35E00100 Service Operations and Strategy #6 Fall 2015 Dynamic Lot Sizing 35E00100 Service Operations and Strategy #6 Fall 2015

Topics Demand management Lot sizing policies Order management Key points Useful material: Hopp, W. & Spearman, M. (2000), Factory Physics, Chapter 2.1-2.4 and 3.1.6 Nahmias, S. (2002) “Alternative Lot Sizing Schemes” Ch 7.2 in Production and Operations Analysis Vollmann, T., W. Berry & C. Whybark (1997) “McLaren’s Order Moment” in Manufacturing Planning and Control Systems

Demand management is a part of the MPC system! MPC boundary Resource planning Production planning Demand management Marketplace (customers and other demand sources) Master production scheduling Front end Engine Back end Vollmann et al. 1997, 313

Need for capacity management depends on the market situation Sales forecasts FGI and Backlog Define production plan rates Business plan Orders Master schedule rough cut Approvals Master schedule Vollmann et al. 1997

Capacity and Demand Control Tools Ways to manage capacity “Stretch” production capacity Speed up the process Schedule downtime (e.g. maintenance) during periods of low demand Squeeze more people in or rent / share extra facilities equipment Workforce management Employ part-timers, seasonal workers, flexible work force Cross-train employees Prepare intelligent schedules for both workers and equipment Strategies for managing demand Organize better Avoid needless division of work (finance, customer service, transport planning, etc.) Design rules and procedures for providing flexibility Manage service levels Adjust delivery promises continuously Utilize different pricing methods Communicate capabilities

Lot Sizing Schemes

Comparison of Lot Sizing Policies Example 1 Comparison of Lot Sizing Policies A component used in a manufacturing facility is ordered from an outside supplier. Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks is: Cost per component is 0.65. The interest rate used to compute holding costs is 0.5 % per week. The fixed ordering cost is estimated to be 200. What ordering policy you recommend and why? Which method would result in the lowest-cost policy for this problem?

Lot for Lot Ordering Basic principle of LFL Production quantity = time-phased net requirements No inventory carried from one period to another Normal assumption in MRP examples For convenience and ease of use Rarely the optimal production rule e.g. Hopp and Spearman 2000, 125

Economic Order Quantity (EOQ) The principle Production quantity = EOQ quantity Information required Fixed setup/ ordering cost A Holding cost h Demand rate D Shortcomings are due to the assumptions of the modell Instantaneous production Immediate delivery Deterministic and constant demand over time Fixed setup cost Products can be analyzed individually e.g. Hopp and Spearman 2000, 49-56

Periodic Order Quantity (POQ) The principle Calculate the time between orders (TBO) using EOQ formula TBO = EOQ / D TBO (rounded to closest integer) shows for how many periods products should be produced or ordered. Fixed order period (FOP) is a similar method. Periods with no demand are skipped. e.g. Hopp and Spearman 2000, 126-127

Part Period Balancing (PPB) The principle Definition of a part-period [# of parts in a lot] * [# of period they are carried in inventory] Combines the procedure of Wagner-Whitin with the mechanics of the EOQ Set the order horizon equal to the number of periods that most closely matches the total holding cost with the set-up cost over that period Steps of the procedure Calculate holding costs per different number of periods Compare when holding cost is closest to set-up costs Stop and repeat e.g. Hopp and Spearman 2000, 127-128

McLaren’s Order Moment (MOM) The principle Evaluates the set-up cost for an integral number of future periods Applies part period (=an unit of inventory carried for one period) accumulation principle directly Lot size is determined by matching the number of accumulated part periods to the number that would be incurred if an order for an EOQ were placed under conditions of constant demand Calculate order moment target (OMT) Two tests are used Tentatively order covers the requirements of periods (r) for which Once accumulated parts reach or exceed the OMT, test if one more period should be included T* = largest integer less than or equal to TBO K = period currently under consideration rj = requirement/demand for period j e.g. Vollman et al. 1997, 445-446

Least Unit Cost (LUC) The principle Choose order horizon that minimizes the cost per unit of demand Define C(T) as the average holding and set-up cost per unit if the current order spans the next T periods Let (r1,…,rj) be the requirements over the j-period horizon . e.g. Nahmias 2001, 369-370

Silver-Meal Heuristic (S-M) The principle Minimize average cost per period over T-period order horizon Define C(T) as the average holding and set-up cost per period if the current order spans the next T periods If we place an order in period 1, for… r1: r2: r3: In general rn: Once Cj > Cj-1 stop, and set Q1 = r1 + r2 +…+ rj-1 and begin process again starting at period j e.g. Nahmias 2001, 368-369

Wagner-Whitin Heuristic The principle (one-way network, path enumeration) Every path through the network = a specific exact requirement policy Assign a value to each arc in the network Determine minimum cost production schedule = shortest path through the network Heuristic that determines the optimal lot size Based on dynamic programming and two lemmas Lemma 1: “Exact requirement policy” An optimal policy has the property that each value of order quantities (Q) is exactly a sum of a set of future demands Lemma 2: If optimal to produce something during period t, then it-1< rt No production / ordering during period t, if enough inventory to satisfy the demand 1 2 4 3 5 e.g. Hopp and Spearman 2000, 59-64

Comparison of Lot Sizing Policies Example 1 Comparison of Lot Sizing Policies A component used in a manufacturing facility is ordered from an outside supplier. Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks is: Cost per component is 0.65. The interest rate used to compute holding costs is 0.5 % per week. The fixed ordering cost is estimated to be 200. What ordering policy you recommend and why? Which method would result in the lowest-cost policy for this problem?

Costs of the Different Lot Sizing Policies Compared Example 1 Costs of the Different Lot Sizing Policies Compared

Ranking of the Policies Example 1 Ranking of the Policies Wagner-Whitin (W-W) 1352 Silver-Meal (S-M) 1379 Periodic Order Quantity (POQ) 1442 McLaren's Order Moment (MOM) 1475 Part Period Balancing (PPB) 1624 Least Unit Cost (LUC) 1891 Lot-for-Lot (LFL) 2000 Economic Order Quantity (EOQ) 2305

Differences in Lot Sizing Policies Lot-for-lot Cost estimation or calculation is not required Least likely to result in capacity problems Likely to cause high changeover costs (produced / ordered every period) EOQ A simple calculation technique Likely to produce cost-wise inefficient solutions if demand is not stable Wagner-Whitin Gives the optimal solution for static problems at one level of the product structure Under some other conditions the optimality is lost Relatively much calculations required S-M, LUC, PPB, MOM Similar methods that give a reasonable compromise between the simple LFL scheduling and the W-W heuristic PPB is easiest in terms of calculations S-M seems to provide the most cost effective solutions on average, and it involves less work than the W-W heuristic

Elements of Marketing Planning Capacity Scheduling Account Selection Orders Customers Forecasting

Manufacturing-Marketing Collaboration Shapiro 1977, 105

Why Orders Fall through the Cracks? Shapiro et al. 1992, 105

Key Points Lot sizing policies Order management Consider the trade-off between holding inventory and changeover By adjusting setup costs, the planner can trade inventory for capacity Simple methods are popular in practice People prefer to understand the solution Heuristics are good because those are relatively robust and intuitive Costs versus responsiveness Order management Information sharing and incentive alignment important Separate orders from customers

Abbreviations Used EOQ = economic order quantity FOP = fixed order period LUC = least unit cost MOM = McLaren’s order moment MRP = material requirements planning OMT = order moment target PPB = part period balancing POQ = periodic order quantity S-M = Silver-Meal heuristic TBO = time between orders W-W = Wagner-Whitin heuristic