Getting out of a (strawberry) jam: An Introduction to Supply Chain Analysis

Transcription

1 Getting out of a (strawberry) jam: An Introduction to Supply Chain Analysis Heng-Soon Gan Melbourne Operations Research The University of Melbourne VIC 3010, Australia h.gan@ms.unimelb.edu.au Kwanniti Khammuang Department of Mechanical and Manufacturing Engineering The University of Melbourne VIC 3010, Australia kwanniti@unimelb.edu.au Andrew Wirth Department of Mechanical and Manufacturing Engineering The University of Melbourne VIC 3010, Australia wirtha@unimelb.edu.au Abstract In order to illustrate how various areas of operations research interact in an actual manufacturing scenario, we propose the use of a strawberry jam-making supply chain model consisting of an inventory partner, a production scheduling partner and a delivery partner. The problem is to minimise the overall supply chain cost consisting of inventory order cost, inventory unit purchasing cost, inventory storage cost, transport booking cost, jam storage cost, delivery travel distance cost and jam arrival earliness and tardiness costs. We report on how we devised and taught this case to First Year Mechanical and Manufacturing Engineering students at the University of Melbourne. 1. Introduction For many years students enrolled in the first year engineering subject, Introduction to Design and Manufacture, at the Department of Mechanical and Manufacturing Engineering, University of Melbourne, were required to undertake a six-week long project. As part of a continuing effort to introduce and promote operations research among first year students with no prior knowledge of OR, we devised a project, for thirty students, based on a supply chain problem. We chose this problem for the following reasons: A supply chain problem can be structured to encompass various operations research models, and hence is able to give a general overview of OR.

2 A supply chain model illustrates how various operations research problems, which are often dealt with individually, even in a widely used operations research text such as Winston (2004), interact and thus provides a broader and a more realistic picture of a production system. With a supply chain model, we can emphasize and demonstrate that optimising each of the supply chain s sub-problems independently may lead to sub-optimal solutions. We note that recently Keller and Kros [INFORMS Transactions on Education 4(2) 2004] and Koksalan and Salman [INFORMS Transactions on Education 4(1) 2003] both reported on the success of teaching operations research using case studies. Given the near universal appeal of the product we decided to set the scene in a strawberry jam-making business. We now proceed to describe the strawberry supply chain. 2. The Supply Chain Problem For this project, students are required to create an initial off-line plan, to be deployed at time T, for the following jam-making supply chain model. An initial offline plan is a plan created in advance to enable the execution of the following activities that ensure the functionality of the supply chain: Fresh strawberry ordering: The strawberry supplier requires that the orders for the amount of fresh strawberries be placed well in advance, say at time T order << T, to facilitate the planning of activities such as strawberry planting, harvesting, packing and delivery and also to ensure the freshness of the strawberries delivered. Jam-making resource planning: The jam-making company wants to ensure that there are sufficient resources, such as utensils, cookware, bottles, refrigerators and freezers, to cope with demand before the initial off-line plan is executed. It is assumed that the jam is made to order. Figure 1 shows the supply chain model used. It consists of the following partners: Customers: The sales department will request that orders from their customers be placed well in advance, say at T request < T order, to acquire some information for the initial off-line planning activity. At time T request, these orders can only be estimates since customers may not know the exact number of bottles of jam needed. Thus, each customer will specify o the minimum and maximum number of bottles of jam required, o the strawberry grade, and o a date, relative to T, on which they expect to receive their orders (the specified due date). At time T, customers will then inform the sales department of the exact order amounts.

3 amount of fresh strawberries, order dates Strawberry supplier fresh strawberries demand amount, strawberry grade, due date Fresh strawberry inventory fresh strawberries Sales Department demand amount, strawberry grade, due date Strawberry jam making strawberry jam Customers strawberry jam Strawberry jam delivery Figure 1: The strawberry jam-making supply chain. Sales Department: The sales department will convey order information placed by customers to the inventory department at times T request and T. Inventory department: Between times T request and T order, the inventory department has to decide on an order quantity, B i, bounded by the minimum and maximum order amounts, for each customer i, so that orders for fresh strawberries can be placed with the strawberry supplier. With this decision, the inventory department will schedule the orders, that is, determine the date on which they expect to receive the fresh strawberries. The costs involved are ordering and unit purchase costs. This inventory schedule will be sent to the strawberry supplier. At time T, when each customer i has decided on an exact order quantity, say E i, any excess orders (E i > B i ) with respect to B i will be treated as a loss in sales and any shortfall in demand (E i < B i ), will be treated as wasted excess strawberries. Strawberry supplier: The strawberry supplier has set limits on the following: o each grade of strawberries ordered per day, and o the total amount of strawberries (sum over all grades of strawberries) ordered per day. There is a delivery lead time involved for each order placed. Based on the inventory schedule provided by the inventory department, the date for each order will be adjusted according to the corresponding lead time involved. This adjustment will generate a more useful schedule for the strawberry supplier, so that planning for activities such as strawberry planting, harvesting, packing and delivery can be made.

4 Production department: This department is responsible for creating a jammaking schedule between times T order and T. The company has four jam-making machines that can be operated in parallel. Each customer s order is treated as a separate job and will not be combined with other orders to form batches. We assume that setup times are negligible and that for each customer, the duration of the job (the jam-making process) is proportional to their order amount. Between times T order and T, the order amount to be produced for each customer i is B i. No jobs can be unnecessarily delayed and once a job has started, it will continue its processing on the same machine until its completion. No job can start before the arrival of the fresh strawberries. If a job does not start at the arrival time of its corresponding fresh strawberries delivery, a storage cost will be incurred, which is proportional to the number of days in storage. At time T, when each customer i has decided on an exact order quantity, E i, the job for each customer i will be updated to min(b i, E i ) and the schedule will be shifted, that is, the job start times will be updated so that no jobs are unnecessarily delayed. Delivery department: The company has only one delivery truck. The delivery department is responsible for generating a delivery plan, that is, determining when the delivery truck picks up the jams and for each pickup, in what sequence the truck should visit the locations. For each pickup the delivery truck makes, an initial pickup cost will be incurred and the travel cost is taken to be proportional to the total travel distance for the pickup. If the jams for any customer are not picked up immediately, a jam storage cost will be incurred, which is proportional to the total storage time. To assess how good an initial offline plan is, the following costs are embedded in the objective function of the supply chain model: fresh strawberry order cost fresh strawberry unit purchasing cost fresh strawberry storage cost fresh excess strawberry wastage cost loss in sales cost delivery truck initial pickup cost delivery truck total travel distance cost jam storage cost earliness or tardiness (relative to the customer s specified due date) cost 3. Teaching Objectives We aim to introduce and promote operations research, an area of study widely regarded among students as challenging, via a supply chain model. In particular, we intend to bring the following points to the students attention during the course of the project:

5 Introduction to operations research problems. Three important areas of operations research (the supply chain s sub-problems), namely inventory control and management, production scheduling and vehicle routing, are introduced in this project. By concentrating on just three sub-problems we, on the one hand, reflect on the complexity of real-world problems, while on the other hand keep the problem sufficiently simple to allow beginners to provide reasonable solutions. Introduction to the basic supply chain structure. A supply chain can be perceived as providing a holistic view of operations research. A supply chain consists of partners interacting with each other. We demonstrate this fact through the three sub-problems mentioned above, by emphasizing the need for information flow between chain partners. Hands-on experience in supply chain optimization. We provide numerical details to the supply chain problem so that students can see the results of their proposed solutions. Students are encouraged to unravel the structure of the problem and propose intuitive (feasible) solutions, instead of using wellestablished mathematical and search techniques. Identification of missing information. We deliberately left out some important information relevant to the supply chain problem. This was done to a real-world scenario where some important information may not always be available to the planner. Students were supplied with the information upon recognizing a need for it. Hints are provided along the way to assist students in identifying the missing information. Occurrence of uncertainties in practical problems. We have introduced uncertainty to the problem by expressing the initial demand by its minimum and maximum value. Students have to decide on a single value for the order size, so that orders for raw materials can be placed. The real demands were determined after the orders are placed. Introduction to optimization techniques. At the end of the project, an introductory lecture was given to highlight the various optimization techniques most commonly used and bring to the students attention the possible applications of these techniques to this supply chain problem. 4. Teaching Program The six-week long project was structured as follows: Week 1: Students are to familiarize themselves with the supply chain, for example the flow of information within the supply chain, the costs involved for each supply chain partner and the overall supply chain cost. Tasks should be delegated among group members. Week 2: Each group is expected to propose solution procedures to each of the supply chain partners using sample data (generated by each group). Week 3: Given a set of initial supply chain data, each group is required to generate an initial plan according to the solution procedures proposed in Week 2.

6 Week 4: A set of perturbations is introduced to the supply chain. Students are to provide a re-active solution in response to the perturbation and evaluate the total supply chain cost of the new plan. Week 5: Each group is required to present their results and findings from previous weeks. Week 6: Supervisors will conclude this week by attempting to answer an important question in planning under uncertainty: What should have been done if information about the perturbations had been known a priori? Supervisors will discuss the method of deterministic planning, robust planning and on-line planning. Proactive and reactive methods of planning under uncertainty will also be discussed. 5. Teaching Tools We provided the students with the following documents to describe the requirements of the project: Company Background Sheet: This document contains a full description of the supply chain problem and suggestions about useful tools and graphical representations that could aid the solution-seeking process. Task Sheet: The teaching program is documented here. Report Sheet: This document outlines the contents of the group report to be submitted on a weekly basis. Data Sheet: Data for the supply chain problem is documented here. The perturbed data will only be distributed to the students during Week 4 of the project. To assist our presentation in Week 6, we designed and developed the following tools: Presentation slides: The presentation is divided into two parts. The first part of the presentation encompasses different optimisation techniques and discusses computational intractability. The second part of the presentation describes the formulation of a mixed-integer program for the supply chain problem, illustrates a spreadsheet-based supply chain optimiser (heuristics are used here), introduces the idea of robust planning and examines various methods to hedge against uncertainty in the supply chain problem described in this paper. Supply chain spreadsheet: A MS Excel workbook is used as an input-output interface for the supply chain problem. Heuristics for the inventory control, production scheduling and vehicle routing problems were written with Visual Basic for Applications (VBA). Users will need to run the heuristics sequentially (starting with inventory control, production scheduling and finally vehicle routing) and the total supply chain cost will be evaluated upon completion of the vehicle routing heuristic. Mathematical program formulation: A mathematical program has been formulated and coded in LINGO (with an MS Excel interface). Since the problem is a generalization of a travelling salesperson problem, we do not intend to solve

7 it optimally. The purpose of this formulation and coding is to demonstrate the possibility of solving optimization problems with commercially available optimisers. 6. Student Grouping Grouping of students is an important factor for achieving our teaching objectives. Each group consists of three or four students. We experimented with two different groupings. These groupings can be distinguished based on the activities and communication methods used. In the first type of grouping, MYOPIC, each group represents a partner in the supply chain. The groups interact with each other by passing on information to their immediate supply chain successor. Each group, given the information, attempts to minimize their department costs myopically. We also experimented with another student grouping, GLOBAL, where each group is assigned to manage the whole supply chain, in contrast to the grouping suggested above. We allow students to decide on the allocation of work in their own group. For instance, each member of the group may assume the role of a supply chain partner. Our experience with these grouping methods revealed the following: Group members in MYOPIC will be idle much of the time due to the dependency of their input information to the problem on their upstream partners. Whereas group members in GLOBAL will be active most of the time. Individual interviews with students disclose that they are in favour of GLOBAL from this viewpoint. MYOPIC group members can only gain insight in their specific part of the supply chain. On the contrary, GLOBAL group members have the flexibility to look at the supply chain problem holistically. MYOPIC mimics a real life supply chain scenario whereby each partner attempts to selfishly maximise their own benefit. On the other hand, GLOBAL reflects an idealised supply chain where the global benefit is preferred to a local one. 7. Student Responses and Feedback As mentioned earlier, we strongly encourage students to propose solutions based on their intuition and level of understanding of the supply chain problem. We have collated interesting responses, via conversations with students, as listed below: Recall that between times T request and T order, the inventory department has to decide on an order quantity, B i, bounded by the minimum (L i ) and maximum (U i ) order amounts, for each customer i. At time T, when each customer i has decided on an exact order quantity, E i, any excess orders (E i > B i ) with respect to B i are considered a loss in sales and any shortfall in demand (E i < B i ), is regarded as waste. Students used one or more of the following quantities to determine the order quantity B i : 1. The minimum order amount, L i.

8 2. The maximum order amount, U i. 3. The average of the L i and U i, that is, (L i + U i )/2. 4. The weighted average given by (LS*U i + WS*L i )/(LS + WS), where LS is the unit cost due to loss in sales and WS is the unit cost attributed to wasted strawberries. During the initial phase of this project, almost all the students made wild guesses for B i. Quantities (1) and (2) were the most popular. However, with our guidance, they eventually recognised that these quantities either maximize the loss in sales or the wastage costs. Their immediate response to this is to use quantity (3). Some groups invested more time on this issue ultimately came up with quantity (4), which is a better estimate for B i, since it risk-adversely minimises either the loss in sales or wastage costs. For the inventory partner, we noticed that students generally placed orders as close as possible to the order limit, with the intention of minimizing the order cost and reaping the benefit of bulk ordering. We observed students using the following methodologies to determine the raw strawberry ordering dates: o One method is to subtract the lead-time and the processing time from the due date (the date on which customers expect to receive their jam). The processing time of each order is estimated from its corresponding jam order amount, assuming processing starts as early as possible. This method is too optimistic, since there are insufficient resources to produce all the jam at once. Also, the delivery time is not taken into consideration. o Another method considered is generally similar to the one described above, except that the processing time of the jam is assumed to be a fixed value for all customers. The fixed value is taken to be the largest processing time of all orders. Students generally came up with the following rule to determine the jam-making schedule: Orders will be processed on the first available machine, in order of increasing raw strawberry arrival dates. For orders with identical arrival dates, priority will be given to the order with the earliest due date. If the all arrival and due dates are similar, ties are broken arbitrarily. This scheduling rule is intuitive and (locally) effective, since it minimizes the raw strawberry storage costs. For the vehicle routing sub-problem, there is a balance between the jam storage cost, pickup cost and the earliness and tardiness cost. The following responses were observed: o Order delivery grouping: The strawberry jams will be delivered as soon as they are ready. The students argued that since the daily cost of jam storage is significantly larger than the pickup cost, for most orders, bulk delivery is not beneficial in this setting. Another rule used by students is to perform a delivery when there are at least k orders ready to be delivered. Although this rule will generally decrease the pickup cost and distance cost due to travelling to-and-fro the delivery depot, we will see an increase in the jam storage cost.

9 Some groups proposed that only one delivery should be made. In this case, any jams that are ready on an earlier date would have to wait until the last batch of jams is ready before it can be delivered. Obviously, this rule will incur very high storage and tardiness costs, despite minimal pickup and to-and-fro delivery depot travel distance cost. o Routing: For groups that suggested relatively small delivery groupings, a complete enumeration method was used to determine the route with minimal distance and earliness and tardiness costs. Some groups randomly generated a set of routes and selected the best (with respect distance and earliness and tardiness costs) within the set. Some groups enthusiastically developed spreadsheets and computer programs to ease the computation of their solutions. Note that we hinted to the students of this possibility but we did not expect any implementation from them since computer knowledge is not a pre-requisite for this subject. Therefore we were suitably impressed with their efforts. Based on this response, we strongly infer that students enjoy the problem and its level of difficulty. The students obviously realized that manual computation of the solutions is slow and other methods would allow a larger range of solutions to be explored, within a reasonable time. Students generally agree that the project provided them with useful and valuable insights into supply chain management and optimization. They experienced the enormity and complexity of the supply chain problem, despite the simplifications made to the sub-problems. More importantly, they felt that their hands-on experience gained through this project has positively assisted the development of their problem solving and analytical skills. However, most students wished that more time were allocated for this project due to the extent of the problem. 8. Possible Extensions The supply chain problem can be customized, without exhaustive modifications, to achieve teaching objectives for different categories of students. We suggest the following: Beginners: We assume that students belonging to this category have no prior knowledge of operations research and optimisation techniques. The structure of the supply chain problem outlined in this paper, whereby intuitive solutions are expected and sub-problems are clearly defined, suits this category. Intermediate: Students in this category, typically final year engineering and operations research undergraduates or MBA students, are assumed to have basic knowledge of mathematical programming. To cater for their needs, the supply chain problem can be presented as described in this paper. However, students are required to a devise separate mathematical program for each sub-problem, by ignoring their information dependency. To demonstrate the main characteristics of a supply chain, students are then required to account for the

10 information dependency and suggest heuristics, for example greedy heuristics, to solve for the problem. Advanced: Advanced students are assumed to be familiar with mathematical programming, possess knowledge of search techniques and to some extent, have been exposed to various areas and applications of operations research. Students undertaking a master degree in operations research or industrial engineering fall in this category. The problem presented to this category of students should be restructured in a form of a case study, where sub-problems are not distinctly defined. Firstly, students in this category are expected to model this problem mathematically. Then, they will design, implement and compare various heuristics and search techniques and finally provide discussions of their results. Suggestions for possible extensions and improvements to the solution procedures proposed are required. Students could also build a simulation model to test for the robustness of their plans to disruptions and uncertainties. Another possible extension to our supply chain problem is to embed real-time disruptions, which will then require students to implement reactive procedures. To enable students to acquire hands-on experience in designing and executing reactive procedures when disruptions occurs in the supply chain, a simulation model can be constructed to better capture the nature of the perturbations. The simulation model will run and pause at every disruption, allowing the student to decide on the action to be taken. The simulation will continue when an action is invoked. 9. Summary We have proposed the use of a simplified supply chain model to introduce and promote operations research among students with no prior knowledge of the field. The supply chain problem presented here can be easily extended to cater for more technically advanced students. Student feedback indicates that the problem presented was challenging and solving it has improved their analytical skills. They have, all in all, enjoyed the project. References Keller, C.M. and J.F. Kros, (2004), "VA-TX Investment Corporation: Credit Card Division," INFORMS Transactions on Education, Vol. 4, No 2, Koksalan, M. and F.S. Salman (2003), Beer in the Classroom: A Case Study of Location and Distribution Decisions, INFORMS Transactions on Education, Vol. 4, No 1, Winston, W. L. (2004), Operations Research Applications and Algorithms, 4 th edition, Duxbury, Belmont, CA.