Description:FIELD OF INVENTION
[001] The present invention relates to a method for optimizing fulfillment center operations to ensure timely delivery of goods. Particularly, the present invention relates a system and method for determining optimal wave design in fulfillment centers. More particularly, the present invention relates to a system and method to optimize wave cut-off and determine processing capacity within each cut-off based on hourly reservation patterns of the fulfillment centers, thereby minimizing Pre-mother hub (MH) loss and thus ensuring timely delivery of goods.

BACKGROUND OF THE INVENTION
[002] The rapid growth of e-commerce has created a compelling need for on-demand and large-volume delivery. E-commerce industries created fulfillment center (FC) to handle large volume delivery. The fulfillment center is a part of the supply chain and serves as the hub for all logistics processes needed to get a product from the seller to the customer.
[003] The fulfillment centers are built to meet the required speed of the demand and supply as speed is one of the critical metrics for an e-commerce company. The fulfillment centers (FC) of an e-trailer typically assign approved orders to waves (defined by some cut-off timings) and dispatch them to the next destination in the network. The waves are a type of order fulfillment strategy in which orders are grouped together into “waves” based on factors such as due date, order size, and product availability. These waves are then picked simultaneously instead of individually.
[004] When a customer places an order on the online platform, promise engine receives the order and assigns it to an FC based on the availability of inventory. At the Fulfillment centers (FC), orders are dispatched in waves where each wave is associated with a cutoff time and processing capacity. As the cut-off time represents the deadline by which an order must be placed to qualify for same-day processing and shipping.
[005] Each unit that is promised gets assigned to the wave and has to be dispatched by the wave cutoff time (also known as dispatch by date time or DBD) from the FC to and Mother Hub (MH). When orders are received by the Fulfillment centers (FC), they are aggregated into a picklist and assigned to a picker for them to be dispatched by the cut-off time. An FC takes at least Pick to Dispatch time (ranges from 30 to 180 minutes) for an order to be picked, packed and dispatched to the Mother Hub( MH). So, only the orders that are placed before the P2D time of a cut-off can be processed within that cut-off. These orders are dispatched to the Mother Hub (MH) by last possible handover time (LPHT). Thereby, the last possible handover time (LPHT) acts as a cut-off time between the FC and MH so that the shipment gets connected to the earliest possible line-haul.
[006] Due to large volume delivery many times the orders don’t dispatched by the last possible handover time (LPHT) resulting in a delay and orders have to wait for over 24 hours at the FC. The delay in of over 24 hours at FC is defined as the Pre- Mother Hub (MH) loss. One of the major problems in the following system is that the percentage of orders that are not connected to the earliest available LPHT connection during Promise (alternately, the difference between assigned LPHT and the order approval time is more than 24 hours assuming one LPHT connection per day) are categorized into Pre-MH loss. Some of the reasons for an order missing a connection within 24 hours could be attributed to one of the following reasons:
[007] • Lead time constraints (Inter-wave P2D loss): The orders that are placed within the Pick to Dispatch (P2D) time of cut-off cannot be connected to LPHT even though a cut-off is available. This is because the fulfillment center needs at least P2D time for processing and dispatching orders.
[008] • Wave synchronization loss: The orders cannot be connected to the earliest LHPT because of the unavailability of a cut-off between the approval time of order and LPHT.
[009] • Wave capacity constraint (inter-wave capacity loss): This loss occurs due to lack of the capacity with the fulfillment center for assigning the cut-off even though the cut-off is available prior to LPHT connection.
[0010] Further, there are several non-patent literatures that relate to a system and method for optimizing operations of the fulfillment center. One such traditional approach was developed by Ceven and Gue wherein an analytical model was developed to determine the number of waves and their timings for a fulfillment system operating on a daily deadline. The cited non-patent literature disclosed that the optimized wave release strategy can significantly improve the ratio of shipments on time in comparison to a simple rule of thumb. However, the approach disclosed in the cited non-patent literature was limited to a daily deadline. The cited non-patent literature discloses a metric known as Next schedule deadline (NSD) that measures the fraction of orders that are processed within a 24-hour period. However, the cited non-patent literature fails to disclose a method to obtain the Fulfillment center (FC) cut-off timing.
[0011] Another traditional approach was developed by Gademann, Vandenberg, and Vanderhoff. The cited non-patent literature discloses an approach to batch orders for wave picking in a parallel-aisle warehouse. The batch lead times are optimized using branch & bound algorithm along with a heuristic.
[0012] Therefore, in view of the problem associated with the state of the art, there is a need to develop a system and method to optimize wave cut-off and processing capacity within each cut-off based on hourly reservation patterns of the fulfillment centers, thereby minimizing Pre-mother hub (MH) loss and thus ensuring timely delivery of goods.

OBJECTIVES OF THE INVENTION
[0013] The primary objective of the present invention is to provide a system and method for determining optimal wave design in fulfillment centers.
[0014] Another objective of the present invention is to provide a system and method for optimal wave design in fulfillment centers for achieving an optimal last possible handover time (LPHT) timings and connections.
[0015] Another objective of the present invention is to minimize Pre-MH loss by providing optimal wave design based on different inputs.
[0016] Another objective of the present invention is to provide a system and method for achieving an optimal capacity profile.
[0017] Another objective of the present invention is to provide a system and method for achieving an optimal number of shifts, shift timings, and break schedules.
[0018] Another objective of the present invention is to provide a system and method to provide the optimal truck connection from the fulfillment center.
[0019] Another objective of the present invention is to provide a system and method to optimize wave cut-off and determine processing capacity within each cut-off based on hourly reservation patterns of the fulfillment centers, thereby minimizing Pre-mother hub (MH) loss and thus ensuring timely delivery of goods.
[0020] Another objective of the present invention is to determine optimal wave cut-offs & cut-off level capacities using a mixed integer programming-based optimization model, to minimize the Pre-MH loss.
[0021] Another objective of the present invention is to provide optimized wave cut-off in case of multiple deadlines (cut-off time) due to different LPHT connections.
[0022] Yet another objective of the present invention is to provide a system and method to obtain the optimal P2D time of a fulfillment center.
[0023] Another objective of the present invention is to identify the most effective set of wave cut-offs for order dispatch in the fulfillment center using a mixed integer programming-based optimization model while considering factors such as order priority, item location, and staffing constraints.
[0024] Yet another objective of the present invention is to determine the optimal cut-off and processing capacity within each cut-off for each fixed LPHT in an FC.
[0025] Other objects and advantages of the present invention will become apparent from the following description taken in connection with the accompanying drawings, wherein, by way of illustration and example, the aspects of the present invention are disclosed.

SUMMARY OF THE INVENTION
[0026] The present invention relates to a method for determining optimal wave design in fulfillment center. The method involves collecting inputs and determining constraints by a user through an operating device; calculating the hourly reservation capacity of a fulfillment center by a user through an operating device; computing Inter-wave capacity loss based on the calculated hourly reservation capacity as well as pre-computing losses through a processing unit based on the instructions received from an optimization model; providing inputs parameter and constraints obtained in step, hourly capacity computed, and inter-wave capacity loss and pre-computing losses to an optimization model through the operating device to initiate optimization process; and running optimization algorithm installed in the optimization model and simultaneously providing instructions to a processing unit to analyze the parameters to provide optimal number and timings of cut-offs while adhering to constraints and thereafter determining the processing capacity within each cut-off based on cutoff time & assigned hourly capacity, ensuring minimized Pre-MH loss.

BRIEF DESCRIPTION OF DRAWINGS
[0027] An understanding of the present invention may be obtained by reference to the accompanying drawings, when taken in conjunction with the description herein and in which: Figure 1 and Figure 2 illustrates a flowchart of method for determining optimal wave design in fulfillment centers;
[0028] Figure 3 (a, b) illustrates a graphical representation depicting hourly demand/capacity in response to time point; and spillage in response to time point, respectively;
[0029] Figure 4 (a) illustrates graphical representation depicting overshooting of overflow due to Insufficient capacity; and Figure 4 (b) illustrates a graphical representation depicting steady state overflow i.e. capacity close to demand; Figure 5 illustrates a graphical representation depicting Pre-MH loss change with order pattern variation; and
[0030] Figure 6 illustrates a graphical representation depicting the change in cut-offs with order pattern variation.

DETAILED DESCRIPTION OF THE INVENTION

[0031] The following description describes various features and functions of the disclosed system with reference to the accompanying figures. In the figures, similar symbols identify similar components, unless context dictates otherwise. The illustrative aspects described herein are not meant to be limiting. It may be readily understood that certain aspects of the disclosed system can be arranged and combined in a wide variety of different configurations, all of which have not been contemplated herein.
[0032] Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope of invention. In addition, descriptions of well-known functions and constructions are omitted for clarity and conciseness.
[0033] Features that are described and/or illustrated with respect to one embodiment may be used in the same way or in a similar way in one or more other embodiments and/or in combination with or instead of the features of the other embodiments.
[0034] The terms and words used in the following description are not limited to the bibliographical meanings, but, are merely used to enable a clear and consistent understanding of the invention. Accordingly, it should be apparent to those skilled in the art that the following description of exemplary embodiments of the present invention are provided for illustrative purpose only and not for the purpose of limiting the invention.
[0035] It is to be understood that the singular forms “a”, “an” and “the” include plural referents unless the context clearly dictates otherwise.
[0036] The expression “optimal wave design” used in the present disclosure refers to identification of optimal set of wave cut-offs for order dispatch.
[0037] The term “wave-cut off” and the term “cut-off” may be interchangeably used in the present disclosure.
[0038] The term “wave cut-off” or “cut-off” used in the present disclosure refers to the deadline to complete a batch of orders before the batch is transferred to the next stage of processing.
[0039] The expression “optimal wave-cut off” and the expression “optimal cut-off” may be interchangeably used in the present disclosure.
[0040] The expression “optimal wave-cut-off” or “optimal cut-off” used in the present disclosure refers to an ideal time to complete a batch of orders.
[0041] The term “Pre-MH loss” used in the present disclosure refers to the percentage of orders missing their earliest connections during promise due to fulfillment center constraints.
[0042] The expression “hourly reservation of fulfillment center” used in the present disclosure refers to the number of orders received in an hour in the fulfillment center.
[0043] The expression “hourly capacity of fulfillment centers” used in the present disclosure refers to the hourly processing capacity available in the fulfillment center.
[0044] The phrase “Last Possible Handling Time (LHPT)” used in the present disclosure refers to the maximum allowable time to complete order preparation before loading the order onto the earliest truck connection or any other transportation means.
[0045] The phrase “Pick to Dispatch (P2D time)” used in the present disclosure refers to the time taken for processing, packing, and shipping orders for further processing.
[0046] It should be emphasized that the term “comprises/comprising” when used in this specification is taken to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.
[0047] Accordingly, the present invention relates to a method for optimizing fulfillment center operations to ensure timely delivery of goods. Particularly, the present invention relates a system and method for determining optimal wave design in fulfillment centers. More particularly, the present invention relates to a system and method to optimize wave cut-off and determine processing capacity within each cut-off based on hourly reservation patterns of the fulfillment centers, thereby minimizing Pre-mother hub (MH) loss and thus ensuring timely delivery of goods.
[0048] In an embodiment, the present invention relates to a system for optimal wave design in fulfillment centers. The system comprises an operating device, an optimization module installed in the operating device, and a processing unit integrated within the operating device. The system comprises of the following components:
(a) Operating device – The system comprises an operating device that serve as a platform for the user to provide inputs via an interface.
(b) Optimization module – An optimization module is installed in the operating device serving as an interface for the user to input the data. In an embodiment, an optimization algorithm is integrated in the optimization module to determine optimal wave cut-off timings and capacities, so as to minimize Pre-MH Loss as well as improve delivery speed.
(c) Processing Unit – A processing unit is integrated within the operating device and functionally coupled with the optimization module embedded with the optimization algorithm to directly execute the instructions received from the optimizing algorithm, which involves performing computational tasks required for optimizing wave cut-off timings and capacities to minimize Pre-MH loss.
[0049] In an embodiment, the operating device may be selected from a group consisting of, such as, but not limited to, mobile device, computer, laptop, and the like.
[0050] In an embodiment, as shown in Figure 1 and Figure 2, the present invention provides a method for determining optimal wave design in fulfillment centers. The method comprises the following steps:
(a) collecting inputs and determining constraints by a user through an operating device;
(b) calculating the hourly reservation capacity of a fulfillment center by a user through an operating device;
(c) computing Inter-wave capacity loss based on the hourly reservation capacity calculated in step (b) as well as pre-computing losses through a processing unit based on the instructions received from an optimization model;
(d) providing inputs parameter and constraints obtained in step (a), hourly capacity computed in step (b), and inter-wave capacity loss and pre-computing losses computed in step (c) to an optimization model through the operating device to initiate optimization process; and
(e) running optimization algorithm installed in the optimization model and simultaneously providing instructions to a processing unit to analyze the parameters provided in step (d) to provide optimal number and timings of cut-offs while adhering to constraints and thereafter determining the processing capacity within each cut-off based on cutoff time & assigned hourly capacity, ensuring minimized Pre-MH loss.

[0051] In an exemplary embodiment, the inputs collected in step (a) may be selected from a group consisting of such as, but not limited to, hourly order pattern, LPHT connection times, LPHT connection load/volume, FC processing capacity, FC shifts & timings, P2D time or a combination thereof. The inputs are described herein in detail:
? Hourly order pattern: As shown in Figure 3(a), the hourly order pattern at an FC may be computed by averaging the hourly approved orders over a few business as usual (BAU) days. Further, disaggregating these hourly order numbers based on the time discretization required for the model. For instance, if the cut-offs can be placed at 15-minute intervals, the hourly demand pattern will be split into 4 equal parts.
? LPHT connection times: The LPHT connections may be provided by the network planning team. The LPHTs may be typically spread out throughout the day.
? LPHT connection load/volume: The LPHT connection load/volume refers to handling capacity (in units) that can be shipped to a destination on a BAU day (for each LPHT). The LPHT load/volume may be obtained by averaging out the volume it shipped over a few BAU days. The optimization model may either consider all the LPHTs or may select the Pareto lanes that cover 95-98% of the overall load.
? FC processing capacity: The FC processing capacity is the total processing capacity (manpower) on a business as usual (BAU) day. This is typically considered to be 1.2X times the total orders/reservations on a BAU day.
? FC shifts & timings: Most of the FCs operate in 2 shifts and their shift timings may be pre-defined. Cut-offs can only be placed during the shift timings.
? P2D time: P2D time may vary from one FC to another. It typically ranges from 30 to 180 minutes depending on the size and the infrastructure capacity of the FC.
[0052] In another exemplary embodiment, the constraints determined in step (a) may be selected from a group consisting of, such as, but not limited to, the time between consecutive cut-offs, count of cut-offs, maintaining hourly run rate, adhering to 11/11 cut-offs, or a combination thereof. The constraints are described herein detail:

• Time between consecutive cut-offs: Minimum time must be maintained between two consecutive cut-offs. This is required to ensure that the FC ops get sufficient time to prepare the pick lists and assign them to pickers. This minimum time is typically the P2D time but can vary based on the FC’s order processing constructs.
• Count of cut-offs: FCs can provide their preference on the number of cut-offs based on their planning strategy. This can either be a strict constraint or can be left to the model to select the optimal number of cut-offs.
• Maintain hourly run rate: In case FC deploys manpower the same as of number of orders for every point, the Inter-wave capacity loss will be zero. As the hourly order pattern varies significantly from one hour to another, it may get challenging for FC to deploy manpower mimicking the order pattern. FC tends to deploy manpower maintaining a constant hourly rate either within a shift or at least within a cut-off. For the initial optimization model scope, uniformly distributed the shift capacity to each hour within the shift.
• Adhering to 11/11 cut-offs: Due to 11/11 network constructs (Order by 11 PM and delivery by the next day at 11 AM), FCs are forced to have certain cut-offs adhering to network connections. The number of 11/11 cut-offs can range from 1 to 3 depending on FC’s location & 11/11 construct needs. Based on the 11/11 cut-off timings input, the optimization model may be required to fix these cut-offs irrespective of Pre-MH loss.

[0053] In an embodiment, the hourly reservation capacity of a fulfillment center calculated in step (b) involves splitting the FC’s total daily capacity across the shifts. In an exemplary embodiment, In the case of a 2-shift construct, we can define X% capacity in the first shift (day shift) and (100-X) % capacity in the second shift (night shift). The shift capacity is then uniformly distributed across the shift to get an hourly capacity. For instance, assuming 100K units be the total daily capacity of FC and there are two 9-hour shifts with a capacity split of 55% & 45% in the first shift & second shift respectively. The hourly processing capacity in the first shift may be given by 100??*0.55/9 =6111 units and the second shift by 100??*0.45/ 9 =5000 units.
[0054] In an embodiment, as shown in Figure 3(b), the Inter-wave capacity loss computed in step (c) involves splitting capacity into discretized time-points based on the computed hourly capacity split provided as an input. The overflow at each time-point may be computed. The overflow at the latest cut-off before LPHT may be considered as an approximation for inter-wave capacity loss.

Let ??0 represent units overflown at time ?? = 0.
???? represents demand reservation at time ??, and
???? represents capacity available at time ??.

The overflow for the following periods is given by:

[0055] Computing overflow at time point 0: A multi-day period may be considered, and overflow may be computed for every time point as per equation (1) with an assumption of overflow at time-point 0 of Day-1 to be zero (??0=0). Overflow at a time-point for the modeling day may be the averaged value across all the days (leaving Day 1, as overflow for time may be considered as zero).
[0056] Figures 4a and Figure 4b show overflow build-up over time in two scenarios. 5 days (5*24=120 time points) are shown in the plot. Figure 4a shows the scenario where capacity is lesser than demand reservation in which case, overflow shoots up over time and keeps increasing. Figure 4b shows the scenario where capacity is close (1.2X) to demand in which case, overflow over time attains a steady state and based on capacity distribution, overflow values for a time-point take the same value after Day 2.

Let ??t ?? represent units overflown at time t averages across multiple days (5-day time-period (5*24=120 time points with a one-hour discretization).

For a N-day & K time-point discretization, this may be generalized as

[0057] In an embodiment, the pre-computed losses computed in step (c) involve pre-computation of losses for modeling purposes for possible combination of LPHT & cut-off points. This parameter is provided as an input to the optimization model. For a given LPHT connection ??, all prior time-points (including LPHT’s connection time) may be considered as possible cut-off points.
[0058] In an embodiment, the optimization model runs using multiple configurations of hourly reservation capacity splits defined by the planning team to identify and select the scenario with the least pre-MH loss.
[0059] In an embodiment, the optimization model determines the Pre-MH loss before performing the method for determining optimal wave design in the fulfillment center. The optimization model assigns weightage (between 0-1) to each LPHT connection based on the proportion of volume/units a connection ships to the total dispatched volume. Hence, total pre-MH loss (in units) for an FC is defined as the weighted sum of LPHT’s pre-MH loss. Pre-MH loss for a connection ?? is defined as:

The percentage of orders that are not connected to the earliest available LPHT connection during Promise (alternately, the difference between assigned LPHT and the order approval time is more than 24 hours assuming one LPHT connection per day) are categorized into Pre-MH loss.
Pre-MH loss = % orders not connected to earliest LPHT connection
There are several factors for an order missing a connection within 24 hours. The factors are describe herein below:
• Lead time constraints (pick to dispatch/Inter-wave P2D loss)
• Wave synchronization loss
• Wave capacity constraint (inter-wave capacity loss)
[0060] In an exemplary embodiment, the optimization model is implemented using PULP 2.7.0 library (python) and solved using Gurobi 10.0.0 on a 8-thread Intel Core Processor.
In an embodiment, the parameters and variables provided to the optimization model are described herein in detail:
• Sets

• Parameters

• Variables

• Pre-computed losses:

[0061] The Inter-wave P2D loss for an LPHT connection ?? with latest cut-off at time ?? is given by:

[0062] Wave sync loss for a LPHT connection ?? with latest cut-off at time ?? is given by:

[0063] Inter-wave loss for a LPHT connection ?? with latest cut-off at time ?? is given by:

[0064] Total Pre-MH loss for a LPHT connection ?? assuming its latest cut-off at time point ?? is given by

• Constraints:
[0065] Obtaining the latest cut-off point for an LPHT connection: An auxiliary binary variable ??+t,l takes 1 if there exists a cut-off from time ?? + 1 to ?? else 0.

[0066] An appropriate value of ??1 ?????? is the cardinality of set T Loss value for a connection: Loss for an LPHT connection ?? based on selected cut-off time point ?? is given by the below equations:

(1) Constraint 10a poses an upper bound on the loss term
(2) Constraint 10b forces loss at time point ?? to be zero if the cut-off doesn’t exist at ??.
(3) This loss can be non-negative for any cut-off that is before LPHT connection ??. ?? ??, has to be zero for a cut-point ?? if another cut-off exists from ?? + 1 to ??. If such a cut-off exists, take value 1 based on constraints 8 & 9 forcing the loss term to be zero.
(4) Constraint 10b along with 10d computes loss at the latest cut-off point before connection ??. Total loss for a connection with weightage.
[0067] Total loss for an LPHT connection ?? with its weightage W?? is defined by:

[0068] Min P2D time between cut-offs. There should be at least P2D time units’ difference between two consecutive cut-offs.

[0069] Choice of Number of cut-offs. Users prefer to have choice on a number of cut-offs which varies from one FC to other. Let N?? denote number of cut-offs that user requires. This constraint is optional and can be defined by the user.

[0070] No cut-offs during non-shift hours. Cut-offs shouldn’t be placed during non-working hours/non-shift hours.

[0071] Mandatory 11x11 cut-offs. Cut-offs has to be placed at predefined 11x11 cut-offs provided by network teams.

[0072] Link between days: To tackle the day-crossover issue, the time horizon should be at least 2 days (as the cut-off for an LPHT of day 2 can present on day (1). All possible combinations of (t,l) i.e. possible LPHT & cutoff combinations for a 2-day horizon are enumerated. LPHT losses are considered only for Day 2 and cut-offs can exist on both Day 1 & Day-2 with a constraint that cut-offs should be placed at the same time on both days.

where ?? represents count of discretized time-points of a day
• Objective function:
The objective is to minimize total Pre-MH loss

[0073] The following illustrates the experimental result for the implementation of the optimization model and should not be construed to limit the scope of the invention.
Experimental Data:
[0074] Pre-MH loss for scenarios: Table 1 shows the Pre-MH loss for two large FCs (FC-1 and FC-2) under various settings. Description of columns that describe settings of the scenario are provided below:
• Scenario: Name of the scenario
• P2D: P2D time (in mins)
• 11/11 CO: Presence of 11/11 cut-offs constraint or not
• #cut-offs: Number of cut-offs
• #capacity split: capacity distribution across shifts
• #constraints: Number of constraints in the model
• #variables: Number of variables in the model
• #non-zeros: Number of non-zeros entries in the matrix created by math model
Scenario P2D 11/11 # COs Cap Split #constraints #variables #non-zeros Inter Wave P2D Wave Sync Inter wave Cap Pre-MH Loss
FC1_Scenario_1 75 Yes 6 55/45 9444 3264 162542 1.61% 2.13% 2.79% 6.54%
FC1_Scenario_2 75 No 6 55/45 9444 3264 162542 1.86% 1.78% 2.57% 6.22%
FC1_Scenario_3 75 Yes 6 50/50 9444 3264 162542 1.89% 1.80% 3.94% 7.63%
FC1_Scenario_4 75 Yes 6 60/40 9444 3264 162542 1.89% 1.80% 4.82% 8.51%
FC1_Scenario_5 75 Yes 7 55/45 9444 3264 162542 1.65% 1.62% 2.79% 6.06%
FC1_Scenario_6 75 Yes 8 55/45 9444 3264 162542 1.62% 1.04% 2.98% 5.64%
FC2_Scenario_1 45 Yes 6 55/45 12292 4224 212726 1.18% 3.33% 4.22% 8.74%
FC2_Scenario_2 45 Yes 6 50/50 12292 4224 212726 1.18% 3.33% 5.44% 9.96%
FC2_Scenario_3 45 Yes 6 60/40 12292 4224 212726 1.02% 3.59% 4.66% 9.26%
FC2_Scenario_4 45 Yes 7 55/45 12292 4224 212726 1.15% 1.75% 4.77% 7.67%
FC2_Scenario_5 45 Yes 8 55/45 12292 4224 212726 1.04% 1.69% 4.15% 6.87%
FC2_Scenario_6 45 No 6 55/45 12292 4224 212726 0.91% 2.36% 4.60% 7.86%
FC2_Scenario_7 45 No 7 55/45 12292 4224 212726 0.66% 2.27% 4.11% 7.05%
FC2_Scenario_8 45 No 8 55/45 12292 4224 212726 0.49% 1.11% 4.69% 6.28%
FC2_Scenario_9 45 Yes 6 54/46 12292 4224 212726 2.51% 3.38% 5.65% 11.54%
Table 1
[0075] The last 4 columns show the total and the individual components of the Pre-MH loss. ForFC-1, the least Pre-MH loss is obtained with a 55/45 capacity split and 6 cut-offs. Also, as the number of cut-offs increases from 6 to 8, the Pre-MH loss reduces. This is due to the decrease in wave-sync loss with increased cut-offs. Similar trends were reported at FC-2.
[0076] Sensitivity Results: The sensitivity of the optimization model result was examined with respect of the changes in the hourly order pattern and capacity.
[0077] Change of Hourly Order pattern: Scenarios were run to check the effect of order pattern on Pre-MH loss and change of cut-offs.
[0078] As shown in Figure 5, a simulation of total orders ranging from 90% of actual demand to 110% of demand in intervals of 5% was conducted. The X-axis represents the total orders % as of a static BAU demand (??) and the Y-axis represents Pre-MH loss. Pre-MH loss increases with an increase in orders as capacity is the same in all scenarios and hence based on reservation/order pattern change, Inter-wave capacity loss increases. To solve this, cut-offs should be changed and changes in cut-off timings are shown in Table 2.
[0079] As the cut-off timings are changing with variations in order/reservation pattern. 4 out of 6 cut-offs remained the same and there is a change in two cut-offs when demand is moving from 0.95X to 1X. This pattern may not be consistent across all FCs. This signifies the need to understand change in demand patterns at least at a weekly frequency and quickly change cut-offs to minimize Pre-MH loss.
Cut-off 0.9D 0.95D D 1.05D 1.1D
CO-1 1:00 1:00 1:00 1:00 1:00
CO-2 12:00 12:00 3:00 3:00 3:00
CO-3 15:00 15:00 15:00 15:00 15:00
CO-4 17:00 17:00 16:30 16:30 16:30
CO-5 20:00 20:00 18:00 18:00 18:00
CO-6 22:00 22:00 22:00 22:00 22:00
Table 2
[0080] Change of capacity: Scenarios were run to check the effect of capacity on Pre-MH loss and cut-off placements. As shown in Figure 6, capacity is varied from 1.1X to 1.3X of total orders/reservations in intervals of 5%. Pre-MH loss was reduced with an increase in capacity and the effect was similar to the change of orders pattern with fixed capacity. However, Pre-MH varied from around 3.5% to 9.5% in this case as compared to a 4.9% to 7.5% variation. This indicates capacity has a huge impact on Pre-MH loss as compared to order pattern change and Pre-MH is more sensitive to capacity change. To solve this cut-off, have to be changed and changes in cut-off timings are shown in Table 3.
Cut-off 1.1D 1.15D 1.2D 1.25D 1.3D
CO-1 1:00 1:00 1:00 1:00 1:00
CO-2 3:00 3:00 3:00 12:00 12:00
CO-3 15:00 15:00 15:00 15:00 15:00
CO-4 16:30 16:30 16:30 17:00 17:00
CO-5 18:00 18:00 18:00 20:00 20:00
CO-6 22:00 22:00 22:00 22:00 22:00
Table 3

[0081] The present invention exhibits the following advantages:
• The present invention ensures enhancement of delivery speed and satisfaction of customers.
• The present invention ensures reduction in pre-MH loss, resulting in faster processing of orders and dispatch.
• The present invention aims to ensure efficient utilization of resources, leading to cost-saving and operational optimization.
[0082] While this invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims.
, Claims:WE CLAIM:

1. A method for determining optimal wave design in fulfillment center, comprising steps of:
(a) collecting inputs and determining constraints by a user through an operating device;
(b) calculating the hourly reservation capacity of a fulfillment center by a user through an operating device;
(c) computing Inter-wave capacity loss based on the hourly reservation capacity calculated in step (b) as well as pre-computing losses through a processing unit based on the instructions received from an optimization model;
(d) providing inputs parameter and constraints obtained in step (a), hourly capacity computed in step (b), and inter-wave capacity loss and pre-computing losses computed in step (c) to an optimization model through the operating device to initiate optimization process; and
(e) running optimization algorithm installed in the optimization model and simultaneously providing instructions to a processing unit to analyze the parameters provided in step (d) to provide optimal number and timings of cut-offs while adhering to constraints and thereafter determining the processing capacity within each cut-off based on cutoff time & assigned hourly capacity, ensuring minimized Pre-MH loss.
2. The method as claimed in claim 1, wherein the inputs collected in step (a) are selected from a group consisting of hourly order pattern, LPHT connection times, LPHT connection load/volume, FC processing capacity, FC shifts & timings, P2D time or a combination thereof.
3. The method as claimed in claim 1, wherein the constraints determined in step (a) are selected from a group consisting of the time between consecutive cut-offs, count of cut-offs, maintaining hourly run rate, adhering to 11/11 cut-offs, or a combination thereof.
4. The method as claimed in claim 1, wherein the hourly reservation capacity of a fulfillment center calculated in step (b) involves splitting the FC’s total daily capacity across the shifts.
5. The method as claimed in claim 1, wherein the hourly reservation capacity of a fulfillment center calculated in step (b) involves splitting the Inter-wave capacity loss computed in step (c) involves splitting capacity into discretized time-points based on the computed hourly capacity split provided as an input.
6. The method as claimed in claim 1, wherein the pre-computed losses computed in step (c) involve pre-computation of losses for possible combination of LPHT & cut-off points.
7. The method as claimed in claim 1, wherein the optimization model runs using multiple configurations of hourly reservation capacity splits defined by the Planning/FC design team to identify and select the scenario with the least pre-MH loss.
8. A system for performing method for determining optimal wave design in fulfillment center as claimed in claim 1, comprising:
• an operating device serving as a platform for the user to provide inputs via an interface;
• an optimization module installed in the operating device;
• an optimization algorithm embedded in the optimization module for determining optimal wave cut-off timings and capacities to minimize Pre-MH Loss; and
• a processing unit integrated within the operating device and functionally coupled with the optimization module to directly execute the instructions received from the optimizing algorithm to perform computational tasks required for optimizing wave cut-off timings and capacities to minimize Pre-MH loss.
9. The system as claimed in claim 8, wherein the operating device is selected from a group consisting of mobile device, computer, or laptop.