W ⁇ , and Wl .
• Figure 6B illustrates the total availability of resources Rj, R 2 , and R 3 over the period T. In Figure 6B, vertical axis 619 corresponds to the total availability. Curve
• edge 621 of curve 620 is the result of summing curves 606, 608, and 610 over the overlapping time units identified by bracket 622.
• Edge 621 indicates that 2 resources may be available for scheduling during the time units identified by bracket 622.
• Resource priority refers the preferential rating of each resource and is assigned by the user. For example, priority may refer to an employee's seniority. Seniority is a privileged status obtained by an employee based on the length of continuous service to an employer. Employees having more seniority than other employees are assigned a higher priority value than employees with less seniority.
• Resource data may also include minimum and maximum shift lengths for which the resource can be scheduled.
• a shift is a contiguous time interval during an availability time interval in which a resource is scheduled to work.
• minimum and maximum shift lengths place limits on how long a resource can be scheduled to work during an availability time interval.
• an employee with a minimum shift length of 4 hours and a maximum shift length of 9 hours can be assigned to any shift during an availability time interval that is not less than 4 hours in length and not more than 9 hours in length.
• Demand refers to the number of resources needed to satisfy expected customer needs for a given workload during a given interval of time. For example, the demand for a call center can be determined by forecasting the number and kinds of incoming calls received per unit time.
• FIGs 7A-D are plots of hypothetical demand curves for the four workloads W ⁇ , W ⁇ , W ⁇ , and W 2 3 described above with reference to Figure 5.
• horizontal axes, such as axis 701 correspond to the period T
• vertical axes, such as axis 702 correspond to the demand for resources.
• demand is represented by curves that indicate the number of resources needed at a given time unit t and is denoted by dernand(t).
• dernand(t) For example, in Figure 7A, demand for workload W ⁇ (507 in Figure 5) over the period T is represented by curves 703 and 704.
• Edge 705 indicates that 2 resources are needed to satisfy customer needs over the time interval 706, and edge 707 indicates that 1 resource is needed to satisfy customer needs over the time interval 708.
• the demand curves shown in Figure 7A-D also include an indication of the importance of satisfying demand. Importance is time-unit dependent and is determined by assigning a value to meeting demand over specific time intervals because satisfying customer demand may be more important in the operation of a business at certain times. Importance determination is outside the scope of the method of the present invention. Figures 7A-D identify three different levels of importance.
• Cross-hatched regions such as region 709 in Figure 7C, identify the highest level of importance, hash-marked regions, such as region 710 in Figure 7C, identify a medium level of importance, and unshaded regions, such as regions 711 and 712 in Figure 7C, identify a lowest level of importance.
• Costs and qualifications includes components of the expenses that the method of the present invention attempts to decrease, such as assignment cost and workload cost.
• Assignment costs are the cost of scheduling a resource to a particular workload. In other words, for each workload that a resource can perform, there is an associated assignment cost. For example, for an employee resource, the employee's pay rate is a component of assignment costs. For an equipment resource that operates on gasoline, the price per gallon may be a component of assignment costs.
• assignment costs associated with labor can include health care costs and an employee's reluctance to work a particular workload.
• Figure 8-11 show tables of assignment costs, workload costs, minimum average qualification, and the qualification associated with each workload described above with reference to Figure 5. Note that the entry values shown in each table represent hypothetical costs and values assigned to workload qualifications. These values are included to aid in illustrating the methods of the present invention, described in greater detail below, and are not intended to represent actual values determined in the practice of the present invention. Note that determining the entry values shown in Figures 8-11 is outside the scope of the present invention.
• Figure 8 is a table of assignment costs for the hypothetical resources described above with reference to Figure 6.
• entries 801- 801 identify the cost of assigning resource Rj, R 2 , and R 3 (501-503 in Figure 5) to their respective eligible workloads , W? , W? , and W 2 3 (507-510 in Figure 5). For example, entries 801-
• Workload costs represent the costs associated with failing to satisfy demand for a particular workload. For example, consider a retail store that has a task called "sales.” The task "sales" has two workloads: “ woman's shoes” and "men's accessories.” Sales people can work one or both of these workloads depending upon their eligibility. Sales in the shoe department are $1,000 per hour per sales person, while sales in the men's department are $300 per hour per sales person.
• FIG 9 is a table of hypothetical workload costs for the workloads shown in Figure 5.
• entries 901-904 identify hypothetical workload costs for workloads , W 3 , and , respectively.
• Cost and qualifications also includes the minimum average qualification level needed for each workload.
• the minimum average qualification represents the average level of ability to be maintained in each workload at all times. For example, the task "cashier" in a retail store may include a low qualification workload “checking” and a higher qualification workload “returns.” A lower minimum average qualification value is therefore assigned to the workload "checking" than to the workload "returns.”
• Figure 10 is a table of hypothetical minimum average qualifications to be maintained for each workload shown in Figure 5.
• entries 1001-1004 identify the minimum average qualifications needed to perform workloads W , W? , W ⁇ , and Wl , respectively.
• cost and qualifications includes qualification values associated with each resource.
• the qualification value represents a resource's ability to perform a particular workload. The qualification value is determined by evaluating each resource's qualifications for performing eligible workloads. For example, a typical retail-store staff may be composed of mixed levels of expertise for each workload.
• FIG. 11 is a table of the hypothetical qualification levels for each resource per workload.
• entries 1101-1103 indicate that resource R 3 has a qualification value 3 for workload w ⁇ , a qualification value of 2 for workload W? , and a qualification value of 1 for workload W 2 3 , respectively.
• each resource is assigned a resource-rank-function value according to the following equation:
• P priority
• NT number of tasks a resource can carry out
• TNT total number of tasks available
• MRAC maximum resource assignment costs
• MORAC maximum overall resource assignment costs
• MOQ maximum overall qualification of the resources
• AQ average qualification of a resource
• Tot total time the resource is already scheduled for.
• the resource _rank Junction represents one of many possible embodiments for ranking each resource.
• the values given by the resource rank Junction are used to rank the available resources in order from the resource having a lowest resource-rank- function value to a resource having a highest resource-rank-function value.
• the resources are scheduled in rank order beginning with the lowest ranked resource and ending with the highest ranked resource.
• Figure 12 is a table displaying the input variables and the resource_rankJunction determined for hypothetical resources Rj, R2, and R3 described in Figure 5.
• each resource is listed.
• the priority assigned to each resource is given.
• the number of tasks each resource is able to perform is given.
• NT is assigned the value 2 for resource Rj because resource Rj is able to perform workloads in the tasks Tj and T3 (see in Figure 5).
• NT is assigned the value 3 for resources R 2 and R 3 because both resources R 2 and R3 are eligible to perform workloads in all three tasks T], T 2 , and 7 ⁇ (see Figure 5).
• TNT is assigned the value 3 for each resource because the total number of tasks is 3 (see Figure 5).
• Column 1205 includes values assigned to the variable MRAC.
• MRAC 1213 is assigned the value 3 for resource R3 (see entry 802 in Figure 8).
• MORAC is assigned the value 4 because 4 is the largest assignment cost value (see entry 804 in Figure 8).
• MOQ is assigned the value 3 for each resource (see entry 1002 in Figure 10).
• AQ is given for each resource.
• the entries all have the value "0" because the resources have not yet been assigned.
• the rank of each resource is given, determined by substituting the respective values of each resource into the resource _rank Junction.
• the resources are scheduled in order of increasing resourcej-ankjunction, beginning with the resource having the lowest resource_rank Junction value. For example, resource R 3 is scheduled first because resource R 3 is the lowest-ranked resource (see entry 1214 of Figure 12).
• the qualification cost is the cost associated with assigning a particular resource to a particular workload.
• the qualificationjcost is first determined for the lowest-ranked resource according the resource _rank Junction described above with reference to Figure 12. For example, because resource R 3 has the lowest resource rank Junction value, the qualification_cost is determined for each workload that resource R3 is eligible to perform. Determination of the qualificationjcost is based on the unscheduled resources. For example, the qualificationjcost for the lowest-ranked resource R 3 is based on the qualification values described above with reference to Figures 10 and 11.
• Figures 13 and 14 are tables illustrating determination of the qualificationjcost for resource R 3 .
• Figure 13 is a table of ave_qualification of unscheduled resources Rj and R 2 . The ave_qualification is determined for resources having a resource rank Junction value higher than resource R 3 . In Figure 13, entries
• 1301-1303 are the average qualification values for the resources Rj and R 2 .
• ave_qu ⁇ lification(R 3 , W 2 3 ) entry 1303 is determined by averaging qualification values for resources Rj and R 2 and for the workload W 2 3 ((2 + 0)/2; see entries 1104 and 1105 in Figure 11).
• Figure 14 is a table of qualificationjcost values determined by subtracting entries 1301-1303 from entries 1001, 1002, and 1004 in
• embodiments of the present invention are directed to scheduling a lower ranked resource before a higher ranked resource, typically higher ranked resources have higher priority with respect to workloads.
• the workload demand curves associated with the lower ranked resources are adjusted by subtracting the availability of the unscheduled higher ranked resources.
• the lower ranked resources are scheduled based on the assumption that higher ranked resources have already been scheduled.
• the availability of unscheduled resources Rj and R 2 is subtracted from the workload demand curves associated with the lowest ranked resource R 3 in order to determine the demand for resource R 3 .
• Figure 15 is a plot of the availability of remaining unscheduled resources Rj and R 2 .
• horizontal axis 1501 corresponds to the period T
• vertical axis 1502 corresponds to the number of available resources.
• Curve 1503 represents the availability of unscheduled resources Rj and R 2 after scheduling resource R 3 and is referred to as the remaining availab ⁇ lity.
• Availability curve 1503 is determined by summing availability curves 606-609 for the resources Rj and R 2 in Figure 6A over the period T. Note that availability curve 1503 can also be determined by subtracting availability curves 610 and 611 from availability curve 620 shown in Figure 6B.
• Figures 16A-C are plots of raw jdemand curves for the lowest-ranked resource
• FIG. 16A-C horizontal axes, such as horizontal axis 1601, correspond to the period T, and vertical axes, such as vertical axis 1602, correspond to the raw demand for workloads Wl , W ⁇ , and W 2 3 ⁇
• the raw-demand curve 1603 in Figure 16A represents the raw demand for workload which is determined by subtracting the remaining j vailability, described above with reference to Figure 15, from demand(t) curve for workload W ⁇ , shown in Figure 7 A.
• positive-valued regions such as regions 1604-1606 of workload , identify the unsatisfied demand resulting from scheduling resources Rj and ? 2 to the workloads, such as workload W ⁇ .
• the positive-valued regions identify the demand for the lowest- ranked resource R 3 .
• Negative-valued regions such as region 1607, identify overstaffing that can result from scheduling resources Ri and R to identical workloads.
• dem _ cost (t) raw _ demand t + ⁇ overall _ minimum ⁇ + 1.0
• ⁇ overall _minimum ⁇ the absolute value of the overall minimum of the raw demand for all workloads the resource is able to perform.
• Figures 17A-C are plots of the demandjcost for each workload the resource R 3 is eligible to perform.
• horizontal axes such as horizontal axis 1701
• vertical axes such as vertical axis 1702
• the dem_cost(t) curves 1703-1705 represent the demjcost(t), for each workload the resource R 3 is eligible to perform.
• the overall jninimum of the raw demand for resource R3 is "-2," as indicated by edges 1608 and 1609 in Figures 16B-C.
• curve 1703 is determined by adding the absolute value of the overall-minimum value "2" plus the value "1" to the raw_demand(t) shown in Figure 17A.
• Figures 18A-C are plots of the weight list determined for the workloads .
• Weight list curves 1803-1805 are determined according to the equation weight ist for each workload resource R 3 is eligible to perform
• the weight Jist value is "17" over the time interval 1806 and is computed by substituting the value "2" for the workloadjcost (entry 901 in Figure 9); the value “1.5” for the qualificationjcost (entry 1401 in Figure 14); the value "1.5” for the importance, as described above with reference to Figure 7A; the value "4" for the demjcost (time interval 1706 in Figure 17A); and the value "1” for the assignmentjcost (801 in Figure 8) into the equation weight Jist(t).
• all possible candidate shifts are generated for the lowest-ranked resource based on the minimum and maximum shift length provided in the resource data described above.
• Resources are scheduled so that the length of each shift is between the minimum and maximum specified shift lengths. Beginning with the minimum shift and ending with the maximum shift, candidate shifts are generated by incrementally enlarging the length of each shift by the time unit t. For example, an employee that specifies a minimum shift length of 7 hours and a maximum shift length of 9 hours can be scheduled to shifts of lengths 7, 7.25, 7.5, 7.75, 8, 8.25, 8.5, 8.75, and 9 hours, where the time unit t is 0.25 hours.
• the resource R 3 has a minimum shift length of 2 time units and a maximum shift length of 5 time units, the possible shifts lengths, in time units, are 2, 3, 4, and 5 time units.
• Figure 19 illustrates the set of all possible candidate shift assignments for the resource R 3 .
• the four horizontal axes 1901-1904 correspond to the period T, and square bracketed time units, such as time units 1905 and 1906, identify the first and second availability time intervals 610 and 611, shown in Figure 6 A, that are associated with resource R 3 .
• each horizontal axis is associated with all possible shifts of the same time unit length, and the shifts are staggered by one time unit in order to span each availability time interval.
• the candidate shifts associated with period 1902 are all 3 time units long, and candidate shifts 1907-1910 represent all shifts of 3 time units that can be scheduled during the availability time interval 1911, as indicated by dashed lines 1912 and 1913.
• a near optimal schedule for a resource is determined by selecting shifts or combinations of shifts based on their associated weight value, weight(s).
• Figures 20A-C illustrate determination of weights for candidate shift 1907, shown in Figure 19.
• Curves 2004- 2006 coincide with curves 1803-1805, shown in Figure 18.
• time intervals 2001-2003 identify time units corresponding to candidate shift 1907.
• the time units are each assigned the value "1.”
• the weight(s) values associated with candidate shift 1907 are the areas identified by shaded regions 2007-2009, respectively.
• FIG. 21 shows the weight values computed for each candidate shift shown in Figure 19.
• order 3 -tuples located to the right of each candidate shift, such as 3-tuple 2101, give the computed weight(s) values for the candidate shifts associated with each weight Jist shown in Figures 18A-C, and are determined as described above with reference to Figures 20A-C.
• the elements of 3- tuple 2101, associated with shift 1907, are "33,” "29,” and "67.5,” as described above with reference to Figures 20A-C.
• FIGs 22-23 illustrate possible shifts assignments for resource R 3 based on the weight(s) values shown in Figure 21.
• the schedule for resource R 3 can be determined by selecting those shifts having the largest weight(s) values. For example, examination of weight(s) values for each candidate shift in Figure 21 reveals that shifts 2106 and 2107 have the largest weight(s) values "88.5" and "49," respectively, for the workload Wl .
• resource R3 can be scheduled to perform workload wl , as indicated by shifts 2201 and 2202.
• combinations of shifts can be used to determine a near optimal schedule for resource provided the candidate shift lengths do not exceed the maximum shift length constraint.
• shifts 1907 and 2108, shown in Figure 25 can be combined to give a first shift 2301 having total weight(s) value "108.5 (67.5 + 39)," and a shifts 2109 and 2110, shown in Figure 25, can be combined to give a second shift 2302 having total weight(s) value "53.5 (39.5 + 14).”
• each shift may also be subject to a minimum gap between shifts constraint. The minimum gap between shifts is the amount of continuous time off between shifts.
• a minimum gap between shifts constraint of 16 hours allows an employee to go home eat, sleep and return to work.
• the minimum gap between shifts constraint is a parameter that achieves resource satisfaction.
• Figures 24A-B illustrate the concept of a minimum gap between shifts within a single period.
• the minimum gap 2401 between shifts is located between the end of a first shift 2402 and the beginning of a second shift 2403.
• the minimum gap 2401 between shifts 2401 constraint ensures that the end of the first shift 2402 is not to too close in time to the beginning of the second shift 2403.
• the availability time intervals are adjusted by shortening the length of either one or both of the availability time intervals.
• the distance 2404 between the end 2405 of the first availability time interval 2406 and the beginning 2407 of the second availability time interval 2408 is less than the minimum gap between shifts 2409.
• the length of the first and second availability time intervals 2406 and 2408 can both be shortened by one time unit to accommodate the minimum gap 2409 by shifting end 2405 of availability time interval 2406 to end 2410 and shifting beginning 2407 of availability time interval 2408 to the beginning 2411.
• Figure 25 illustrates the concept of shortening the availability time interval for the last shift in the first period in order to increase the length of the availability time interval for the first shift in the second period.
• the length of the last availability time interval 2501 in the first period and the minimum gap 2502 between shifts shortens the length of the first availability time interval 2503 of the second period.
• gap 2905 is removed from the availability time interval 2501 and minimum gap 2502 shifts to minimum gap 2506.
• the availability time interval 2503 is expanded by gap 2507 to the time interval 2508.
• the increased availability time interval length 2508 increases the range of time over which the first shift of the second period can be scheduled.
• Figures 26A-C are plots of updated demand curves for workloads , and wl , after resources R3 has been assigned to the shifts shown in Figure 23.
• the demand curves shown in Figures 26A-C are determined by subtracting the shifts assignments shown in Figure 23 from the corresponding demand curves shown in Figure 7A, B, and D. Dashed line enclosed regions 2601-2605 identify the demand satisfied by assigning resource R 3 to the workloads show in Figure 23.
• the demand curves shown in Figures 26A-C are used in subsequent scheduling of the next lowest- ranked resource Rj (see Figure 12). In step 1310, the workloads having demand completely satisfied are removed.
• step 1311 if more resources are available for scheduling, such as resources Rj and R 2 , then steps 1304-1311 are repeated, otherwise, control passes to step 1312.
• step 1312 the optimal resource schedule is output.
• Implementation Figures 27-30 provide a series of control-flow diagrams that describe the method of determining a near optimal schedule of resources, as described above with reference to Figures 5-26.
• Figure 27 is a control-flow diagram that represents one of many possible embodiments of the present invention.
• step 2701 the input is composed of resource data and site 2702, described above with reference to Figures 5 and 6, demand 2703, described above with reference to Figures 7A-D, and cost and qualification 2704, described above with reference to Figures 8-11.
• step 2705 the input described above with reference to step 2701 is passed to the routine "Scheduler.”
• the routine "Scheduler” converts the input into an at least near optimal resource schedule.
• I step 2706 output consist of the at least near optimal schedule.
• Figure 28 is a control-flow diagram for the routine "Scheduler” that represents one of many possible embodiments of the present invention.
• the routine "Scheduler” determines a near optimal schedule of resources that increases customer satisfaction and resource satisfaction and lowers operating costs.
• step 2801 the input described above with reference to step 2701 in Figure 27 is provided.
• step 2802 a resource jrank Junction value, described above with reference to Figure 12, is determined for each resource.
• steps 2804-2811 are repeated for each resource beginning with the resource having the lowest resourc jrank Junction value and ending with the resource having the highest resource rank Junction value.
• steps 2805-2806 are repeated for each workload a resource can perform.
• step 2805 the routine "Determine Weight List" is called.
• step 2806 if more workloads are available, then step 2805 is repeated, otherwise, control passes to step 2807.
• step 2807 the weight lists determined in steps 2804-2806 are passed to the routine "Shift Scheduling" and a near optimal shift schedule is determined for lowest-ranked resource.
• step 2808 resource availability is adjusted as described above with reference to Figures 24-25.
• step 2809 resource task characteristics such average qualifications (see Figure 13) is updated, and the demand for each workload is updated, as described above with reference to Figures 26A-C.
• step 2810 workloads having no demand are removed.
• step 2811 if more resource are available for scheduling, then step 2804 is repeated, otherwise control passes to step 2812.
• step 2812 a near optimal resource schedule is output.
• Figure 29 is a control-flow diagram of the routine "Determine Weight List" that represents one of many possible embodiments of the present invention.
• This routine determines a weight list value for each time units over the period T associated with each workload.
• qualification costs are determined according to the qualificationjcost equation, as described above with reference to Figure 14.
• availability is determined, as described above with reference to Figure 15.
• raw demand is determined according to the rawjdemand equation, as described above with reference to Figures 16A-C.
• raw demand is adjusted according to the demandjcost equation, as described above with reference to Figures 17A-C.
• the weight list is determined according to weight_list equation, as described above with reference to Figures 18A-C.
• Figure 30 is a control-flow diagram of the routine "Shift Scheduling" that represents one of many possible embodiments of the present invention.
• This routine determines a near optimal schedule based on the weight list determined in the routine "Determine Weight Lists.”
• step 3001 candidate shifts are generated as described above with reference to Figure 19.
• steps 3003-3006 are repeated for each shift determined in step 3001.
• steps 3004 and 3005 are repeated for each weight Jist determined in the routine "Determine Weight Lists.”
• step 3004 the weight Jist equation is integrated over the shift time intervals determined in step 3001.
• step 3005 if more workloads are available, then step 3004 is repeated, otherwise control passes to step 3006.
• step 3006 if more shifts are available, then step 3003 is repeated, otherwise control passes to step 3007.
• step 3007 shifts having the largest weight Jist value are selected, as described above with reference to Figures 22-23.
• the present invention has been described in terms of a particular embodiment, it is not intended that the invention be limited to this embodiment. Modifications within the spirit of the invention will be apparent to those skilled in the art. For example, an almost limitless number of different implementations of the many possible embodiments of the method of the present invention can be written in any of many different programming languages, embodied in firmware, embodied in hardware circuitry, or embodied in a combination of one or more of the firmware, hardware, or software. In alternate embodiments, capacity can be taken in to account in scheduling resources to ensure that tasks are scheduled within open hours and do not exceed employee maximums.
• Capacity is the combination of business hours and the maximum number of resources that can perform a task during a particular interval of time.
• fixed assignments can be accommodated. Fixed assignments are specific shifts for resources. Resources are scheduled to work a fixed shift regardless of demand and can be fixed by task or by resource. In alternated embodiments, where the resources are employees, the present invention can include the scheduling of meetings. If the resources are equipment, the present invention can include scheduling regular periods of maintenance. In alternate embodiments, the minimum and maximum time per period can be implemented to place limits on the amount of time a resource is scheduled during a scheduling period. In alternate embodiments, the maximum number of shifts can be used to limit the number of shifts a resource can work during a scheduling period.
• constraints such as absolute, hard, and soft constraints can be placed on the variables of the present invention.
• absolute constraints can be placed on variables, such as tasks, workload eligibility, capacity, and resources availability, to ensure that the values assigned to these variables are not changed or violated.
• Hard constraints can be used to rank variables so that an absolute constraint or a hard constraint with a higher rank takes precedence over lower ranked variables.
• Soft constraints can be assigned to variables of lesser importance than variables associated with absolute and hard constraints.

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