Ping Cao School of Economic and Management, Shanghai Institute of Technology, Shanghai, China

Transcription

1 doi: / Payent Scheduling Probles of Software Projects fro a Bilateral Perspective Ping Cao School of Econoic and Manageent, Shanghai Institute of Technology, Shanghai, China Jian Zhang* School of Air Transportation, ShanghaiUniversity of Engineering Science, Shanghai, China *Corresponding author(e-ail: zhangj9860@sina.co) Abstract This study exaines the capital-constrained payent scheduling proble related to software projects. An optiization odel for the payent schedules of software projects is constructed fro the joint perspective of the and the contractor in software outsourcing projects. Then, a heuristic siulated annealing algorith is designed to solve the odel. Finally, a case study is presented to validate the odel. The results show that the outsourcing benefits for both parties are closely related to the tiing and aount of the payent. And both the parties could use this odel to select appropriate strategies during the contract signing stage. Key words:payent Scheduling, Software Outsourcing, Heuristic Siulated Annealing Algorith, Optiization Model. 1. INTRODUCTION The project payent scheduling proble (PPSP) is an iportant part of cash flow anageent related to the objective of capital net present value (NPV) axiization (Waligora, 2014). A reasonable arrangeent with regard to the tiing and aount of payent is a widely discussed research topic in traditional engineering project anageent (Wieseann, 2010). In this context, the objectives of the contractor and the are in conflict, and their concerns related to cash flow as well as their preferences differ. During project execution period, both parties tend to take actions that axiize their own profit instead of reaching a coproise (Sobel, 2009). The ajority in literature is fro s perspective (Paraskevopoulos, 2012; Kone, 2011; Ki and Jr. Ellis, 2010; Kopanos, 2014), while soe are fro providers perspective (Vorontsova and Rusu, 2014).Hence, payent scheduling is a key issue for both the contractor and the. Siilar to the case in traditional engineering projects, the payent scheduling arrangeent of software projects has a direct ipact on the profits of the contractor and the. Whereas with the rapid growth in the nuber of software projects, the high failure rate of software projects has caused concern in the industry. The software industry has coe to realize that any of the anageent techniques and ethods that are coonly used in traditional engineering projects are not suitable for the anageent of software projects (Jorgensen, 2014). While research on software project anageent is iperative, the extant research on software project anageent is not up-to-date. Therefore, research on the payent scheduling of software projects in order to balance the profits of both parties for axiizing the overall profit of the software project has iportant theoretical and practical iplications. In the context of engineering projects, a recent overview of the resource-constrained project scheduling proble has been extensively discussed (eyan and Vanhoucke, 2015). (Bahrai and Moslehi, 2013) introduced cash flow into project scheduling and constructed an optiization odel of cash flow that would axiize the NPV. (He, 2014) studied ultiple execution odes of the project payent scheduling arrangeent and developed two heuristic algoriths siulated annealing and tabu search for the ulti-ode PPSP. They copared the perforance of these algoriths on a randoly constructed data set.eyan presented a payent scheduling odel in which the tiing and aounts of payent would be deterined in a single-ode resource-constrained project at activities copletion ties (eyan and Vanhoucke, 2015). And then they extended a new scheduling technique to solve ulti-ode resource-constrained project scheduling proble by eploying genetic algorith and penalty functions (eyan and Vanhoucke, 2016). Because of the unique nature of the cash flow and the periodicity of profits in software projects, these prior studies are not applicable to the payent conditions of software outsourcing projects, since they focus on general engineering projects. Moreover, these studies rarely considered the liits of the total aount of capital. The cash flow of software projects differs fro that of general engineering projects in specific ways (Gorla and Soers, 2014). First, the contractor in a software project includes the expenditure incurred during project developent as well as the operational and aintenance expenses of the software systes. Second, the s 216

2 can obtain profits only after the delivery and operation of the software, and they receive profits periodically. Finally, the payent scheduling arrangeent of software projects usually involves certain capital constraints. This study exaines the payent scheduling proble of software projects (SPPSP) under certain capital constraints. A atheatic odel for this issue is constructed with the ai of axiize profits fro the individual perspectives of the contractor and the and fro a joint perspective. The operational and aintenance expenses concerning the contractor s profitsare includedin the odel.in the eantie, the s profits fro different periods arealso calculated with respect to a reference point according to the tie cost of capital, in order to reflect the characteristics related to the s profits and tiing in software projects. In addition, a corresponding heuristic siulated annealingalgorith is designed to solve the odel. Finally, the research findings are explained with a case study. 2. RESEARCH FRAMEWORK 2.1. Basic Research Assuptions The research ethod adopted in this study is based on activity. That is, the project was explained using an activity-on-arc (AOA) network. The arrow represents the activity, while the node represents the event. The basic assuptions of this study are as follows: 1) The graph of the project activity network can be drawn accurately. 2) The schedule and expenses of the software project activities are known and certain; there is a deadline agreed on by both parties. 3) The aount to be paid is decided through negotiations when the contract is signed by both parties. 4) The project payent is based on ilestone events. If the project contains l ilestone events, a part of the project payent has to be paid after a ilestone event is copleted. 5) The s profits are received in installents after the delivery of the software. This aount of cash flow can be discounted until the copletion of the project through the cash flow within the operation period of the software after its operation begins. 6) The aount of every installent of payent is calculated according to specific ratios of the contractor s accuulative earned value. 7) The contractor can put in different degrees of effort q. Tiing and costs are different under different degrees of effort q Seiotic Definitions and Definitions of SPPSP In a certain software project, the nuber of activities, events, and ilestones are assued to be N, M and, respectively. The ain seiotic definitions adopted in this study are as follows: ES : the earliest tie that event starts S : the latest tie that event starts η: distribution ratio of the activity s expenses between the start and the end of the activity d ij : duration of project activities (i,j) U: total payent of the project contract D 1 : project deadline D 2 : software usage period t: variable during the period of project execution (t = 0,1,,D 1 ) τ: variable during the period of software usage ( τ=1,,d 2 ) B τ : s profit in the τthinstallent (τ = 1,,D 2 ) C τ : s aintenance expenses in the τthinstallent The expense of event n is c n. Therefore, c the expense required to coplete event is expressed as: (1) c c q (1 ) c n nq nn 1 nn 2 N 1 adopts event as the start of the activity, while N 2 adopts event as the end of the activity. c nq is the expense related to the degree of effort put in by the contractor for qaount of tie. ω n is the earned value of event n. Therefore, ω, the earned value of event, is: n (2) nn2 y t is the 0-1 variable of whether event takes placeduring period t. x is the 0-1 variable of whether the payent of event is ade. P k (k=1,2,,k ) represents the aount paid at the kth installent of payent. B τ represents the s profits during the τ th period.both parties pursue the payent scheduling for project profit 217

3 axiization, which is represented by *={T*,P*}, where P*is the set of the best payent aounts P*={p k ; k=1,2,,k}while T* is the set of the tie intervals over which the event takes place T* { t, y 1; 1,2,, M}. t 3. CONSTRUCTION OF SPPSP OPTIMIZATION MODE 3.1.Contractor s SPPSP Optiization Model During the execution of the software project, it is assued that the has to ake Knuber of payents to the contractor(k=+1), with one payent ade at the start of the project, and the rest of the payents ade at each ilestone event. Assuing the profit after period tis discounted to the profit at the start of the project as exp( t) (1 ) t, where is the discounted rate during the execution phase of the project. Fro the perspective of the contractor, an optiization odel of SPPSP can be constructed as: ax NPV p (exp( t) y x ) c [exp( t) y ] (3) provider K M S M k t t k 1 1 t ES 1 t ES S s.t. y 1 1,2,, M, (4) t ES t M 1 S x K (5) v w y t d y t v 1,, M 1; w 2,, M (6) vt vw wt tev tew x K T M T ( p x y )) y T 1,2,, D (7) k t t k 1 t0 1 t0 K k 1 p U k 1,2,, K (8) k 1 l or 1 0 else (9) 1 yt 1 or 0 (10) The target function in equation (3) is the axiized NPV of the contractor s cash flow; the constraint conditional in equation (4) ensures that event takes place within the tie window [E, ]; the constraint in equation (5) represents K, the nuber of payents; equation (6) refers to the precedence constraint relationship between the start and the end of the event in event (v,w). Equation (7) is the constraint of the payent aount. The aount of payent does not exceed a ratio β (0 β 1+π) of the accuulative value earned by the contractor during the period T, π being the contractor s arginal value. Equation (8) ensures that the su of the total payent corresponds to the total aount of payent designated in the project contract. Equation (9) represents that payent was ade at the start of the project and at each ilestone event Client s SPPSP optiization odel The s involveent is periodic as his/her payent to the contractor is ade over ultiple instances during the execution of the project. His/her profit can be obtained only after the delivery and start of operation of the software. Moreover, the s profit is captured not at one go but gradually during the usage period of the software. In other words, the s profit is periodic. The expenditure related to the operation and the aintenance fee of the syste need to be included in the odel. The s profit and costs at the τ th period are discounted to the reference point (t = 0) according to the tie value of the capital: exp( ) (1 ), where μis the annual discount rate. An SPPSP optiization odel was constructed fro s perspective: D2 K M S 1 k t 1 k 1 1 tes ax NPV [ ( B C )(exp( )]exp( D ) p (exp( t) y x ) (11) K T M T s.t. ( pk x yt )) yt T 1,2,, D (12) 1 k 1 t0 1 t0 218

4 D2 1 The target function in equation (11) is the axiized NPV of the s cash flow. In equation (11), ( B C )(exp( ) represents the profit discounted at each period until the payent oent (τ = 1) when the project is copleted. Multiplying it by exp( D1 ) would discount the profit to the starting oent (t = 0) of the project. The constraint in equation (12) ensures that the payent aount is not lower than a fixed ratio βof the contractor s accuulative earned value. The other constraint conditions are the sae as those in the SPPSP odel fro the contractor s perspective Integrated SPPSP Model The preferences of the and the contractor with regard to payent scheduling are different. Under the fixed condition of the total value of the contract, the contractor can gain a higher NPV and obtain extra profits fro early payents if each payent tie is as early as possible, and the payent aount at the early stages is larger.on the other hand, if each payent tie is arranged at a later stage, and the payent aount at the later stages is larger, the would gain a larger profit. Therefore, research on this issue fro the joint perspective of both parties is essential to arrive at a payent scheduling arrangeent that is utually agreeable. The jointly integrated SPPSP optiization odel is expressed as: ax NPV NPV NPV pc provider D2 M S t ES [ ( B C )(exp( )]exp( D ) c [exp( t) y ] S t (13) s.t. y 1 1,2,, M, (14) t ES t v w y t d y t v 1,, M 1; w 2,, M (15) vt vw wt tev tew The constraint condition of this odel is the sae as the constraint in equation (3), and constraint condition (7) is adopted in this odel. 4. HEURISTIC SIMUATED ANNEAING AGORITHM FOR SPPSP MODE The PPSP was proven to be an NP-hard proble; the SPPSP odel shows that it involves a ixedinteger nonlinear prograing issue, which is also an NP-hard proble. In the SPPSP, the set of payent events, i.e., which payents are ade at the starting event and at the ilestone event, is known. As long as the event schedule T* and the payent aount P*are known, the payent scheduling *={T*,P*}can be certain. Based on the characteristics of the SPPSP, the optial scheduling arrangeent [12, 13] for a software project with different payent events was calculated using the heuristic siulated annealing algorith. The steps of the algorith are as follows: Step 1: Ascertain the initial solution T 0. Without violating the precedence relationship constraint as a precondition, arrange a realization tie at rando within the tie window during each event to arrive at a realization tie vector T of an event. If the realization tie of ending event in T is no later than the project deadline D 1, T is accepted as the plausible realization tie vector T 0 of the initial event. Repeat this step until a plausible T 0 is obtained. Calculate P 0 and project profit NPV 0. Step 2: The initial teperature is t = Tep 0. The ending teperature is Tep f. The cooling speed is μ(0<μ<1). The search precision is ξ. Because of the length of the Markov chain, = 10 N (N is the nuber of events in the project). Step 3: T0 is derived using the neighbor point T1. Excluding the starting event, an event is selected at rando fro the rest of the events. Ensuring the satisfaction of the network precedence relationship as a precondition, a unit is altered at rando within the tie window of the realization tie of the event. Whether the realization tie of the ending event exceeds the deadline of the project is exained. If not, a feasible neighbor point T1 of the present T0 is obtained. Otherwise, the operation is repeated until a feasible T1 is obtained. The NPV is included in the calculation of T1. Step 4: If ΔNPV = NPV1-NPV0 > 0, the neighbor point is the present solution: T0 T1,NPV0 NPV1. Otherwise, a rando nuber R is derived between [0,1]. If R eδnpv/t, the neighbor point is accepted as the present solution: T0 T1,NPV0 NPV1. Otherwise, T1 is rejected. 219

5 Step 5: The revised teperature is Tep1 μtep0. If Tep1 > Tepf is satisfied, return to Step 3. If the condition is not et, the search process is stopped. Step 6: The final results T0 and NPV0 are produced as the search output. The search process coes to an end. 5. CASE ANAYSIS 5.1.Project Paraeters Figure 1 depicts the AoA network for a software project that coprises 16 events and 20 activities. The nuber on each arc represents the serial nuber of the activity. This study used the case of a hypothetical project to validate the proposed odel. In this hypothetical case, an enterprise is set to invest 3 illion dollars for the construction of an enterprise resource planning (ERP) syste; 5% of the aount is pre-payent that is to be settled upfront. After the planning and preliinary design stage, the syste is expected to be operational in 80 weeks. Considering that the ERP syste will be in operation for 5 years, the cash flow aounts of the profit and expenditure (operational and aintenance fee) each year after the syste starts operation are shown in Table Figure 1. Network of software project Table 1. Cash flow aount of the profit and expenditure of the ERP project of an enterprise Tie τ(year) Profit Bτ (in $10,000) Expenditure Cτ(in $10,000) The distribution ratio η of the activity expenses fro the start to the end of the event is 0.5. β = 85%. The discount rate α is 0.032%, which was the weekly interest rate of Bank at the tie. The discount rate μ is 5.94%, which was the annual interest rate of borrowing of the bank at the tie. The 's payent to the contractor is ade in five installents. The calculation results in Table 2 show the earned values of each activity, the work period, and the costs. Table 2. Earned value, work period, and cost of each activity of ERP project Earned value Work period Cost Earned value Work period Cost Activity n Activity n (in $10,000) (week) (in $10,000) (in $10,000) (week) (in $10,000) Results The tie window [E, ] in which each event takes place was calculated using the known data in Table 2, and the costs of each event (c ) and the earned value (ω ) were calculated using equations (1) (2). Five ilestones were set for the project, and payents were ade at each of the ilestone events. The prepaid aount of 5% was paid at the start of the project; therefore, only 95% of the contract price (2.85 illion dollars) was paid at the five ilestone events. The optial payent scheduling *={T*,P*} fro the different 220

6 perspectives and at the different ilestone events (the sets of ilestone events are {2,6,11,15,16}and {3,9,12,14,16}) are listed in Table 3. Table 3. Optial payent scheduling fro different perspectives Payent event set 2,6,11,15,16 3,9,12,14,16 Perspective Optial payent scheduling NPV provide NPV NPV PC contractor Joint contractor Joint P*={12.92,109.16,59.93,48.45,54.55} T*={0,8,20,36,36,36,36,26,46,36, 54,61,75,69,77,80} P*={12.92,62.82,92.58,62.14,5} T*={0,8,20,40,40,36,42,26,46,65,54,61,75,69,77,80} P*={12.92,62.82,92.58,62.14,5} T*={0,8,20,40,40,36,42,26,46,65,54,61,75,69,77,80} P*={43.27,102.53,65.71,23.29,50.21} T*={0,8,20,36,36,36,36,26,46,36,54,61,75,69,77,80} P*={32.81,99.3,65.71,32.64,54.55} T*={0,8,20,45,40,36,42,26,46,65,54,61,69,69,77,80} P*={12.92,62.82,92.58,62.14,5} T*={0,8,20,40,40,36,42,26,46,65,54,61,75,69,77,80} Analysis The results presented in Table 3 indicate significant differences between the contractor's and the 's net cash flow and desirable payent scheduling. In this exaple, the contractor's axiized profit is NPV prov = 14.71, and the 's profit is the lowest (NPV = 73.05). In contrast, later payent points and larger aounts of payent at later payent events would lead to greater profits for the. When the 's axiized profit value is 76.37, the profit of the contractor is lower (12.04). Thus, the following conclusion could be drawn: under the condition of fixed payent aounts and payent points (ilestone events), the profits of both outsourcing parties are related to the payent point and the payent aount. Regarding the arrangeent of the payent aount, the contractor usually prefers the earliest possible payent tie and hopes to settle larger aounts of payent at an earlier payent points. Hence, if the ai is to axiize the contractor's profit, the contractor should consider reducing the project costs as the higher priority. If the ai is to axiize the 's profit, the should consider obtaining greater than expected profit at the end of the project as early as possible to be a high priority and reducing project costs as a low priority. Therefore, when deciding the payent scheduling for software projects, both outsourcing parties should balance each other s profits and deterine a utually agreeable payent schedule. 6. CONCUSION This study exained the optiization of payent scheduling in the context of software projects. Under certain capital constraints, optiization odels for payent scheduling related software outsourcing projects were constructed fro the perspectives of the and the contractor in the project, and fro the joint perspective. The proposed odels included the unique characteristics of the payent events and the cash flow of a software project. By using the event-based ethod, Profit axiization odels were constructed fro the perspectives of the contractor and the. Additionally, a profit axiization odel fro the joint perspective of both parties was constructed to balance the profits of the two parties. The proposed odels reflect the characteristics of software project payent. Based on the characteristics of the proposed odels, a heuristic siulated annealing algorith was designed to solve the odels. Finally, the payent fro three perspectives was calculated using a hypothetical case study to obtain the optial payent scheduling. The results of the calculation showed that the optial payent stages vary depending on the different perspectives. For instance, the optial payent schedule for a contractor is the exact opposite of the optial payent schedule for a. This study indicates that describing the contractor's profit using the net cash flow can accurately reflect the real profits of the contractor, the, and both parties together. Both the parties involved in software outsourcing could use this odel to select appropriate strategies for negotiations during the contract signing stage. It should be noted that the study in this paper is based on the assuption that the event occurrence ties can be arranged without considering resource constraints. However, this is not the case in any practical circustances where the resource availability for the contractor is liited. Therefore, SPPSP under resource constraints ay be a worthwhile proble for further investigation in this direction. Acknowledgeent This work was supported by the national fund of social science(10cg005). 221

7 REFERENCES Bahrai F., and Moslehi G.(2013)"Study of payent scheduling proble to achieve contractor agreeent", The International Journal of Advanced Manufacturing Technology, 64 (1-4),pp Gorla N., and Soers T. M.(2014)"The ipact of IT outsourcing on inforation systes success", Inforation & Manageent, 51 (3),pp He Z., Wang N., and i P.(2014)"Siulated annealing for financing cost distribution based project payent scheduling fro a joint perspective", Annals of Operations Research, 213 (1),pp Jorgensen M.(2014)"Failure factors of sall software projects at a global outsourcing arketplace", Journal of Systes and Software, 92,pp Ki J., and Jr. Ellis R. D.(2010)"Coparing Schedule Generation Schees in Resource-Constrained Project Scheduling Using Elitist Genetic Algorith", Journal of Construction Engineering and Manageent- ASCE, 136 (2),pp Kone O., Artigues C., opez P., and Mongeau M.(2011)"Event-based MIP odels for resource-constrained project scheduling probles", Coputers & Operations Research, 38 (1SI),pp Kopanos G. M., Kyriakidis T. S., and Georgiadis M. C.(2014)"New continuous-tie and discrete-tie atheatical forulations for resource-constrained project scheduling probles", Coputetrs & Cheical Engineering, 68,pp eyan P., and Vanhoucke M.(2015)"A new scheduling technique for the resource-constrained project scheduling proble with discounted cash flows", International Journal of Production Rearch, 53 (9),pp eyan P., and Vanhoucke M.(2016)"Payent odels and net present value optiization for resourceconstrained project scheduling", Coputers & Industrial Engineering, 91,pp Paraskevopoulos D. C., Tarantilis C. D., and Ioannou G.(2012)"Solving project scheduling probles with resource constraints via an event list-based evolutionary algorith", Expert Systes with aapplications, 39 (4),pp Sobel M. J., Szerekovsky J. G., and Tilson V.(2009)"Scheduling projects with stochastic activity duration to axiize expected net present value", European Journal of Operational Research, 198 (3),pp Vorontsova A., and Rusu.(2014)"Deterinants of IT Outsourcing Relationships: A Recipient Provider Perspective", Procedia Technology, 16,pp Waligora G.(2014)"Discrete-continuous project scheduling with discounted cash inflows and various payent odels-a review of recent results", Annals of Operations Research, 213 (1),pp Wieseann W., Kuhn D., and Ruste B.(2010)"Maxiizing the net present value of a project under uncertainty", European Journal of Operational Research, 202 (2),pp