Motivated by a major PC manufacturer in consumer electronics industry, we study ... Keywords: Consumer electronics supply chain; air transportation; assembly.
METHODOLOGIES FOR SYNCHRONIZED SCHEDULING OF ASSEMBLY AND AIR TRANSPORTATION IN A CONSUMER ELECTRONICS SUPPLY CHAIN Abstract Motivated by a major PC manufacturer in consumer electronics industry, we study the problem of synchronization of assembly manufacturing and final deliveries using air transportation to achieve accurate delivery with minimized delivery cost in consumer electronics supply chain (CESC). The customer orders are shipped to the customers by cargo flights. Orders are allocated to the available flight capacities based on customer delivery dates. Synchronization is considered to match the assembly completion of each order with the departure time of its predetermined allocated flights. We decompose the synchronization problem into two sub-problems consisting of an air transportation allocation problem and an assembly scheduling problem. The first sub-problem is formulated as an Integer Linear Programming (ILP) model. Two solution methodologies are proposed for the second sub-problem. Computational results indicate that the proposed methodologies can achieve considerable cost reduction compared to the existing industry practice. Keywords:
Consumer
electronics
manufacturing; synchronization.
supply
chain;
air
transportation;
assembly
1. Introduction This study is motivated by a large Make-to-Order (MTO) based PC assembly manufacturer who faces challenges in synchronizing the schedule of assembly with air transportation in the supply chain. The assembly manufacturing is based on customer orders. The components required for the assembly of final products are generally stored in inventory in advance or procured as and when required by the assembly line. Orders are received through phone, fax, World Wide Web (WWW) and other channels. The acceptance of an order is based on the product quantity and the due-date of the order. On acceptance of an order, the components are transferred to the assembly line. After several modules of assembly processes, the finished products are transferred to local airport without delay.
The finished products are delivered to respective customers by air transportation. Generally, there are several flights available with different transportation capacities at different departure times in a particular planning period and their total transportation capacity is always larger than the quantity of all the accepted orders within each planning period. Costs or penalties are incurred by delivering the customer order either earlier or later than the due date. The delivery earliness costs could result from the need for storage and insurance. The delivery tardiness cost includes customer dissatisfaction, contract penalties, loss of sales, and potential loss of reputation. Orders transferred to the airport ahead of their flights’ departure times incur waiting penalties. The penalties are particularly for handling and storage of the goods in airport. Unlike the basic assembly and transportation cost of the products, these penalty costs can be minimized by achieving better synchronization in CESC.
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The problem under study consists of two tasks. The first task is to allocate accepted orders to the available flights’ capacity based on due-dates, and the second task is to determine a schedule for the assembly that minimizes the waiting time before air transportation, considering the scheduled departure times of the allocated flights. Transportation allocation is constrained by the assembly capacity, i.e., the allocation should be balanced with assembly capacity and the assembly schedule should minimize the waiting time of the orders before air transportation.
The Just-in-Time production philosophy has lead to a growing interest both in production and transportation scheduling problems considering earliness and tardiness penalties. However, research in these two areas is mainly focussed independently and there has been a very scant treatment of synchronization of these two to achieve the delivery accuracy, even though this is a sizable sector of industry. In this paper, we study the problem of synchronization of air transportation allocation and assembly scheduling, and present solution methodologies with the objective of minimizing delivery costs.
The remainder of the paper is organized as follows: section 2 discusses related work. Section 3 gives the formulation of air transportation allocation problem and describes the heuristic methodologies for achieving the synchronization of assembly and air transportation. Section 4 details the computational experiment design. The relative performance of the two proposed solution methodologies among themselves as well as in comparison with existing industry practice is discussed in section 5. Conclusions and the further work are discussed in the last section.
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2. LITERATURE REVIEW The distribution of finished goods to customers plays an important role in supply chain management. Due to market globalization, coordination among different stages in the supply chain to achieve ideal overall system performance has become more practical and has received attention from both industry practitioners and academic researchers. With the popularity of just-in-time concepts, companies now tend to reduce their inventory levels in order to be competitive. This trend has created a closer interaction between the stages in a supply chain and has increased the practical usefulness of integrated models. In such an integrated system, the linkage between job scheduling (the production stage) and finished goods delivery (the distribution stage) is extremely important. Traditional approaches separately and sequentially consider machine scheduling and job delivery, without effective coordination between the two. However, making two decisions separately without coordination will not necessarily yield a global optimal solution. Substantial ineffectiveness may result when decision-making between the two stages is poorly coordinated, especially when transportation resources are scarce in the system (Chang and Lee, 2004).
Production scheduling literature, in general, has addressed problems without taking into account the final delivery and transportation requirements after processing the jobs on machines. Only a few researchers have considered the joint optimization of machine scheduling and job transporting. The first study explicitly considering the transportation issue is by Maggu and Das (1980). They studied a two-machine flow-shop makespan problem in which they assumed that there are unlimited buffers on both machines and a sufficient number of transporters available to transport jobs from one machine to the other with job-dependent transportation times. The problem was solved by using a generalization of Johnson's rule (Johnson, 1954). Potts (1980) and Hall and Shmoys
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(1992) studied a single-machine problem with unequal job arrival times and delivery times. In their model, they implicitly assumed that a sufficient number of vehicles are available in the system in order to deliver a processed job to the customer immediately. They provided a heuristic with a worst-case analysis. Woeginger (1994) studied the same problem in the parallel-machine environment with equal job arrival times and provided a heuristic with a worst-case analysis.
Machine scheduling problems with jobs delivered in batches after processing is reported in Herrmann and Lee (1993), Chen (1996), and Cheng et al. (1996). They did not consider transportation times, i.e., it was assumed that deliveries can be made instantaneously. Lee and Chen (2001) studied machine scheduling problems with explicit transportation considerations. Two types of transportation situations are considered in their models. The first type, Type-1, involves intermediate transportation of jobs from one machine to another for further processing. The second type, Type-2, involves the transportation provided to deliver finished jobs to their destinations. Jobs are delivered in batches by transporter(s). They assumed that all jobs require the same physical space on the transporter. Both transportation capacity and transportation times are considered in their models. This class of scheduling problems are computationally difficult.
While there have been few studies in the literature dealing directly with the problem of synchronization of machine scheduling and air transportation for outbound logistics, there have been some discussion on synchronization of production and road transportation with emphasis on vehicle routing scheduling problem. Blumenfeld et al. (1991) examined the cost-effectiveness to synchronize production and transportation schedules on a production network which consists of one origin and many destinations. The trade-offs between production setup, freight transportation, and inventory costs on
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the network are analyzed and synchronized schedules are developed. Fumero and Vercellis (1999) proposed an integrated optimization model for production and distribution planning with the aim of optimally coordinating important and interrelated logistics decisions such as capacity management, inventory allocation, and vehicle routing. Ruiz-Torres and John (1997) investigated the interaction of production scheduling and routing/transportation on a logistic network by simulation. The results indicate that low manufacturing-logistics cost and a high customer service level can both be maintained by an appropriate combination of scheduling and routing rules. Chen (2000) addressed the problem of integrating production and transportation scheduling in a MTO environment with the aim of minimizing the total cost which consists of transportation cost, tardiness penalty cost and overtime production cost. Sarmiento and Nagi (1999) reviewed work on integrated analysis of production-distribution systems. To the best of our knowledge, only the following one reference is found similar to the flight allocation problem. Tyan et al. (2003) studied the freight consolidation problem of grouping different shipments from supplier into a larger shipment at the consolidation point. A mathematical programming model has been developed to assist the evaluation of consolidation policies for a special class of freight consolidation at an integrated global logistics company.
Studies have been published addressing the saving and benefits on co-ordination and integration of manufacturing and supply operation in electronic manufacturing. Feo et al. (1995) describe a decision support system known as INSITES designed to assist the dayto-day electronics assembly operations in Texas Instruments. The emphasis is on the heuristic techniques to solve the scheduling problem. Magyar et al. (1999) also present heuristics on solving single machine optimization problems in electronics assembly in order to maximize the throughput of the machine. Werner et al. (2003) present a
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simulation approach to generate the schedule in electronics production. There is also a growing trend of applying expert system in manufacturing companies, including electronics manufacturing companies (Metaxiotis et al., 2002). The expert system contains the knowledge needed for solving a specific problem: heuristics, fuzzy decision system (Custodio et al., 1994), knowledge based simulation technique (Tayanlthi, et al. 1992), artificial neural network, expert knowledge and dispatching rules (Li et al. 2000). Metaxiotis et al. (2002) also mentioned that the usefulness of expert system will be further recognized when integration is carried out using operations research techniques.
The problem of synchronized scheduling and transportation allocation was introduced by Li et al (2004a). The transportation allocation problem is formulated as an integer programming model. Heuristic methodology using backward scheduling to achieve synchronization is demonstrated using a numerical study. Li et al (2004b) formulated the problem of synchronized scheduling and transportation allocation as two independent mixed integer linear programming problems and solved them independently to achieve synchronization with the objective of minimization of cost of transportation of delayed orders in special flights. The savings in costs and the benefits of synchronization in a supply chain are multi-fold particularly in CESC. This motivated us to further expand the contribution based on the above reported work to develop a methodology on synchronized scheduling of air transportation allocation and assembly.
3. RESEARCH METHODOLOGY The synchronization problem is investigated in this section by adopting a two stage approach which involves decomposing the overall problem into two sub-problems, consisting of an air transportation allocation problem and an assembly scheduling problem. The air transportation allocation problem is formulated as an Integer Linear
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Programming (ILP) Problem with earliness tardiness penalties for orders. For the assembly scheduling problem, it is basically required to sequence the orders on the assembly to minimize the waiting times of orders before air transportation. Hence the second sub-problem is modelled as a scheduling problem with earliness penalties. The air transportation problem is solved first to obtain the transportation allocation. Then the assembly scheduling problem is solved based on the results of the air transportation problem to obtain the release time of each order.
The novelty of the proposed methodology is the introduction of the concept of synchronization between the two sub-problems. In the formulation of each sub-problem, the synchronization issue is taken into account. Synchronization is incorporated into the ILP model of the air transportation problem by the constraint that matches the flight allocation with the production rate of the assembly. In other words, the allocated orders should be supplied on time by sufficient assembly capacity. The assembly due-date of each order is determined by departure time of the flight that the order allocated to, which is determined by the ILP model. As mentioned in the literature review section, the existing models consider the production scheduling problem and the air transportation problem separately. The air transportation allocation is executed based on experience or simple logic in practice. A simple heuristic, which is commonly applied in industry, is illustrated in detail in section 5. We formulate the two sub-problems based on the following assumptions: • The assembly flow shop is treated as a single machine. • Setup time is included in the processing time of assembly manufacturing. • Total assembly manufacturing time of an order is directly proportional to the order’s quantity
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• Each flight has normal capacity with normal transportation cost, and special capacity with special transportation cost for orders that exceed normal capacity. • Orders released into assembly flow shop for the planning period are delivered within the same planning period which means no assembly backlog. • In general, an order received in one period will be released into assembly flow shop in the next period. • There is only one destination of transportation. • All the packed products are the same weight and same dimension. • There are multiple flights in the planning period. • Business processing time and cost, together with loading time and loading cost for each flight are included in the transportation time and transportation cost. • Local transportation time and cost are included in assembly time and assembly cost. Local transportation transfers products from the assembly plant to airport. • Order fulfilment is considered to be achieved when the order reach the destination airport on time i.e., customer due-date. • Orders can be split and allocated into more than one flight and delivered separately. • Orders can be split and processed separately at assembly flow shop. • The assembly process is not impacted by the unpredictable events such as machine break down, shortage of material, etc. In the following sections we present the formulation of the air transportation allocation problem, and heuristics based on backward and forward scheduling for synchronizing the assembly schedule with air transportation allocation.
3.1. Transportation Allocation Problem We define the following notations:
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i
the order index, i =1, 2, …. N;
f
the flight index, f =1,2,……F;
Df
the departure time of flight f at the local place;
Af
the arrival time of flight f at the destination;
NCf
the transportation cost per unit of the product allocated to the normal capacity of flight f; the transportation cost per unit of the product allocated to the special capacity of
SCf
flight f; NCapf the available normal capacity of flight f; SCapf the available special capacity of flight f; Qi
the quantity of order i;
αi
the per unit delivery earliness penalty cost (per hour) of order i;
βi
the per unit delivery tardiness penalty cost (per hour) of order i;
di
the due-date of order i;
PEif
the per unit delivery earliness penalty cost for order i when it is transported by
flight f; PEif= Max(0,di-Af)* αi PLif
(1)
the per unit delivery tardiness penalty cost for order i when transported by flight f; PLif= Max(0,Af-di)* βi
Zif
the quantity of order i allocated to flight f ;
Xif
the quantity of the portion of order i allocated to flight f’s normal capacity;
Yif
the quantity of the portion of order i allocated to flight f’s special capacity;
PR
the production rate of assembly manufacturing.
(2)
The transportation model allocates orders to the existing transportation capacity with minimum cost. The factors which are taken into account in the transportation model are: 10
(a) the number of available flights for the distribution planning horizon, (b) the departure and arrival time of the flights, (c) the designated capacity and the corresponding transportation cost, and (d) the possible special capacity in each flight with the corresponding freight cost. The model is expressed as follows: Min
∑∑ NC i
f
f
X if + ∑∑ SC f Yif + ∑∑ PEif Z if + ∑∑ PLif Z if i
f
i
f
i
(3)
f
Subject to: X if + Yif = Z if
for all i, f
(4)
∑X
for all f
(5)
for all f
(6)
for all i,
(7)
if
≤ NCap f
i
∑ Y ≤ SCap ∑ ( X +Y ) = Q if
f
i
if
if
i
f
f
∑∑
( X if +Yif ) ≤ D f PR
for all f,
(8)
f =1 i
Xif, Yif, Zif > 0 and integers
(9)
The decision variables are: Xif, Yif, and Zif and they take integer values. The objective is to minimize overall total cost which consists of total transportation cost for the orders allocated to the normal flight capacity, total transportation cost for orders allocated to the special flight capacity, total delivery earliness penalty cost and total delivery tardiness penalty cost. Constraint (4) ensures that the quantity of the proportion of order i allocated into flight f consists of both quantities of the proportion of order i allocated into normal capacity of flight f and the proportion of order i allocated to special capacity of flight f. Constraint (5) ensures that the normal capacity of flight f is not exceeded. Constraint (6) ensures that the special capacity of flight f is not exceeded. Constraint (7) ensures that an order i is completely allocated. Constraint (8) ensures that allocated orders do not exceed production capacity. It ensures that allocated quantity can be supplied based on assembly capacity. The output of this model is the order allocation. Once an order’s transportation
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allocation is decided, its transportation departure time is determined. Since local transportation time is assumed to be included in the assembly processing time, the order’s due-date for assembly manufacturing is determined.
3.2. Assembly Scheduling Problem In the assembly scheduling problem, a release time is determined for each order to minimize the average waiting time (AWT) before transportation. AWT is defined as the mean of sum of the waiting times for all orders. The results of transportation allocation model are the input data for the assembly scheduling problem which includes the orders, quantity and transportation departure time. Orders may be split and allocated to different flights. The split orders will be treated independently in assembly. The transportation departure time is taken as the due date of assembly for each order. The assembly schedules adhere to the following conditions: (i) only one order can be processed in assembly at a time (ii) pre-emption is not allowed which means that the processing of a order cannot interrupted by another order and (iii) the processing time of each order is known, and is obtained by multiplying the order quantity with per unit processing time. We propose two methodologies for assembly scheduling problem in this section.
3.2.1. Forward scheduling Heuristic (FSH) Normally in practice, the schedules are constructed using dispatching rules and follow a forward dispatch method. In forward scheduling, the jobs are sequenced one by one, starting from the first job, to achieve feasible and compact schedules. The approach usually generates non-delay schedules.
A non-delay schedule is one in which no
machine is kept idle at any time when at least one job is waiting for processing. Longest Processing Time (LPT) rule is selected for dispatching and loading an order on the assembly. It is proved by Panwalkar (1982) that LPT minimizes total earliness in single
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machine scheduling in the situation of no tardiness. Since there may be split orders in allocation, the sequence determined by LPT rule may be adjusted to combine the split orders to facilitate assembly manufacturing while maintaining the transportation schedule of the split orders.
The general scheme for FSH is:
Step 1: Group orders that are allocated to the same flight, and sequence the groups by the rule of earliest flight departure time first
Step 2: Use LPT rule to sequence the orders within the each group.
Step 3: Assembly batching of split orders (ABSO): This step is used to combine the split orders in a batch for assembly so that split orders in transportation can be treated as a whole order in assembly. This step is applied only in the situation when an order is split and allocated to two adjacent flights. If the first proportion of the split order is sequenced to be the last one in the order sequence of the first flight, the next proportion of the split order which allocated to the second flight is adjusted to be the first one in the second flight’s order sequence. This is to facilitate the assembly processing of an order.
Step 4: Calculate each order’s release time by forward dispatch method starting from the first order to the last order.
Step 5: Compute the AWT between assembly and transportation.
The number of groups in the planning period corresponds to the number of flights that transport orders to customer destination, determined by transportation allocation model. Each order group consists of a set of orders and they have identical assembly due-date.
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To illustrate FSH, consider a problem having five orders and three flights defined in Table 1 and Table 2. The cell values 3(1) and 3(2) in the first column of Table 1 indicate that order 3 is split into two sub-orders. The transportation allocation of each order is listed in the third column of Table 1. Each flight’s departure time can be obtained in Table 2. Figure 1 displays the resulting schedule on the Gantt chart. This Gantt chart shows the schedule from the perspective of what time each order is scheduled for the assembly process.
Table 1. Order processing times and transportation allocation
Table 2. Flight departure times
Figure 1. Illustration of FSH
By applying first two steps of FSH, the sequence in the last group should be order 4, followed with order 3(2). However, when applied ABSO, the two orders are interchanged. It is because that order 3(1) is sequenced as the last job in second group. Therefore, orders 3(1) and 3(2) can be processed one after another which means order 3 processed without interruption in assembly. For the final sequence generated by FSH, the obtained value of AWT is 3.4.
3.2.2. Backward Scheduling Heuristic (BSH) Backward scheduling is the reverse of the forward scheduling approach and schedules are defined on a reverse time frame. The start time and completion time of the same job in forward scheduling mode is related to the completion time and start time of the same job in backward scheduling mode. In other words, the completion time of each job is determined first. The release time (or start time) for each job is then obtained using the
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determined completion time. To arrive at a schedule after using backward scheduling approach, the processing sequence is reversed, and the schedule time frame is reversed back to forward time frame.
The backward scheduling heuristic presented in this section considers inserted idle times between processing of orders. FSH is a straightforward method that schedules orders one by one from the beginning time of the planning period. The main objective is to make sure that each order can meet its assembly due-date, which is the departure time of its allocated flight. FSH presented in the previous section does not minimize the total earliness effectively. This is overcome by adopting a backward approach that inserts idle times between order groups. Within each group, jobs are scheduled one by one without inserted idle time, since all jobs have the common assembly due-date. To minimize order earliness before transportation, the favourable completion time for each order is their corresponding flight departure time. Idle times are inserted between order groups only when the release time of orders in the succeeding group is later than the current order group due date.
Steps of BSH are the same as FSH except for step 4. Backward scheduling is used in step 4 in BSH instead of forward scheduling in FSH.
Step 4: Sequence the orders from their assembly due-date or the release time of the first order in the succeeding order group, whichever is smaller. Calculate each order’s release time by backward dispatch method starting from the last order to the first order.
To illustrate BSH, consider the problem defined in Table 1 and Table 2. Figure 2 displays the resulting schedule obtained using BSH in a machine Gantt chart. The AWT is 1, which is only about 29.4% of the value obtained using FSH.
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Figure 2. Illustration of BSH
4. EXPERIMENTAL DESIGN In order to validate the efficiency of the presented methodologies, a series of computational experiments were carried out using randomly generated test problems. Table 3 shows the parameters and their ranges chosen based on the representative data taken from industry practice. Table 3. Summary of Experimental design
The number of jobs N ranges from 10 to 100, with the number of flights F ranges from 3 to 20. The problem size is determined by the number of jobs and the corresponding number of flights. Generally, N equals 5F in each problem except the first problem with 10 jobs 3 flights. Thus, there are total of 10 different sized problems are considered for evaluation.
The planning period is set to 24 hours for this problem. For each generated problem, the first flight’s departure time is set to be 24/N. We assume to have a fixed interval of 24/N between the flights’ departure times. Thus the remaining flights’ departure times are determined. The transportation times of all flights from departure to destination is set to 2 hours (as only one destination is considered). This is assumed based on the information obtained from the industry. Order due-date is drawn from a uniform distribution varying between 3rd and 26th hour. Once the quantity of each job for a given instance is generated, the value of production rate is generated from a discrete uniform distribution as: PR = TQ * Uniform [1, 1.5]/24, where TQ is total quantity which equals the sum of all the order’s quantity. Five instances are generated for each problem, which gives a total of 50 test
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problems. LINGO 8.0 system is used to construct the mathematical programming model. Assembly scheduling heuristics have been coded in Microsoft visual basic 6.0 and all the tested problems are solved using a Pentium 4, 2.4 GHz computer with 256 MB RAM.
5. RESULTS, ANALYSIS AND DISCUSSIONS The objective of the computational study in this section is primarily to analyze the relative performance of the proposed methodologies with industry practice approach. The performance of two proposed heuristics BSH and FSH for assembly scheduling is also compared with one another by integrating them with air transportation allocation model. To evaluate the contribution of proposed methodologies, we compare them with the EDD+FCFS heuristics which is commonly used in the current industry practice. The scheduling approach followed in industry mainly consists of two steps:
Step 1: Schedule job orders using Earliest Due Date (EDD) rule for the assembly. The accepted orders corresponding to the planning period are assigned into assembly manufacturing based on their due dates and released by EDD policy.
Step 2: First Come First Serve (FCFS) for transportation. Within the planning period the completed products when transferred to airport are allocated to the flights based on FCFS rule based on availability of capacities in flights.
The air transportation allocation model provides optimal allocation for the orders considered in the planning period. As mentioned in section 3.2, the results of ILP model are the input data for the assembly scheduling problem. The performance of the proposed heuristics, BSH and FSH for the assembly scheduling problem are evaluated using AWT between assembly and transportation. LPT rule minimizes total earliness in the situation of no tardiness optimally. But the sequencing rule is used together with ABSO which
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will change the final sequence facilitating the assembly process when job orders of similar types need to processed in two successive jobs groups. Hence to evaluate the performance of the application of LPT in Step 2, we choose to use EDD rule, the commonly applied rule in practice, where due-date refers to the customer due-dates. Table 4 summarizes the AWT values of all the test problems using LPT and EDD sequence rules, applied in Step 2 for both BSH and FSH. The results are presented in terms of average values of the five instances for each experiment configuration. We denote the problem by NjFf where N is the number of jobs and F is the number of flights in the problem. For example, there are 10 jobs and 3 flights in the first problem and it can be denoted as 10j3f. Table 4. Performance of BSH and FSH
Table 4 shows the performance of the two heuristics for the assembly scheduling problem. BSH heuristic is found to perform relatively better in comparison with FSH heuristic for all the test instance sizes in minimizing AWT. It is observed that LPT rule provides smaller AWT value compared to EDD rule in all the evaluated test problems when used in both the heuristics. BSH heuristic yields 43% to 95% of AWT reduction over FSH for different sized problems when LPT rule is applied. When EDD rule is applied, BSH yields 53% to 93% of AWT reduction over FSH for different sized problems. It is also interesting to note that for BSH, the AWT values decrease as the problem size increases. It indicates that BSH provides better solutions in comparison with FSH for large problem sizes which involve complex scenarios with large number of orders and flights.
The synchronization obtained using BSH and transportation allocation ILP model is compared with the industry practice approach (i.e., ‘EDD+FCFS’ heuristics) to evaluate
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the obtained improvements using the different size test problems considered in this study. The improvements observed when using BSH is measured by the reduction of AWT, and the savings obtained by using the ILP model is evaluated by total cost reduction over ‘EDD+FCFS’ heuristics. Table 5 shows that the proposed methodology can significantly reduce AWT value by 52% to 93% compared to the EDD+FCFS heuristics for different sized problems. The proposed methodology also yields 5.1% to 30.2% of delivery cost reduction per day (24 hr planning period) over the EDD+FCFS heuristics. It suggests that the proposed methodology can achieve more accurate delivery with smaller cost and reduced waiting time before transportation compared to current industry practice method.
Table 5. Performance of BSH and EDD+FCFS heuristics
The significant contribution of the proposed methodology has several management implications. 1. The transportation allocation model helps in capacity planning. Once the orders to be transported in a planning period are decided, the transportation allocation can be obtained using the ILP model. This is helpful for daily transportation capacity planning. It helps in avoiding the worst situation of no flight capacity to transport the finished orders. This is basically due to the fact that the transportation capacity is always larger than the order quantity to be transported, which are the inputs to the ILP model. Hence, the unallocated flight capacities can be handled in advance. The allocated normal/special capacities of each flight could be negotiated with airlines in advance with a possibility of shipping the products at a lower cost.
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2. Delivery synchronization and reduction in logistics costs: Delivery earliness and tardiness penalties for each order can be assigned according to the priority of the customer. Then, the optimal delivery is guaranteed by the ILP model. In other words, the total cost which consists of transportation cost and delivery penalty cost is minimized. Higher delivery penalty cost and higher transportation cost generally lead to larger gap between the results of ILP model and the result of ‘EDD+FCFS’ heuristic. Another viewpoint of cost saving is the reduction of AWT by BSH compared to ‘EDD+FCFS’ heuristic. The temporary finished goods inventory always leads to storage cost, insurance cost, capital opportunity cost, etc.
3. Evaluation of alternate production planning and scheduling decisions: The methodology can be used to evaluate various decisions in the situation of handling large quantities of orders. The decision alternatives can be consideration of different flights, schedules, and acceptance of orders. The decision leading to lower cost can be selected for execution by the proposed methodology. This helps the planners for making decisions in volatile situations such as acceptance of an important emergency order, flight cancellation, order cancellation, and customer priority changing.
6. CONCLUSIONS The paper models a synchronized assembly scheduling and air transportation allocation problem observed in a consumer electronics supply chain. The synchronization problem is modelled as two sub-problems: the air transportation allocation problem and the assembly scheduling problem. The air transportation allocation problem is formulated as an Integer Linear Programming model and heuristics are proposed for the assembly
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scheduling problem. Optimal transportation allocation is obtained by solving the ILP model. The computational results show that the proposed BSH heuristic for assembly scheduling can effectively reduce order waiting time between assembly and transportation compared to another proposed heuristic FSH, and the industry practiced heuristic EDD+FCFS.
The proposed transportation allocation model plus the BSH
heuristic provide considerable total cost reduction compared to the industry practice heuristic. This study indicates that the combination of optimal transportation allocation, backward scheduling and a proper sequence rule can achieve good delivery performance with reduced cost in complex CESC.
Even though the methodology was developed for a special application of a major PC assembly manufacturer, the methodology can be easily adopted by other applications in context of fixed transportation departure time and arrival time in MTO supply chain. This work can be extended in several ways by considering multi-machine production scenario with multi-destination transportation with more product varieties for the requirements of global manufacturers, who face demands from various markets scattered all over the world.
Acknowledgements This work was supported by the Singapore-MIT alliance and School of Mechanical & Production Engineering, Nanayang Technological University, Singapore.
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23
Figure 1. Illustration of FSH
1
2
3(1)
3(2)
4
Assembly
0
4
8
12
Figure 2. Illustration of BSH
1
2
3(1)
3(2)
4
Assembly
0
4
8
24
12
Table 1. Order processing times and transportation allocation
Order 1 2 3(1) 3(2) 4
Processing time 2 2 1 1.5 3
Allocated to flight 1 2 2 3 3
Table 2. Flight departure times Flight 1 2 3
Departure time 4 8 12
25
Table 3. Summary of the experimental design Problem Parameter
Values
Number of orders N
10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Number of flights F
a
3,
4, 6, 8, 10, 12, 14, 16, 18, 20
Flight departure time Df
Fixed interval of 24/N between departure times
Normal capacity Ncapf
Uniform[200,800]
Special capacity Scapf Transportation cost of per unit product allocated to normal capacity NCf Transportation cost of per unit product allocated to special capacity SCf Order quantity Qi
Uniform[200,400]
Order due date di order delivery earliness penalty cost (per unit per hour) αi order delivery tardiness penalty cost (per unit per hour) βi Production rate PR
Uniform[2,26]
TQ * Uniform [1,1.5] /24
Instances
5
Uniform [5,7] Uniform [8,10] Uniform[50,200]
Uniform [3,5] Uniform [5,8] a
TQ means total quantity which equals the sum of all the order’s quantity.
26
Table 4. Performance of BSH and FSH
Problem
AWT-BSH
AWT-FSH
LPT
EDD
LPT
EDD
10j3f
2.24
2.74
5.39
5.89
20j4f
1.23
1.59
5.97
6.32
30j6f
1.05
1.36
3.93
4.25
40j8f
0.76
0.97
4.55
4.74
50j10f
0.62
0.84
3.44
3.67
60j12f
0.43
0.57
4.47
4.60
70j14f
0.42
0.56
4.99
5.11
80j16f
0.33
0.45
4.41
4.52
90j18f
0.31
0.41
4.44
4.54
100j20f
0.27
0.36
4.48
4.56
27
Table 5. Performance of BSH and EDD+FCFS heuristics Problem
AWT
Total cost
BSH
EDD+FCFS
Reduced
ILP
EDD+FCFS
Reduced
10j3f
2.24
4.69
52.24%
28912.80
32194.16
10.19%
20j4f
1.23
5.24
76.53%
38987.34
43627.56
10.64%
30j6f
1.05
3.93
73.28%
57747.52
80796.34
28.53%
40j8f
0.76
4.27
82.20%
70613.80
75773.76
6.81%
50j10f
0.62
3.29
81.16%
74257.79
78280.45
5.14%
60j12f
0.43
3.97
89.17%
84825.28
97499.37
13.00%
70j14f
0.42
3.68
88.59%
92772.10
133009.00
30.25%
80j16f
0.33
3.87
91.47%
106701.29
123572.64
13.65%
90j18f
0.31
3.98
92.21%
114869.94
133106.13
13.70%
100j20f
0.27
3.86
93.01%
121620.23
149662.19
18.74%
28
